An Investigation into Topology Optimization for Weight Saving and Mechanical Property Enhancement of FDM 3D Printed Objects

An Investigation into Topology Optimization for Weight Saving and Mechanical Property Enhancement of FDM 3D Printed Objects | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article An Investigation into Topology Optimization for Weight Saving and Mechanical Property Enhancement of FDM 3D Printed Objects Kaelin azariah d King, Haniyeh (Ramona) Fayazfar, Saumang Swarup Sharma, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7178669/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 10 Dec, 2025 Read the published version in The International Journal of Advanced Manufacturing Technology → Version 1 posted 5 You are reading this latest preprint version Abstract This study provides a theoretical investigation into the union of topology optimization (TO), additive manufacturing and composite materials for the manufacturing industry. Additionally, the added weight saving and structural performance enhancement benefits of lattice structures are examined. In this study, a single-seater chair made of both Polylactic acid (PLA) and a PLA/Wood composite material was subjected to a TO study in efforts of reducing the overall material usage and enhancing its structural performance. A static analysis was used to conduct comparative analyses to examine the behavior of TO technology to change in material properties, to highlight the superiority of computational TO when compared to design- based optimization, as well as to examine the added benefit of lattice structures. Through this study, a composite lattice structure was created in efforts of defining a unified lattice structure that provided optimal structural reinforcement of the multi-mode deforming chair. It was found that the TO technology was largely dependent on material characterization as it relates to the aggressiveness of material penalization. In addition, the composite lattice structure was highlighted for its superior weight-saving property while still maintaining competitive mechanical performance over the FCC and Diamond TPMS lattice models. Topology Optimization (TO) Additive Manufacturing Wood Composite Lattice Structures Sustainable Materials Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 1. Introduction Today’s manufacturing industry is one of the major contributors to environmental degradation due to the consumption of large amounts of unsustainable energy and material inefficiency [ 1 ]. Topology optimization, TO, is a powerful computational technique used within the engineering and design industries which aims to optimize material distribution within a given domain based on a set of constraints, boundary conditions, and objectives in efforts of reducing the material usage, lightweighting, and enhancing mechanical properties. TO helps to answer two of the most important questions in engineering design; where can the material be safely removed without jeopardizing structural integrity and how can material be distributed, in what geometry, to optimize the mechanical properties of the structure. Moreover, TO is used in the manufacturing industry to enhance material efficiency by reducing the amount of material needed to meet the functional requirements of the product. TO has undergone tremendous advancements since its introduction in 1988 by BendsØe and Kikuchi [ 2 ] and has since found common applications in various industries such as aerospace, automotive, civil, and biomechanics. With this advancement, various computational methods have been developed, all obtaining the same goal of increasing material efficiency while maintaining or improving structural integrity, using varying approaches. Density-based methods are one of the most frequently used in TO and are based on representing the material distribution as a continuous field of varying density throughout the design domain. In this method of TO analysis, the density value at each point of the specimen is a representation of the volume fraction of material at that specific geometric location. Additionally, density based TO methods can be carried out on a macro and microscopic level, optimizing the microstructural design to develop material properties. Furthermore, microstructural topology optimization (MTO) combines TO and microstructural optimization for simultaneous optimization at a macro and microscopic scale [ 3 ]. Solid Isotropic Microstructure with Penalization (SIMP), usually known as Simple Isotropic Material with Penalization, is an algorithmic approach to TO executed by eliminating elements with density values within a restricted domain. This method uses either an optimality criterion (OC) or a mathematical programming (MP) method for calculating thresholds where any value of thickness within this interval is penalized. Additionally, Optimal Microstructures with Penalization is a method which follows the principle of MTO by eliminating intermediate density values within an interval on a microscale. This means that first the solution is optimized for each finite element and optimal microstructure, derived rigorously for the particular type of design constraints and objective functions [ 4 ]. Other approaches to TO have been developed over the years such as Non-Optimal/Near Optimal Microstructures (NOM), Dual Discrete Programming (DDP), and Optimized Density Distribution (ODD); however, of these, SIMP is the most used in TO software. One of the major shortcomings of TO is that the optimizer has limited consciousness of the intended real-world application of the optimized model and bases the analysis on the given inputs, boundary conditions, constraints, and objectives. To this end, the optimizer can generate a model that is structurally competent and stable during the identical conditions simulated, however, no accountability is given to events of potential misuse. Therefore, it is the responsibility of the engineer to ensure the optimized model is sufficiently robust to withstand relevant unideal events as done in this study. Another challenge encountered in TO is the complex geometric bodies produced from the analysis. These resulting designs cannot be manufactured by most modern manufacturing technologies and would pose a costly expense during mass manufacturing. As a result, additive manufacturing (AM) has played a vital role in the applications of TO technology due to its ability to create intricate geometries. Additionally, the use of AM is favored over subtractive methods such as CNC machining for improved material efficiency. More specifically, extrusion-based AM, for example, Fused Deposition Modeling (FDM), has further improved the ability for topologically optimized structures to be manufactured in less time and has also provided the ability for the structures to be printed in a wide spectrum of materials. Research conducted by Ntintakis et al. [ 5 ] confirmed the usefulness of the linkage between TO and FDM based AM. In this study, downsized furniture models, with variable wall thicknesses, were printed through FDM and subjected to compression testing. The compression test results were used within the TO analysis which thereafter produced a structure with superior stability and reduced von mises stresses when compared to the unoptimized model. Furthermore, Hu et al. [ 6 ] presented a paper with the aim of confirming the competence of FDM technology and TO for advanced industrial applications, including TO adoption in the aerospace industry. In this study, a space membrane was remodeled using TO to reduce the membrane’s tendency to tear. It was found that the topology optimized strengthening ribs produced an overall structure with a greater tensile strength and tearing capacity than the stand-alone structure. In addition, the research highlighted the advantage of composite materials as the strengthening ribs manufactured with SCF/PEEK (short carbon fiber and poly-ether-ketone) outperformed the PEEK manufactured strengthening ribs, halting membrane crack growth, avoiding membrane tears, and ensuring the spacecraft’s orbital lifetime. Hu et al. not only highlighted the capability of TO and FDM 3D printing but also demonstrated the potential for the integration of composite materials with TO for further mechanical property enhancement. The current study aims to highlight the use of TO technology in the furniture manufacturing industry to produce sustainable, structurally competent, and material-efficient furnishings. A single seater chair was chosen as the test specimen for this research. The incorporation of a composite PLA/Wood material was investigated with the hindsight of manufacturing production-ready, topology optimized, wooden furniture items. Through this, the behavior of the computational optimizer, to a change in material properties, PLA vs PLA/Wood composite, was observed. Additionally, a comparison between a computational topology optimized (CTO) and a design-based-optimized (DBO) chair with the aim of material saving, was conducted to highlight the superiority of CTO and its multi-objective ability. Moreover, this paper investigated the use of lattice structures for additional design optimization and material saving. Four specimens were used for this comparative study, solid un-optimized chair, solid optimized chair with a diamond Triply Periodic Minimal Surface (TPMS) lattice structure, optimized chair with Face Centered Cubic (FCC) lattice structure and chair with a custom composite lattice structure. Lattice structures were chosen to be a field of interest due to their extremely excellent energy absorption capacity per unit mass and porous/multi-cell structures which aid in increased material efficiency and weight saving [ 7 ]. 2. Materials and Methods The bulk model of the chair was sketched using SolidWorks CAD software. The chair was 3D-printed with a solid rectangular base with dimensions 49.37 mm x 40 mm x 40.11 mm. This was used as the primary design space. Additionally, the chair was designed with a slightly reclined back, giving the chair an overall height of 73 mm. All dimensions of the chair were made to create a test specimen which was a 10% model of a standard full-size dining table chair. This was done to allow for the 3D printing of the chair for further experimentation. For accuracy of results all the boundary and loading conditions were scaled by an equivalent factor of 0.10 to provide similitude between the lab scale test chair and the testing loads applied. The TO software used is nTopology which employs the SIMP method. All meshing, testing, analysis, and lattice creation were conducted within nTopology. 2.1. Meshing and Boundary Conditions When defining the properties of the mesh used for analysis, a bias toward accurate experimental results in both the TO and the static analysis was chosen over fast computational time. Too fine of a mesh would create excessively long computational times therefore a mesh convergence study was performed by successively refining the mesh and checking if the results stabilized. This ensured that the results were not significantly affected by mesh sizes beyond the point of convergence and the mesh produced accurate results. The loads used in the boundary conditions were intended to simulate real-world application. The loads applied to the chair were scaled by the same factor of the geometrical dimensions for accuracy of results. The load was applied to two specific surfaces: the backrest and the seat of the chair. The loading conditions were adapted for similar research conducted by Zhou et al [ 8 ]. An additional load was applied to the edge of the seat of the chair to simulate the force the legs would apply in the event of unconventional seating. For the static analysis the base of the chair was placed under a displacement restraint. Figure 1 . shows the computer aided design (CAD) of the chair and the loads applied to the chair for analysis. Additionally, Table 1 breaks down the sections of the chair for example, chair back, chair seat, edge of seat and base, and the subsequent loading conditions experienced during sitting. All meshing and boundary conditions were constant throughout the investigation. The material of the test specimen was changed from PLA to PLA/Wood composite to conduct the comparative study between the two materials. Table 1 Experimental Boundary Conditions Parts Load Vector (N) Using Conditions x y z Chair Back -75 0 0 Sitting back force Chair Seat 0 0 100 Normal seating load Edge of Seat 50 0 100 Unconventional Seating Base Restrained 2.2. Material Characterization Two materials were used in this study for analysis: PLA and a PLA/Wood composite material. The mechanical property criteria were used to conduct all finite element analyses of TO are Poisson’s Ratio, and Young’s Modulus. A constant Poisson ratio of 0.33 was used for both materials. The PLA was characterized by a Young’s Modulus of 4.4 GPa. It must be noted that the 3D printed PLA/Wood composite material used in this subject was innovatively developed and investigated in previous authors’ study [ 9 ]. Figure 2 . shows results from the author’s investigation providing experimental data on the percent elongation at the breaking point, tensile modulus and tensile strength for varying compositions of PLA and wood composite filament. The 60:40 ratio of PLA and wood composite was chosen as the material of choice for the testing of the TO and to examine the behavior of the computational model when subjected to a change in material compared to PLA. The PLA/Wood selected had an approximate tensile modulus of 2.0 GPa, approximately half that of the PLA material. 2.3. Analysis A static analysis was conducted with the aforementioned materials, meshing, and boundary conditions. A reference analysis was conducted for the un-optimized bulk chair model, as well as for all other optimized iterations for a comparative analysis. The parameters studied in the static analysis were Displacement, Von Mises Stress, Principal Stress, and Principal Strain. Additionally, a weight-saving parameter in terms of the volume percentage, difference between the un-optimized and optimized body, was used to investigatematerial efficiency. 2.4. Topology Optimization The TO analysis was performed using the SIMP method. The objectives and constraints chosen for the PLA material study were derived from several test iterations and decided upon based on the desired outcome. The overall objective of this analysis was to minimize the design responses. These design responses included structural compliance, displacement response and stress response. Firstly, a minimization of the structural compliance and strain energy, allowed for the optimizer to create a structure with a high level of stiffness. The minimization of the displacement response was aimed at creating an optimized structure with reduced displacement of the chair back. This location was selected due to the high displacement region noted from the static analysis of the bulk chair model. Lastly, stress response minimization prompted the optimizer to create a structure with an overall reduction in high stress regions. The constraints for the TO were bound to two volume fraction constraints and Planar Symmetry Constraint. The volume fraction was constrained to a scalar value of 0.3, which prompted the optimizer to create a resulting topological structure with a 30% volume reduction from the bulk model. Additionally, a planar symmetry constraint allowed for the resulting topology-optimized structure to be more predictable and manufacturable by producing a structure that is symmetrical about a pre-described plane. This was made possible because the chair was subjected to symmetrical loads. It must be noted that the TO objectives and constraints were edited from the PLA specimen in the PLA/Wood chair study. The TO analysis was conducted on the PLA specimen first; therefore, based on the results produced, the objectives made for the PLA specimen were able to become constraints with specific threshold values in the following studies. A minimization of structural compliance was maintained as the objective in the PLA/Wood chair optimization. As opposed to having the other objectives that were used in the PLA specimen, such as minimizing displacement response and stress response, these were used as constraints with maximum value of the inputs. From the analysis of the final model of the PLA specimen, the max displacement and stress values were used as the displacement and stress maximum constraints, and the optimizer was set to aim for maximum displacement and stresses that were less than these values. Other constraints included planar symmetry, for a symmetrical body across the section of the chair, and volume fraction, which was set to 0.3. 3. Results and Discussion The static analysis results for the virgin PLA and PLA/Wood composite 3D printed parts were used as a reference model for all TO models for material efficiency and structural integrity investigations. The post-processing of the optimized 3D-printed part involved the smoothening of the 3D printed part surface which was initially left rough after optimization. During computational post processing of both 3D printed chairs, PLA and PLA/Wood composite, the stability of the topology optimized chair was reinforced by the addition of a support leg and base (Fig. 4 .b). These additions were merged onto the body of the chair with the use of filets in order to prevent the high stress region created by sharp geometrical bends. 3.1 Topology Optimization 3.1.1. Solid PLA Results The maximum displacement of the un-optimized, non-topology optimized, model was found to be 0.0288 mm. This displacement was primarily confined to the top of the chair back (Fig. 3 . a). This maximum displacement region remained in the same location in the optimized model; however, the maximum value increased to 0.0428 mm. In the optimized model, a medium displacement region was found at the edge of the chair seat with an approximate value of 0.0214 mm. In terms of von mises stress, an increase in the maximum von mises stress was found in the optimized model. The value of the von mises stress increased from 2.51 MPa to 3.56 MPa from un-optimized to optimized, respectively. The maximum von mises stress location remained unchanged being located at the edge of the chair seat and in the bend made by the back and seat of the chair (Fig. 4 .d). The maximum principal stress of the un-optimized bulk model was found to be 2.44 MPa. This maximum principal stress region was placed in the bend made by the back and seat of the chair (Fig. 4 .e). It was also noted that principal stress distribution can be seen in the chair back, decreasing upon ascent. Additionally, high principal stress regions were found on the topology optimized model with the additional regions being found in the bends made by the support structures under the seat of the chair under chair support structures (Fig. 4 .e). The max principal stress was found to have increased to 3.56 MPa in the topology optimized model. Similarly, the principal strain increased in the optimized model from a value of 4.99e-4, un-optimized, to 6.89e-4. The maximum strain region for the un-optimized and topology optimized models was found in the bend of the back and seat of the chair (Fig. 4 . f). In the un-optimized model, additional high strain regions were found at the corners of the edge of the seat, while the optimized model noted the presence of mid-strain regions over the surface of the back of the chair and seat with an approximate value of 3.44e-4. Table 2 . summarizes these results and also provides the weight saving percentage of the PLA topology optimized model, 59.9%. This percentage is a comparison between the volume of the un-optimized model to that of the topology optimized model. Table 2 PLA Specimen Static Analysis Results Geometry Max Displacement (mm) Max Von Mises Stress (MPa) Max Principal Stress (MPa) Max Principal Strain Weight Saving (%) Solid un-optimized model 0.0288 2.51 2.44 4.99e − 4 59.9 Solid optimized model 0.0428 3.56 3.30 6.89e − 4 Absolute Difference 0.0139 1.05 0.857 1.89e − 4 3.1.2. Solid PLA/Wood composite Results The maximum displacement for the un-optimized model was found to be 0.0637 mm located at the top of the back of the chair (Fig. 4 . e). The maximum displacement decreased to a value of 0.0487 mm with a relocation of the maximum region to the edge of the seat (Fig. 5 . c) from the un-optimized to optimized model, respectively. Additionally, a decrease in the maximum von mises stress was found in the optimized model. The maximum von mises stress was found to be 3.17 MPa for the un-optimized model. This small maximum von mises stress region for the un-optimized model was located in the bend created by the intersection of the back and seat of the chair (Fig. 4 . f). Additional maximum von mises stress regions were noted at the corners of the edge of the seat. Mid-stress regions can be seen surrounding the high-stress regions with an approximate value of 1.58 MPa. On the contrary, the maximum von mises stress of the optimized model was found to be 3.12 MPa. Similar to the un-optimized modelly, while the location of the maximum von mises stress region was found in the bend created by the back and seat of the chair, more high stress regions were found at the corners of the edge of the seat and the bottom of the front legs (Fig. 5 . d). Surrounding these high stress points are mid-stress regions with an approximate value of 1.56 MPa. Additional mid stress regions can be found in the creases of the bends made by the supporting legs. A continued reduction was noted in the principal stress of the optimized model when compared to the un-optimized model, from 2.38 MPa, un-optimized model, to 2.32 MPa, optimized model. A high stress region was noted to be located in the bend made by the back and seat of the chair for both un-optimized and optimized models, with mid-stress regions being present throughout the topology optimized model (Fig. 5 . e). On the other hand, an increase in the principal strain was seen going from a value of 1.13e − 3 , un-optimized, to 1.28e − 3 , optimized model. Similarly, the maximum principal strain region was found to be in the bend created by the back and seat of the chair (Fig. 5 . f). Table 3 summarizes these results and displays the weight saving percentage of the PLA/Wood composite material model, 44.0%. Table 3 Analysis of PLA/Wood Specimen Static Analysis Results Geometry Max Displacement (mm) Max Von Mises Stress (MPa) Max Principal Stress (MPa) Max Principal Strain Weight Saving (%) Solid un-optimized model 0.0637 3.17 2.38 1.13e − 3 44.0 Solid optimized model 0.0488 3.12 2.32 1.28e − 3 Absolute Difference 0.0149 0.0473 0.0543 1.48e − 3 It was observed that results from the static analysis alone do not directly determine the safe operational use of the chair. Therefore, to evaluate and compare the structural integrity of the chair under load, we considered the yield strengths of the materials used PLA and PLA/Wood composite. Thus, we can assess whether the structures could safely withstand the applied loads by comparing the maximum stresses obtained from the static analysis with the yield strengths of these materials. If the maximum stress is lower than the yield strength of the material, indicating safe operational use. 3.2. Impact of Material Properties on Topology Optimization TO is dependent upon the material properties of the specimen. From this end, the optimizer is able to distribute material to efficiently and effectively use material for weight saving and structural integrity. In this study, a test was performed to determine exactly the behavior of the optimizing software to a change in material properties. This investigation examined the topology-optimized model of the chair for both PLA and PLA/Wood composite (40 wt% wood and 60 wt% PLA) to evaluate the effect of material properties on TO of the chair. The test was conducted with all parameters, boundary conditions, objectives, and constraints, being held constant. The weight saving percentage was based on a volume fraction calculation used to measure the percentage change in volume from the initial bulk model to the optimized model. Results displayed that the PLA-optimized chair produced a weight saving value of 59.9%, compared to the PLA/Wood specimen producing 44.0%. In other words, the final optimized model of the PLA and PLA/Wood chair was reduced to 40.1% and 56.0% of the bulk chair, respectively (Fig. 6 ). The drastic difference in volume reduction after optimization can be attributed to the differences in material properties of the PLA and the PLA/Wood composite. The 60:40 PLA/Wood composite material was selected due to its superior tensile modulus when compared to the other tested composite ratios, however, the PLA/wood material still reported a tensile modulus of approximately half that of PLA, 2.0 GPa and 4.4 GPa, respectively [ 9 ]. The term Young’s modulus, tensile modulus, elastic modulus, modulus of elasticity, and stiffness are referring to the mechanical property that measures the stiffness of a certain material [ 10 ]. Young’s modulus is the ratio of the applied stress on the material to the strain associated with that applied stress. From that, it can be determined that the Young’s modulus has a directly proportional relationship with applied stress. As a result, TO takes advantage of this relationship and allows for more aggressive material removal in high stiffness materials, such as metals, due to their high stress capacity. The trends presented in the static analysis help to validate the claim that the optimizer enables greater material removal and allows for higher stresses to be applied on stronger materials. From Table 2 , it can be seen that there is an increase in both stresses, von mises and principal, in the PLA optimized chair when compared to the un-optimized bulk model. On the other hand, there was a reduction, from the un-optimized bulk model, in the maximum von mises and principal stress for the PLA/Wood optimized chair (Table 3 ). This indicates that as PLA is the stronger material compared to PLA/Wood, we were able to subject the PLA model to higher stress levels through increased material removal, and on the contrary, reduced the stress levels in the weaker material, PLA/Wood, through less aggressive material penalization. Additionally, a change in materials has little to no effect on the overall geometrical structure of the optimized model (Fig. 6 . b, c). The PLA and PLA/Wood chair have the same core geometry, while only differentiating in material density distribution. Therefore, it can be inferred that the topological structure/shape of the chair is directly related to the boundary conditions and the TO's objectives and constraints. All in all, selecting the different material determines the result produced from TO where the greater the material’s structural properties, the more aggressive the topology optimizer can be in reducing the overall material used for the model. On the other hand, as seen in this test comparing the results produced from PLA and PLA/Wood materials, the topology optimizer is less able to remove large amounts of material for equivalent loading conditions due to the lower stress capacity of the weaker materials. 3.3. Design Optimization Vs Computational Optimization An investigation was conducted to determine the effectiveness and the importance of computational topology optimization (CTO) for material efficiency and structural performance versus designed based optimized (DBO) structures aimed at achieving the same goal. The specimens used for this study were a computational optimization chair and an architecturally designed chair designed to minimize material usage, both in the PLA/Wood composite material. In this study, both the computational topology optimized, and design based optimized models specimens were subjected to common boundary conditions and meshing. Static analysis results highlighted the structural superiority of the computational topology-optimized chair when compared to the DBO model (Table 4 ). This was largely due to the computational optimization method's ability to work on simultaneous objectives, for example minimizing the volume fraction while maximizing structural integrity through structural compliance reduction and stress responses. On the other hand, the design-based chair was primarily aimed at overall material efficiency by reducing the amount of material used for the chair. This however saw a dramatic reduction in the structural performance of the chair. Ultimately, the shortcoming of the design-based TO can be referenced to the inability of the human designer to consider material properties for structural integrity, stress distributions and dynamic responses simultaneously. It must be noted however that the material of the specimen is the major determinant of structural performance, in that, if the DBO model was made of a material with greater structural properties, for example steel, the static analysis results would have indicated a stronger structure despite its thin geometric profile. Table 4 Static Analysis Comparison of Computational Optimization Chair and Architecturally Designed Chair Model Max Displacement (mm) Max Von Mises Stress (MPa) Max Principal Stress (MPa) Max Principal Strain Weight Saving (%) CTO 0.0487 3.12 2.31 0.00128 44.0 DBO 422 93.5 72.6 0.329 81.6 3.4. Lattice Structure for Advanced Optimization A topology-optimized structure can be further optimized for increased structural performance and material efficiency by the incorporation of porous, multi-cell lattice structures, which are commonly used in many engineering industries such as aerospace, biomedical and mechanical design. These structures are suitable for various applications due to their light weighting properties and energy absorption characteristics [ 11 ]. Different lattice structures offer distinct advantages ranging from high compressive strengths to thermal performance; therefore, it is important to understand the intended application. Due to these performance enhancement properties, an investigation into the incorporation of lattice structures within topology-optimized structures was conducted in this study. This study was carried out on the FCC, Diamond TPMS, and a composite lattice structure (Fig. 8 ). The static analysis performance of these structures was examined and compared to the solid topology optimized specimens. Throughout this investigation, multiple parameters were varied such as unit cell size, lattice orientation, and lattice thickness to determine the optimal configuration for the lattice structure. Additionally, a variable thickness lattice feature, otherwise known as gradient latticing, was implemented into the lattice structure for structural performance maintenance as previous research studies have displayed the increased strengthening effect of gradient lattices when compared to uniform lattice structures [ 12 ]. The gradient latticing worked by using the results from the static analysis to determine the regions on the solid optimized chair which had the highest stresses. These high stress regions then saw a localized increase in strut thickness for better stress distribution and support. The lattice structures were designed with the nTopology software in that the topology optimized bodies were shelled with a 1 mm wall thickness and the lattice structure was merged with the shell. It must be noted that the orientation of the lattice structures was positioned in such a way that oriented the truss in the direction of the applied load for maximum reinforcement [ 13 ] (Table 5 ). Table 5 FCC and Diamond TPMS lattice configuration Unit Cell Size (mm) Unit Cell Size (mm) Unit Cell Size (mm) FCC 2x2x2 UVW Min − 0.75 Max − 1.00 Diamond TPMS 6x6x6 UVW Min − 0.25 Max – 0.75 Lattice structures of different geometries offer distinct structural advantages over uniform lattices in applications where a structure experiences multiple modes of deformation. Intricate structures such as the topology-optimized chair can have complex stress distributions and varying modes of deformation across the body. Therefore, the creation of composite lattice structures, constructed from lattices of varying geometries, can greatly improve the material efficiency of the specimen. This is largely due to the fact that each element of the chair would be constructed from a lattice structure which provides reinforcement solely in the direction of potential deformation. With this knowledge, an additional lattice structure was constructed for the investigation. The composite lattice structure was aimed at increasing the weight saving percentage of the chair, while maintaining or improving its structural integrity. To this end, the body of the optimized chair was divided into three sections; back and seat, legs, and mid-body. These sections were highlighted within the static analysis as areas that displayed different modes of deformation, flexural and compression. The back and seat of the chair was made of thin 3mm thick PLA, therefore it was important that if implementing weight saving lattice structure within the shell of the body, the structural performance must not be compromised. The back and seat of the chair were directly subjected to compressive forces acting in the z (vertical) and x (horizontal) directions. As a result, it was noted from the static analysis that the bend created by the joining of the back and seat of the chair would be subjected to flexural deformation. Therefore, hexagonal honeycomb lattice structure was used to fill the shell of the back and seat due to its superior flexural strength [ 13 ]. A relatively small 2x2x2 mm unit cell size in combination with a gradient lattice stress modified was added to the lattice to increase the reinforcing effect of the lattice structure. Similarly, a hexagonal honeycomb lattice structure was used for the mid-body of the chair with a gradient lattice and a larger 4x4x4 mm unit cell. The topology optimized mid-body, with its complex geometry, would be subjected to both flexural and compressive deformation as a result of its unique stress distribution. Therefore, as previous research concluded [ 13 ], hexagonal honeycomb lattice structure would provide dual reinforcement in this application, both flexural and compression. It was noted that the legs and base of the chair were solely subjected to compressive forces in the negative z direction, therefore a 2x2x2mm column lattice structure with a constant truss thickness of 1 mm, for torsion and buckling resistance, was used to provide reinforcement in the direction of the applied load. The lattice sections of the chair were merged together with an increase in thickness around the points where sections of different lattice geometries joined for reinforcement (Fig. 9 ). Table 6 Composite lattice configuration of sections Section Lattice Structure Unit Cell Size (mm) Orientation Thickness (mm) Back and Seat Hexagonal Honeycomb 2x2x2 UVW Min − 0.50 Max − 1.00 Legs Column 2x2x2 UVW Constant − 1.00 Mid-body Hexagonal Honeycomb 4x4x4 UVW Min − 0.75 Max − 1.00 The static analysis results displayed the FCC specimen to be the superior lattice, outperforming diamond TPMS and composite lattice structures in the majority of mechanical property studies. The FCC chair reported the lowest maximum total displacement under deformation with a value of 0.0331 mm (Fig. 10 ). In addition, the lightweight FCC chair produces a von mises stress value approximately equal to that of the solid bulk chair, 3.26 MPa and 3.17 MPa, respectively (Fig. 11). The results for both von mises and principal stress highlighted the great benefit of lattice structures for stress distribution. Despite the von mises and principal stress of both the solid optimized and un-optimized models being less than that of both the lattice light-weighted diamond TPMS and composite lattice models (Fig. 12 ), the solid models noted more concentrated high-pressure regions and less energy distribution. Additionally, the maximum principal strain values mirrored the trend of the principal stress results with the solid models reporting the lowest strain values when compared with the diamond TPMS and composite lattice models; 2.94e-4 solid un-optimized model and 6.95e-4 solid optimized model. The FCC lattice model displayed a principal strain value between the solid un-optimized and solid optimized model, with a value of 6.89e-4 (Fig. 13). Of the latticed light weighted models, the FCC model had the lowest strain value, followed by the composite lattice structure. The relative weight saving was a parameter used to measure the material reduction relative to the solid un-optimized model, bulk model. It was found that the composite lattice model obtained the highest material saving with a value of 70.0%, followed by FCC and diamond TPMS, 69.0% and 68.9%, respectively (Fig. 14 ). All in all, despite the FCC lattice specimen producing superior results in the majority of the mechanical property tests, the composite lattice model closely mirrored these results. Additionally, the composite lattice model possessed the greatest material efficiency evident by its weight saving percentage of 70.0%. 4. Conclusion This study highlights the benefit of TO in combination with additive manufacturing to produce lightweight structures with enhanced mechanical properties, and material efficiency. This research provided evidence for the response of TO technology to the change in material properties, exhibiting the dependence of TO on material property characterization. It was found that the change in material has little to no effect on the overall geometrical shape of the optimized structure but rather, judges the aggressiveness of material penalization during optimization. The research focuses on two materials PLA and PLA/Wood composite, the PLA test model with a modulus of elasticity of 4.0 GPa, approximately double that of the PLA/Wood composite model, displayed a topology optimized solution which saw a weight saving percentage which was 15.9% greater than the weaker PLA/Wood composite model. It was therefore concluded that a strong material, represented by a large Young’s Modulus and subsequently a large tensile strength value, allows the optimizer to remove a greater amount of material due to its higher stress capacity. Ultimately, the superiority of TO is demonstrated in the comparison study between the computational and the design-based topology optimized chairs. The results affirmed the designer community to simultaneously consider material saving and structural performance enhancement, favoring one over the other. On the contrary, TO technology is highlighted for its duality in this region, producing structures where both parameters are controlled. Additionally, the added benefit of lattice incorporation with topology-optimized structures for further weight saving and stress distribution was noted. More specifically, the creation of composite lattice structures, as done in this paper for both PLA and Wood/PLA models, has opened the door for the development of highly efficient structural bodies, infilled with lattice geometries most suitable for the localized form of deformation. This was confirmed by the superiority of the PLA composite lattice model which produced a superior weight saving percentage of 70.0% when compared to the uni-lattice chairs, FCC and diamond TPMS, 69.0% and 68.9% respectively, while still maintaining competitive structural performance. Future work will involve experimenting with the specimens examined in this study to validate all theoretical findings. Additionally, as previously mentioned, the static analysis results produced fail to directly highlight the exact point and mode of mechanical failure; therefore, a future study would incorporate bulking analyses as well as dynamic response analyses for predictions of long-term structural performance, examining both the durability of the TO, FDM and composite materials combination for real-world applications. Moreover, future research will be conducted on the potential involvement of composite lattice structures within high-performance applications for highly efficient structural bodies. Declarations Competing interests The authors declare no competing interests. Funding The financial support of the NSERC grant is greatly appreciated. Author’s contributions The data collection, modeling, analysis and original draft was prepared by Kaelin azariah d King. The idea, conceptualization, supervision, reviewing and editing, overall administration of the research work, final approval of the manuscript was performed by Haniyeh (Ramona) Fayazfar. The reviewing, editing and final approval of manuscript were also performed by Saumang Swarup, Ankit Sahai and Rahul Swarup Sharma. References S. Shahbazi, C. Jönsson, M. Wiktorsson, M. Kurdve, and M. Bjelkemyr, “Material efficiency measurements in manufacturing: Swedish case studies,” Journal of Cleaner Production , vol. 181, pp. 17–32, 2018. doi:10.1016/j.jclepro.2018.01.215 O. Sigmund and K. Maute, “Topology Optimization approaches,” Structural and Multidisciplinary Optimization , vol. 48, no. 6, pp. 1031–1055, 2013. doi:10.1007/s00158-013-0978-6 T. Kumar and K. Suresh, “A density-and-strain-based K-clustering approach to microstructural topology optimization,” Structural and Multidisciplinary Optimization , vol. 61, no. 4, pp. 1399–1415, 2019. doi:10.1007/s00158-019-02422-4 G. I. N. Rozvany, “Aims, scope, methods, history and unified terminology of computer-aided topology optimization in structural mechanics,” Structural and Multidisciplinary Optimization , vol. 21, no. 2, pp. 90–108, 2001. doi:10.1007/s001580050174 I. Ntintakis, G. E. Stavroulakis, and N. Plakia, “Topology optimization by the use of 3D printing technology in the product design process,” HighTech and Innovation Journal , vol. 1, no. 4, pp. 161–171, 2020. doi:10.28991/hij-2020-01-04-03 Q. Hu et al. , “Research into topology optimization and the FDM method for a space cracked membrane,” Acta Astronautica , vol. 136, pp. 443–449, 2017. doi:10.1016/j.actaastro.2017.03.033 H. Yin et al. , “Review on lattice structures for energy absorption properties,” Composite Structures , vol. 304, p. 116397, 2023. doi:10.1016/j.compstruct.2022.116397 Y. Feng Zhou, R. Fa Wang, and Ao Deng, “Topology optimization design of Biology Wooden Furniture,” International Journal of Advanced Engineering and Management Research , vol. 08, no. 02, pp. 81–87, 2023. doi:10.51505/ijaemr.2023.8208 D. Jubinville, J. Sharifi, T. H. Mekonnen, and H. Fayazfar, “A comparative study of the physico-mechanical properties of material extrusion 3D-printed and injection molded wood-polymeric biocomposites - journal of polymers and the environment,” SpringerLink, https://link.springer.com/article/10.1007/s10924-023-02816-y (accessed Aug. 8, 2023). S. Elkatatny, M. Mahmoud, I. Mohamed, and A. Abdulraheem, “Development of a new correlation to determine the static Young’s modulus - Journal of Petroleum Exploration and Production Technology,” SpringerLink, https://link.springer.com/article/10.1007/s13202-017-0316-4 (accessed Aug. 8, 2023). H. Yin et al. , “Review on lattice structures for energy absorption properties,” Composite Structures , vol. 304, p. 116397, 2023. doi:10.1016/j.compstruct.2022.116397 A. Seharing, A. H. Azman, and S. Abdullah, “A review on integration of lightweight gradient lattice structures in additive manufacturing parts,” Advances in Mechanical Engineering , vol. 12, no. 6, p. 168781402091695, 2020. doi:10.1177/1687814020916951 C. Beyer and D. Figueroa, “Design and analysis of lattice structures for additive manufacturing,” Journal of Manufacturing Science and Engineering , vol. 138, no. 12, 2016. doi:10.1115/1.4033957 Cite Share Download PDF Status: Published Journal Publication published 10 Dec, 2025 Read the published version in The International Journal of Advanced Manufacturing Technology → Version 1 posted Editorial decision: Major Revisions Needed 16 Sep, 2025 Reviewers agreed at journal 01 Aug, 2025 Reviewers invited by journal 01 Aug, 2025 Editor assigned by journal 31 Jul, 2025 First submitted to journal 30 Jul, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7178669","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":494326809,"identity":"2084248a-c944-4c76-ba03-3b605c29391b","order_by":0,"name":"Kaelin azariah d King","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Kaelin","middleName":"azariah d","lastName":"King","suffix":""},{"id":494326810,"identity":"1f8c2f9c-2d60-4e72-9af0-9db8be1ba417","order_by":1,"name":"Haniyeh (Ramona) Fayazfar","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Haniyeh","middleName":"(Ramona)","lastName":"Fayazfar","suffix":""},{"id":494326811,"identity":"e8052612-d096-44c4-ba52-e1c3c7821aba","order_by":2,"name":"Saumang Swarup Sharma","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Saumang","middleName":"Swarup","lastName":"Sharma","suffix":""},{"id":494326812,"identity":"fb5fe293-ac5b-41ec-ad4f-8386245d3931","order_by":3,"name":"Ankit Sahai","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA40lEQVRIie3QMQrCMBTG8VcKb4q6Bjr0Ck8CRUHxKimCUxEP4CAI7SK6dvMKguCsBJx0r+CgSycHXaSDiBEcpa2bQ35jyJ98BMAw/hIDkACEYK850PvEGpVMEOUPiUaAjHipWW6031xPw6OoupNbch2AWxvZ4SkvoV2/y+U29RAry2ZMUI/XVkS5CQTEJaqWTlYOI7AWYIW5C93ZRWTy+U5Y6jwIOoUJJIHH/VDpYQwd/ahfmFBy8Rr+VAnEnmhOiHdjVTgsEIfsrurzsTon2aPVnkVRWu63P/Rl+5f7hmEYxlcvHZBBtwtsKKgAAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0001-7333-8967","institution":"Dayalbagh Educational Institute Faculty of Engineering","correspondingAuthor":true,"prefix":"","firstName":"Ankit","middleName":"","lastName":"Sahai","suffix":""},{"id":494326813,"identity":"eef93c0b-9009-4bab-a243-d9cb2ff2eac3","order_by":4,"name":"Rahul Swarup Sharma","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Rahul","middleName":"Swarup","lastName":"Sharma","suffix":""}],"badges":[],"createdAt":"2025-07-21 14:39:06","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7178669/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7178669/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s00170-025-16983-w","type":"published","date":"2025-12-10T15:59:18+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":88899108,"identity":"4a28e11d-3eb0-4c87-b7dd-77e25621a40b","added_by":"auto","created_at":"2025-08-12 13:25:11","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":133557,"visible":true,"origin":"","legend":"\u003cp\u003eCAD image of: (a) Bulk chair, (b) Sitting back force, (c) Sitting force, (d) Sitting edge force, (e) Restrained base of 3D printed chair.\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-7178669/v1/2c1d9891950337be33da8378.png"},{"id":88899535,"identity":"a84bd33a-1a6d-42f9-81f6-b7f834bb5b40","added_by":"auto","created_at":"2025-08-12 13:33:11","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":73537,"visible":true,"origin":"","legend":"\u003cp\u003eMechanical Properties of PLA/Wood composite material [9].\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-7178669/v1/a5ab1f94b6926bcd0e23c731.png"},{"id":88899536,"identity":"4ed36001-745f-432b-b72a-9b5fcb67974e","added_by":"auto","created_at":"2025-08-12 13:33:11","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":402666,"visible":true,"origin":"","legend":"\u003cp\u003eStatic Analysis Results; (a) Displacement, (b) Von Mises Stress (PLA), (c) Principal Stress (PLA), (d) Principal Strain (PLA), (E) Displacement (PLA/Wood), (f) Von Mises Stress (PLA/Wood), (g) Principal Stress (PLA/Wood), (h) Principal Strain (PLA/Wood). In the static analysis results, the color red represents the location of the maximum value regions while blue represents the minimum value on the spectrum for displacement, von mises stress, principal stress and principal strain.\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-7178669/v1/a822de2f934e5a860e803c4f.png"},{"id":88899110,"identity":"66ff6de9-8b49-4501-9c72-fc65f24f9a3d","added_by":"auto","created_at":"2025-08-12 13:25:11","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":314932,"visible":true,"origin":"","legend":"\u003cp\u003eTO Result (PLA); (a) Post TO, (b) Final Model (after post-processing), (c) Displacement, (d) Von Mises Stress, (e) Principal Stress, (f) Principal Strain.\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-7178669/v1/27c691e83f5aa2e71e666bce.png"},{"id":88899538,"identity":"44df4026-7c68-4a6c-8fca-a3420d9c525e","added_by":"auto","created_at":"2025-08-12 13:33:11","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":420750,"visible":true,"origin":"","legend":"\u003cp\u003eTO Result (PLA/Wood composite); (a) Post TO, (b) Final Model (after post-processing), (c) Displacement, (d) Von Mises Stress, (e) Principal Stress, (f) Principal Strain.\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-7178669/v1/444aa1a5699d96526e6d9855.png"},{"id":88899120,"identity":"aa712a74-7546-48e9-b029-b81577b17a0c","added_by":"auto","created_at":"2025-08-12 13:25:11","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":151382,"visible":true,"origin":"","legend":"\u003cp\u003eCAD Model of: (a) Unoptimized chair, (b) Optimized PLA chair, (c) Optimized PLA/Wood chair.\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-7178669/v1/7ea2b50737d9b24306e16b73.png"},{"id":88899540,"identity":"a54e7fce-2378-417a-8dcd-c0fb16848db0","added_by":"auto","created_at":"2025-08-12 13:33:11","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":124568,"visible":true,"origin":"","legend":"\u003cp\u003eCAD: (a) computational optimized chair, (b) architecturally designed chair.\u003c/p\u003e","description":"","filename":"floatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-7178669/v1/127481794a2049bec17f2738.png"},{"id":88899121,"identity":"e337e213-873e-4719-947b-aebd1483b084","added_by":"auto","created_at":"2025-08-12 13:25:11","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":417409,"visible":true,"origin":"","legend":"\u003cp\u003eCAD Image of: (a) Diamond TPMS Lattice Structure, (b) FCC Lattice Structure.\u003c/p\u003e","description":"","filename":"floatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-7178669/v1/5aadc1ab090dc59f8ef326c9.png"},{"id":88899127,"identity":"98c6dbf6-c9c4-4d63-bb2b-f9fe5bb3ebf5","added_by":"auto","created_at":"2025-08-12 13:25:11","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":366593,"visible":true,"origin":"","legend":"\u003cp\u003eCAD of test models: (a) un-optimized bulk, (b) solid optimized, (c) FCC lattice, (d) Diamond TPMS lattice, (e) Composite lattice.\u003c/p\u003e","description":"","filename":"floatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-7178669/v1/cc8019c13ae665fb83ac9478.png"},{"id":88899116,"identity":"38be039c-9b2f-4dd1-97f8-648a96949a0a","added_by":"auto","created_at":"2025-08-12 13:25:11","extension":"jpeg","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":68048,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of Maximum Displacement\u003c/p\u003e","description":"","filename":"10.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7178669/v1/4f2ddb52febb1f4051185246.jpeg"},{"id":88899122,"identity":"e395986d-f582-49bd-b1dc-6704be74587a","added_by":"auto","created_at":"2025-08-12 13:25:11","extension":"jpeg","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":66382,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of Maximum Von Mises Stress\u003c/p\u003e","description":"","filename":"11.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7178669/v1/a0c1058828b2a4138220d1ae.jpeg"},{"id":88899541,"identity":"624edf4c-3a8e-4c8b-a4e8-2c35d83d586f","added_by":"auto","created_at":"2025-08-12 13:33:11","extension":"jpeg","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":69336,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of Maximum Principal Stress\u003c/p\u003e","description":"","filename":"12.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7178669/v1/922fd9f8ffe579da02243d13.jpeg"},{"id":88899543,"identity":"ed841e02-f0ac-4119-a4d0-2158c11df3c5","added_by":"auto","created_at":"2025-08-12 13:33:11","extension":"jpeg","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":70772,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of Maximum Principal Strain\u003c/p\u003e","description":"","filename":"13.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-7178669/v1/b27c697bb20fda68af59dfc6.jpeg"},{"id":88899131,"identity":"5e42093e-0ad5-42d6-b55c-7b72acb3036e","added_by":"auto","created_at":"2025-08-12 13:25:11","extension":"png","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":9556,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of Relative Weight Savings\u003c/p\u003e","description":"","filename":"14.png","url":"https://assets-eu.researchsquare.com/files/rs-7178669/v1/0235636d89f3f2a5b1a87bd3.png"},{"id":98244045,"identity":"1ba1c14d-c37e-4ec8-b06e-6ecba932b164","added_by":"auto","created_at":"2025-12-15 16:12:43","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3424133,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7178669/v1/513b16ef-5a02-4623-9fe3-2cd040c13303.pdf"}],"financialInterests":"","formattedTitle":"An Investigation into Topology Optimization for Weight Saving and Mechanical Property Enhancement of FDM 3D Printed Objects","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eToday\u0026rsquo;s manufacturing industry is one of the major contributors to environmental degradation due to the consumption of large amounts of unsustainable energy and material inefficiency [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. Topology optimization, TO, is a powerful computational technique used within the engineering and design industries which aims to optimize material distribution within a given domain based on a set of constraints, boundary conditions, and objectives in efforts of reducing the material usage, lightweighting, and enhancing mechanical properties. TO helps to answer two of the most important questions in engineering design; where can the material be safely removed without jeopardizing structural integrity and how can material be distributed, in what geometry, to optimize the mechanical properties of the structure. Moreover, TO is used in the manufacturing industry to enhance material efficiency by reducing the amount of material needed to meet the functional requirements of the product. TO has undergone tremendous advancements since its introduction in 1988 by Bends\u0026Oslash;e and Kikuchi [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e] and has since found common applications in various industries such as aerospace, automotive, civil, and biomechanics. With this advancement, various computational methods have been developed, all obtaining the same goal of increasing material efficiency while maintaining or improving structural integrity, using varying approaches.\u003c/p\u003e\u003cp\u003eDensity-based methods are one of the most frequently used in TO and are based on representing the material distribution as a continuous field of varying density throughout the design domain. In this method of TO analysis, the density value at each point of the specimen is a representation of the volume fraction of material at that specific geometric location. Additionally, density based TO methods can be carried out on a macro and microscopic level, optimizing the microstructural design to develop material properties. Furthermore, microstructural topology optimization (MTO) combines TO and microstructural optimization for simultaneous optimization at a macro and microscopic scale [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eSolid Isotropic Microstructure with Penalization (SIMP), usually known as Simple Isotropic Material with Penalization, is an algorithmic approach to TO executed by eliminating elements with density values within a restricted domain. This method uses either an optimality criterion (OC) or a mathematical programming (MP) method for calculating thresholds where any value of thickness within this interval is penalized.\u003c/p\u003e\u003cp\u003eAdditionally, Optimal Microstructures with Penalization is a method which follows the principle of MTO by eliminating intermediate density values within an interval on a microscale. This means that first the solution is optimized for each finite element and optimal microstructure, derived rigorously for the particular type of design constraints and objective functions [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eOther approaches to TO have been developed over the years such as Non-Optimal/Near Optimal Microstructures (NOM), Dual Discrete Programming (DDP), and Optimized Density Distribution (ODD); however, of these, SIMP is the most used in TO software.\u003c/p\u003e\u003cp\u003eOne of the major shortcomings of TO is that the optimizer has limited consciousness of the intended real-world application of the optimized model and bases the analysis on the given inputs, boundary conditions, constraints, and objectives. To this end, the optimizer can generate a model that is structurally competent and stable during the identical conditions simulated, however, no accountability is given to events of potential misuse. Therefore, it is the responsibility of the engineer to ensure the optimized model is sufficiently robust to withstand relevant unideal events as done in this study.\u003c/p\u003e\u003cp\u003eAnother challenge encountered in TO is the complex geometric bodies produced from the analysis. These resulting designs cannot be manufactured by most modern manufacturing technologies and would pose a costly expense during mass manufacturing. As a result, additive manufacturing (AM) has played a vital role in the applications of TO technology due to its ability to create intricate geometries. Additionally, the use of AM is favored over subtractive methods such as CNC machining for improved material efficiency. More specifically, extrusion-based AM, for example, Fused Deposition Modeling (FDM), has further improved the ability for topologically optimized structures to be manufactured in less time and has also provided the ability for the structures to be printed in a wide spectrum of materials. Research conducted by Ntintakis et al. [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e] confirmed the usefulness of the linkage between TO and FDM based AM. In this study, downsized furniture models, with variable wall thicknesses, were printed through FDM and subjected to compression testing. The compression test results were used within the TO analysis which thereafter produced a structure with superior stability and reduced von mises stresses when compared to the unoptimized model. Furthermore, Hu et al. [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e] presented a paper with the aim of confirming the competence of FDM technology and TO for advanced industrial applications, including TO adoption in the aerospace industry. In this study, a space membrane was remodeled using TO to reduce the membrane\u0026rsquo;s tendency to tear. It was found that the topology optimized strengthening ribs produced an overall structure with a greater tensile strength and tearing capacity than the stand-alone structure. In addition, the research highlighted the advantage of composite materials as the strengthening ribs manufactured with SCF/PEEK (short carbon fiber and poly-ether-ketone) outperformed the PEEK manufactured strengthening ribs, halting membrane crack growth, avoiding membrane tears, and ensuring the spacecraft\u0026rsquo;s orbital lifetime. Hu et al. not only highlighted the capability of TO and FDM 3D printing but also demonstrated the potential for the integration of composite materials with TO for further mechanical property enhancement.\u003c/p\u003e\u003cp\u003eThe current study aims to highlight the use of TO technology in the furniture manufacturing industry to produce sustainable, structurally competent, and material-efficient furnishings. A single seater chair was chosen as the test specimen for this research. The incorporation of a composite PLA/Wood material was investigated with the hindsight of manufacturing production-ready, topology optimized, wooden furniture items. Through this, the behavior of the computational optimizer, to a change in material properties, PLA vs PLA/Wood composite, was observed. Additionally, a comparison between a computational topology optimized (CTO) and a design-based-optimized (DBO) chair with the aim of material saving, was conducted to highlight the superiority of CTO and its multi-objective ability. Moreover, this paper investigated the use of lattice structures for additional design optimization and material saving. Four specimens were used for this comparative study, solid un-optimized chair, solid optimized chair with a diamond Triply Periodic Minimal Surface (TPMS) lattice structure, optimized chair with Face Centered Cubic (FCC) lattice structure and chair with a custom composite lattice structure. Lattice structures were chosen to be a field of interest due to their extremely excellent energy absorption capacity per unit mass and porous/multi-cell structures which aid in increased material efficiency and weight saving [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e].\u003c/p\u003e"},{"header":"2. Materials and Methods","content":"\u003cp\u003eThe bulk model of the chair was sketched using SolidWorks CAD software. The chair was 3D-printed with a solid rectangular base with dimensions 49.37 mm x 40 mm x 40.11 mm. This was used as the primary design space. Additionally, the chair was designed with a slightly reclined back, giving the chair an overall height of 73 mm. All dimensions of the chair were made to create a test specimen which was a 10% model of a standard full-size dining table chair. This was done to allow for the 3D printing of the chair for further experimentation. For accuracy of results all the boundary and loading conditions were scaled by an equivalent factor of 0.10 to provide similitude between the lab scale test chair and the testing loads applied.\u003c/p\u003e\u003cp\u003eThe TO software used is nTopology which employs the SIMP method. All meshing, testing, analysis, and lattice creation were conducted within nTopology.\u003c/p\u003e\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003e2.1. Meshing and Boundary Conditions\u003c/h2\u003e\u003cp\u003eWhen defining the properties of the mesh used for analysis, a bias toward accurate experimental results in both the TO and the static analysis was chosen over fast computational time. Too fine of a mesh would create excessively long computational times therefore a mesh convergence study was performed by successively refining the mesh and checking if the results stabilized. This ensured that the results were not significantly affected by mesh sizes beyond the point of convergence and the mesh produced accurate results.\u003c/p\u003e\u003cp\u003eThe loads used in the boundary conditions were intended to simulate real-world application. The loads applied to the chair were scaled by the same factor of the geometrical dimensions for accuracy of results. The load was applied to two specific surfaces: the backrest and the seat of the chair. The loading conditions were adapted for similar research conducted by Zhou et al [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. An additional load was applied to the edge of the seat of the chair to simulate the force the legs would apply in the event of unconventional seating. For the static analysis the base of the chair was placed under a displacement restraint. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. shows the computer aided design (CAD) of the chair and the loads applied to the chair for analysis. Additionally, Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e breaks down the sections of the chair for example, chair back, chair seat, edge of seat and base, and the subsequent loading conditions experienced during sitting. All meshing and boundary conditions were constant throughout the investigation. The material of the test specimen was changed from PLA to PLA/Wood composite to conduct the comparative study between the two materials.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eExperimental Boundary Conditions\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"5\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003eParts\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e\u003cp\u003eLoad Vector (N)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003eUsing Conditions\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003ex\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003ey\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003ez\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eChair Back\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e-75\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eSitting back force\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eChair Seat\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e100\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eNormal seating load\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eEdge of Seat\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e50\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e100\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eUnconventional Seating\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eBase\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"4\" nameend=\"c5\" namest=\"c2\"\u003e\u003cp\u003eRestrained\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\u003ch2\u003e2.2. Material Characterization\u003c/h2\u003e\u003cp\u003eTwo materials were used in this study for analysis: PLA and a PLA/Wood composite material. The mechanical property criteria were used to conduct all finite element analyses of TO are Poisson\u0026rsquo;s Ratio, and Young\u0026rsquo;s Modulus. A constant Poisson ratio of 0.33 was used for both materials. The PLA was characterized by a Young\u0026rsquo;s Modulus of 4.4 GPa. It must be noted that the 3D printed PLA/Wood composite material used in this subject was innovatively developed and investigated in previous authors\u0026rsquo; study [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. shows results from the author\u0026rsquo;s investigation providing experimental data on the percent elongation at the breaking point, tensile modulus and tensile strength for varying compositions of PLA and wood composite filament.\u003c/p\u003e\u003cp\u003eThe 60:40 ratio of PLA and wood composite was chosen as the material of choice for the testing of the TO and to examine the behavior of the computational model when subjected to a change in material compared to PLA. The PLA/Wood selected had an approximate tensile modulus of 2.0 GPa, approximately half that of the PLA material.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\u003ch2\u003e2.3. Analysis\u003c/h2\u003e\u003cp\u003eA static analysis was conducted with the aforementioned materials, meshing, and boundary conditions. A reference analysis was conducted for the un-optimized bulk chair model, as well as for all other optimized iterations for a comparative analysis. The parameters studied in the static analysis were Displacement, Von Mises Stress, Principal Stress, and Principal Strain. Additionally, a weight-saving parameter in terms of the volume percentage, difference between the un-optimized and optimized body, was used to investigatematerial efficiency.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\u003ch2\u003e2.4. Topology Optimization\u003c/h2\u003e\u003cp\u003eThe TO analysis was performed using the SIMP method. The objectives and constraints chosen for the PLA material study were derived from several test iterations and decided upon based on the desired outcome. The overall objective of this analysis was to minimize the design responses. These design responses included structural compliance, displacement response and stress response. Firstly, a minimization of the structural compliance and strain energy, allowed for the optimizer to create a structure with a high level of stiffness. The minimization of the displacement response was aimed at creating an optimized structure with reduced displacement of the chair back. This location was selected due to the high displacement region noted from the static analysis of the bulk chair model. Lastly, stress response minimization prompted the optimizer to create a structure with an overall reduction in high stress regions.\u003c/p\u003e\u003cp\u003eThe constraints for the TO were bound to two volume fraction constraints and Planar Symmetry Constraint. The volume fraction was constrained to a scalar value of 0.3, which prompted the optimizer to create a resulting topological structure with a 30% volume reduction from the bulk model. Additionally, a planar symmetry constraint allowed for the resulting topology-optimized structure to be more predictable and manufacturable by producing a structure that is symmetrical about a pre-described plane. This was made possible because the chair was subjected to symmetrical loads.\u003c/p\u003e\u003cp\u003eIt must be noted that the TO objectives and constraints were edited from the PLA specimen in the PLA/Wood chair study. The TO analysis was conducted on the PLA specimen first; therefore, based on the results produced, the objectives made for the PLA specimen were able to become constraints with specific threshold values in the following studies. A minimization of structural compliance was maintained as the objective in the PLA/Wood chair optimization. As opposed to having the other objectives that were used in the PLA specimen, such as minimizing displacement response and stress response, these were used as constraints with maximum value of the inputs. From the analysis of the final model of the PLA specimen, the max displacement and stress values were used as the displacement and stress maximum constraints, and the optimizer was set to aim for maximum displacement and stresses that were less than these values. Other constraints included planar symmetry, for a symmetrical body across the section of the chair, and volume fraction, which was set to 0.3.\u003c/p\u003e\u003c/div\u003e"},{"header":"3. Results and Discussion","content":"\u003cp\u003eThe static analysis results for the virgin PLA and PLA/Wood composite 3D printed parts were used as a reference model for all TO models for material efficiency and structural integrity investigations. The post-processing of the optimized 3D-printed part involved the smoothening of the 3D printed part surface which was initially left rough after optimization.\u003c/p\u003e\u003cp\u003eDuring computational post processing of both 3D printed chairs, PLA and PLA/Wood composite, the stability of the topology optimized chair was reinforced by the addition of a support leg and base (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e.b). These additions were merged onto the body of the chair with the use of filets in order to prevent the high stress region created by sharp geometrical bends.\u003c/p\u003e\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\u003ch2\u003e3.1 Topology Optimization\u003c/h2\u003e\u003cdiv id=\"Sec9\" class=\"Section3\"\u003e\u003ch2\u003e3.1.1. Solid PLA Results\u003c/h2\u003e\u003cp\u003eThe maximum displacement of the un-optimized, non-topology optimized, model was found to be 0.0288 mm. This displacement was primarily confined to the top of the chair back (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. a). This maximum displacement region remained in the same location in the optimized model; however, the maximum value increased to 0.0428 mm. In the optimized model, a medium displacement region was found at the edge of the chair seat with an approximate value of 0.0214 mm.\u003c/p\u003e\u003cp\u003eIn terms of von mises stress, an increase in the maximum von mises stress was found in the optimized model. The value of the von mises stress increased from 2.51 MPa to 3.56 MPa from un-optimized to optimized, respectively. The maximum von mises stress location remained unchanged being located at the edge of the chair seat and in the bend made by the back and seat of the chair (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e.d).\u003c/p\u003e\u003cp\u003eThe maximum principal stress of the un-optimized bulk model was found to be 2.44 MPa. This maximum principal stress region was placed in the bend made by the back and seat of the chair (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e.e). It was also noted that principal stress distribution can be seen in the chair back, decreasing upon ascent. Additionally, high principal stress regions were found on the topology optimized model with the additional regions being found in the bends made by the support structures under the seat of the chair under chair support structures (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e.e).\u003c/p\u003e\u003cp\u003eThe max principal stress was found to have increased to 3.56 MPa in the topology optimized model. Similarly, the principal strain increased in the optimized model from a value of 4.99e-4, un-optimized, to 6.89e-4. The maximum strain region for the un-optimized and topology optimized models was found in the bend of the back and seat of the chair (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. f). In the un-optimized model, additional high strain regions were found at the corners of the edge of the seat, while the optimized model noted the presence of mid-strain regions over the surface of the back of the chair and seat with an approximate value of 3.44e-4. Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. summarizes these results and also provides the weight saving percentage of the PLA topology optimized model, 59.9%. This percentage is a comparison between the volume of the un-optimized model to that of the topology optimized model.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003ePLA Specimen Static Analysis Results\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"6\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eGeometry\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eMax Displacement (mm)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eMax Von Mises Stress (MPa)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eMax Principal Stress (MPa)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eMax Principal Strain\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eWeight Saving (%)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSolid un-optimized model\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.0288\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e2.51\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e2.44\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e4.99e\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\" morerows=\"2\" rowspan=\"3\"\u003e\u003cp\u003e59.9\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSolid optimized model\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.0428\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e3.56\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e3.30\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e6.89e\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eAbsolute Difference\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.0139\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e1.05\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.857\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e1.89e\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec10\" class=\"Section3\"\u003e\u003ch2\u003e3.1.2. Solid PLA/Wood composite Results\u003c/h2\u003e\u003cp\u003eThe maximum displacement for the un-optimized model was found to be 0.0637 mm located at the top of the back of the chair (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. e). The maximum displacement decreased to a value of 0.0487 mm with a relocation of the maximum region to the edge of the seat (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. c) from the un-optimized to optimized model, respectively.\u003c/p\u003e\u003cp\u003eAdditionally, a decrease in the maximum von mises stress was found in the optimized model. The maximum von mises stress was found to be 3.17 MPa for the un-optimized model. This small maximum von mises stress region for the un-optimized model was located in the bend created by the intersection of the back and seat of the chair (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. f). Additional maximum von mises stress regions were noted at the corners of the edge of the seat. Mid-stress regions can be seen surrounding the high-stress regions with an approximate value of 1.58 MPa. On the contrary, the maximum von mises stress of the optimized model was found to be 3.12 MPa. Similar to the un-optimized modelly, while the location of the maximum von mises stress region was found in the bend created by the back and seat of the chair, more high stress regions were found at the corners of the edge of the seat and the bottom of the front legs (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. d). Surrounding these high stress points are mid-stress regions with an approximate value of 1.56 MPa. Additional mid stress regions can be found in the creases of the bends made by the supporting legs.\u003c/p\u003e\u003cp\u003eA continued reduction was noted in the principal stress of the optimized model when compared to the un-optimized model, from 2.38 MPa, un-optimized model, to 2.32 MPa, optimized model. A high stress region was noted to be located in the bend made by the back and seat of the chair for both un-optimized and optimized models, with mid-stress regions being present throughout the topology optimized model (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. e).\u003c/p\u003e\u003cp\u003eOn the other hand, an increase in the principal strain was seen going from a value of 1.13e\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e, un-optimized, to 1.28e\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e, optimized model. Similarly, the maximum principal strain region was found to be in the bend created by the back and seat of the chair (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. f). Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e summarizes these results and displays the weight saving percentage of the PLA/Wood composite material model, 44.0%.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eAnalysis of PLA/Wood Specimen Static Analysis Results\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"6\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eGeometry\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eMax Displacement (mm)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eMax Von Mises Stress (MPa)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eMax Principal Stress (MPa)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eMax Principal Strain\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eWeight Saving (%)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSolid un-optimized model\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.0637\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e3.17\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e2.38\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e1.13e\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\" morerows=\"2\" rowspan=\"3\"\u003e\u003cp\u003e44.0\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSolid optimized model\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.0488\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e3.12\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e2.32\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e1.28e\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eAbsolute Difference\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.0149\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.0473\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.0543\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e1.48e\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eIt was observed that results from the static analysis alone do not directly determine the safe operational use of the chair. Therefore, to evaluate and compare the structural integrity of the chair under load, we considered the yield strengths of the materials used PLA and PLA/Wood composite. Thus, we can assess whether the structures could safely withstand the applied loads by comparing the maximum stresses obtained from the static analysis with the yield strengths of these materials. If the maximum stress is lower than the yield strength of the material, indicating safe operational use.\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\u003ch2\u003e3.2. Impact of Material Properties on Topology Optimization\u003c/h2\u003e\u003cp\u003eTO is dependent upon the material properties of the specimen. From this end, the optimizer is able to distribute material to efficiently and effectively use material for weight saving and structural integrity. In this study, a test was performed to determine exactly the behavior of the optimizing software to a change in material properties.\u003c/p\u003e\u003cp\u003eThis investigation examined the topology-optimized model of the chair for both PLA and PLA/Wood composite (40 wt% wood and 60 wt% PLA) to evaluate the effect of material properties on TO of the chair. The test was conducted with all parameters, boundary conditions, objectives, and constraints, being held constant. The weight saving percentage was based on a volume fraction calculation used to measure the percentage change in volume from the initial bulk model to the optimized model. Results displayed that the PLA-optimized chair produced a weight saving value of 59.9%, compared to the PLA/Wood specimen producing 44.0%. In other words, the final optimized model of the PLA and PLA/Wood chair was reduced to 40.1% and 56.0% of the bulk chair, respectively (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e).\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe drastic difference in volume reduction after optimization can be attributed to the differences in material properties of the PLA and the PLA/Wood composite. The 60:40 PLA/Wood composite material was selected due to its superior tensile modulus when compared to the other tested composite ratios, however, the PLA/wood material still reported a tensile modulus of approximately half that of PLA, 2.0 GPa and 4.4 GPa, respectively [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. The term Young\u0026rsquo;s modulus, tensile modulus, elastic modulus, modulus of elasticity, and stiffness are referring to the mechanical property that measures the stiffness of a certain material [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. Young\u0026rsquo;s modulus is the ratio of the applied stress on the material to the strain associated with that applied stress. From that, it can be determined that the Young\u0026rsquo;s modulus has a directly proportional relationship with applied stress. As a result, TO takes advantage of this relationship and allows for more aggressive material removal in high stiffness materials, such as metals, due to their high stress capacity.\u003c/p\u003e\u003cp\u003eThe trends presented in the static analysis help to validate the claim that the optimizer enables greater material removal and allows for higher stresses to be applied on stronger materials. From Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, it can be seen that there is an increase in both stresses, von mises and principal, in the PLA optimized chair when compared to the un-optimized bulk model. On the other hand, there was a reduction, from the un-optimized bulk model, in the maximum von mises and principal stress for the PLA/Wood optimized chair (Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). This indicates that as PLA is the stronger material compared to PLA/Wood, we were able to subject the PLA model to higher stress levels through increased material removal, and on the contrary, reduced the stress levels in the weaker material, PLA/Wood, through less aggressive material penalization.\u003c/p\u003e\u003cp\u003eAdditionally, a change in materials has little to no effect on the overall geometrical structure of the optimized model (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e. b, c). The PLA and PLA/Wood chair have the same core geometry, while only differentiating in material density distribution. Therefore, it can be inferred that the topological structure/shape of the chair is directly related to the boundary conditions and the TO's objectives and constraints.\u003c/p\u003e\u003cp\u003eAll in all, selecting the different material determines the result produced from TO where the greater the material\u0026rsquo;s structural properties, the more aggressive the topology optimizer can be in reducing the overall material used for the model. On the other hand, as seen in this test comparing the results produced from PLA and PLA/Wood materials, the topology optimizer is less able to remove large amounts of material for equivalent loading conditions due to the lower stress capacity of the weaker materials.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e\u003ch2\u003e3.3. Design Optimization Vs Computational Optimization\u003c/h2\u003e\u003cp\u003eAn investigation was conducted to determine the effectiveness and the importance of computational topology optimization (CTO) for material efficiency and structural performance versus designed based optimized (DBO) structures aimed at achieving the same goal. The specimens used for this study were a computational optimization chair and an architecturally designed chair designed to minimize material usage, both in the PLA/Wood composite material.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eIn this study, both the computational topology optimized, and design based optimized models specimens were subjected to common boundary conditions and meshing. Static analysis results highlighted the structural superiority of the computational topology-optimized chair when compared to the DBO model (Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). This was largely due to the computational optimization method's ability to work on simultaneous objectives, for example minimizing the volume fraction while maximizing structural integrity through structural compliance reduction and stress responses. On the other hand, the design-based chair was primarily aimed at overall material efficiency by reducing the amount of material used for the chair. This however saw a dramatic reduction in the structural performance of the chair. Ultimately, the shortcoming of the design-based TO can be referenced to the inability of the human designer to consider material properties for structural integrity, stress distributions and dynamic responses simultaneously. It must be noted however that the material of the specimen is the major determinant of structural performance, in that, if the DBO model was made of a material with greater structural properties, for example steel, the static analysis results would have indicated a stronger structure despite its thin geometric profile.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eStatic Analysis Comparison of Computational Optimization Chair and Architecturally Designed Chair\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"6\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eModel\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eMax Displacement (mm)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eMax Von Mises Stress (MPa)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eMax Principal Stress (MPa)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eMax Principal Strain\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eWeight Saving (%)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCTO\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.0487\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e3.12\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e2.31\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.00128\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e44.0\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eDBO\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e422\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e93.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e72.6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.329\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e81.6\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e\u003ch2\u003e3.4. Lattice Structure for Advanced Optimization\u003c/h2\u003e\u003cp\u003eA topology-optimized structure can be further optimized for increased structural performance and material efficiency by the incorporation of porous, multi-cell lattice structures, which are commonly used in many engineering industries such as aerospace, biomedical and mechanical design. These structures are suitable for various applications due to their light weighting properties and energy absorption characteristics [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. Different lattice structures offer distinct advantages ranging from high compressive strengths to thermal performance; therefore, it is important to understand the intended application.\u003c/p\u003e\u003cp\u003eDue to these performance enhancement properties, an investigation into the incorporation of lattice structures within topology-optimized structures was conducted in this study. This study was carried out on the FCC, Diamond TPMS, and a composite lattice structure (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e). The static analysis performance of these structures was examined and compared to the solid topology optimized specimens. Throughout this investigation, multiple parameters were varied such as unit cell size, lattice orientation, and lattice thickness to determine the optimal configuration for the lattice structure. Additionally, a variable thickness lattice feature, otherwise known as gradient latticing, was implemented into the lattice structure for structural performance maintenance as previous research studies have displayed the increased strengthening effect of gradient lattices when compared to uniform lattice structures [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. The gradient latticing worked by using the results from the static analysis to determine the regions on the solid optimized chair which had the highest stresses. These high stress regions then saw a localized increase in strut thickness for better stress distribution and support.\u003c/p\u003e\u003cp\u003eThe lattice structures were designed with the nTopology software in that the topology optimized bodies were shelled with a 1 mm wall thickness and the lattice structure was merged with the shell. It must be noted that the orientation of the lattice structures was positioned in such a way that oriented the truss in the direction of the applied load for maximum reinforcement [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e] (Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e).\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eFCC and Diamond TPMS lattice configuration\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"4\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eUnit Cell Size (mm)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eUnit Cell Size (mm)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eUnit Cell Size (mm)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eFCC\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e2x2x2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eUVW\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eMin \u0026minus;\u0026thinsp;0.75\u003c/p\u003e\u003cp\u003eMax \u0026minus;\u0026thinsp;1.00\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eDiamond TPMS\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e6x6x6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eUVW\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eMin \u0026minus;\u0026thinsp;0.25\u003c/p\u003e\u003cp\u003eMax \u0026ndash; 0.75\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eLattice structures of different geometries offer distinct structural advantages over uniform lattices in applications where a structure experiences multiple modes of deformation. Intricate structures such as the topology-optimized chair can have complex stress distributions and varying modes of deformation across the body. Therefore, the creation of composite lattice structures, constructed from lattices of varying geometries, can greatly improve the material efficiency of the specimen. This is largely due to the fact that each element of the chair would be constructed from a lattice structure which provides reinforcement solely in the direction of potential deformation.\u003c/p\u003e\u003cp\u003eWith this knowledge, an additional lattice structure was constructed for the investigation. The composite lattice structure was aimed at increasing the weight saving percentage of the chair, while maintaining or improving its structural integrity. To this end, the body of the optimized chair was divided into three sections; back and seat, legs, and mid-body. These sections were highlighted within the static analysis as areas that displayed different modes of deformation, flexural and compression. The back and seat of the chair was made of thin 3mm thick PLA, therefore it was important that if implementing weight saving lattice structure within the shell of the body, the structural performance must not be compromised. The back and seat of the chair were directly subjected to compressive forces acting in the z (vertical) and x (horizontal) directions. As a result, it was noted from the static analysis that the bend created by the joining of the back and seat of the chair would be subjected to flexural deformation. Therefore, hexagonal honeycomb lattice structure was used to fill the shell of the back and seat due to its superior flexural strength [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. A relatively small 2x2x2 mm unit cell size in combination with a gradient lattice stress modified was added to the lattice to increase the reinforcing effect of the lattice structure. Similarly, a hexagonal honeycomb lattice structure was used for the mid-body of the chair with a gradient lattice and a larger 4x4x4 mm unit cell. The topology optimized mid-body, with its complex geometry, would be subjected to both flexural and compressive deformation as a result of its unique stress distribution. Therefore, as previous research concluded [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e], hexagonal honeycomb lattice structure would provide dual reinforcement in this application, both flexural and compression. It was noted that the legs and base of the chair were solely subjected to compressive forces in the negative z direction, therefore a 2x2x2mm column lattice structure with a constant truss thickness of 1 mm, for torsion and buckling resistance, was used to provide reinforcement in the direction of the applied load. The lattice sections of the chair were merged together with an increase in thickness around the points where sections of different lattice geometries joined for reinforcement (Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e).\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eComposite lattice configuration of sections\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"5\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSection\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eLattice Structure\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eUnit Cell Size (mm)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eOrientation\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eThickness (mm)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eBack and Seat\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eHexagonal Honeycomb\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e2x2x2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eUVW\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eMin \u0026minus;\u0026thinsp;0.50\u003c/p\u003e\u003cp\u003eMax \u0026minus;\u0026thinsp;1.00\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eLegs\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eColumn\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e2x2x2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eUVW\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eConstant \u0026minus;\u0026thinsp;1.00\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMid-body\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eHexagonal Honeycomb\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e4x4x4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eUVW\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eMin \u0026minus;\u0026thinsp;0.75\u003c/p\u003e\u003cp\u003eMax \u0026minus;\u0026thinsp;1.00\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe static analysis results displayed the FCC specimen to be the superior lattice, outperforming diamond TPMS and composite lattice structures in the majority of mechanical property studies. The FCC chair reported the lowest maximum total displacement under deformation with a value of 0.0331 mm (Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e). In addition, the lightweight FCC chair produces a von mises stress value approximately equal to that of the solid bulk chair, 3.26 MPa and 3.17 MPa, respectively (Fig.\u0026nbsp;11). The results for both von mises and principal stress highlighted the great benefit of lattice structures for stress distribution. Despite the von mises and principal stress of both the solid optimized and un-optimized models being less than that of both the lattice light-weighted diamond TPMS and composite lattice models (Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e12\u003c/span\u003e), the solid models noted more concentrated high-pressure regions and less energy distribution. Additionally, the maximum principal strain values mirrored the trend of the principal stress results with the solid models reporting the lowest strain values when compared with the diamond TPMS and composite lattice models; 2.94e-4 solid un-optimized model and 6.95e-4 solid optimized model. The FCC lattice model displayed a principal strain value between the solid un-optimized and solid optimized model, with a value of 6.89e-4 (Fig.\u0026nbsp;13).\u003c/p\u003e\u003cp\u003eOf the latticed light weighted models, the FCC model had the lowest strain value, followed by the composite lattice structure. The relative weight saving was a parameter used to measure the material reduction relative to the solid un-optimized model, bulk model. It was found that the composite lattice model obtained the highest material saving with a value of 70.0%, followed by FCC and diamond TPMS, 69.0% and 68.9%, respectively (Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e14\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eAll in all, despite the FCC lattice specimen producing superior results in the majority of the mechanical property tests, the composite lattice model closely mirrored these results. Additionally, the composite lattice model possessed the greatest material efficiency evident by its weight saving percentage of 70.0%.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e"},{"header":"4. Conclusion","content":"\u003cp\u003eThis study highlights the benefit of TO in combination with additive manufacturing to produce lightweight structures with enhanced mechanical properties, and material efficiency. This research provided evidence for the response of TO technology to the change in material properties, exhibiting the dependence of TO on material property characterization. It was found that the change in material has little to no effect on the overall geometrical shape of the optimized structure but rather, judges the aggressiveness of material penalization during optimization. The research focuses on two materials PLA and PLA/Wood composite, the PLA test model with a modulus of elasticity of 4.0 GPa, approximately double that of the PLA/Wood composite model, displayed a topology optimized solution which saw a weight saving percentage which was 15.9% greater than the weaker PLA/Wood composite model. It was therefore concluded that a strong material, represented by a large Young\u0026rsquo;s Modulus and subsequently a large tensile strength value, allows the optimizer to remove a greater amount of material due to its higher stress capacity. Ultimately, the superiority of TO is demonstrated in the comparison study between the computational and the design-based topology optimized chairs. The results affirmed the designer community to simultaneously consider material saving and structural performance enhancement, favoring one over the other. On the contrary, TO technology is highlighted for its duality in this region, producing structures where both parameters are controlled. Additionally, the added benefit of lattice incorporation with topology-optimized structures for further weight saving and stress distribution was noted. More specifically, the creation of composite lattice structures, as done in this paper for both PLA and Wood/PLA models, has opened the door for the development of highly efficient structural bodies, infilled with lattice geometries most suitable for the localized form of deformation. This was confirmed by the superiority of the PLA composite lattice model which produced a superior weight saving percentage of 70.0% when compared to the uni-lattice chairs, FCC and diamond TPMS, 69.0% and 68.9% respectively, while still maintaining competitive structural performance.\u003c/p\u003e\u003cp\u003eFuture work will involve experimenting with the specimens examined in this study to validate all theoretical findings. Additionally, as previously mentioned, the static analysis results produced fail to directly highlight the exact point and mode of mechanical failure; therefore, a future study would incorporate bulking analyses as well as dynamic response analyses for predictions of long-term structural performance, examining both the durability of the TO, FDM and composite materials combination for real-world applications. Moreover, future research will be conducted on the potential involvement of composite lattice structures within high-performance applications for highly efficient structural bodies.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003ch2\u003eCompeting interests\u003c/h2\u003e\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e\u003c/p\u003e\u003ch2\u003eFunding\u003c/h2\u003e\u003cp\u003eThe financial support of the NSERC grant is greatly appreciated.\u003c/p\u003e\u003ch2\u003eAuthor\u0026rsquo;s contributions\u003c/h2\u003e\u003cp\u003eThe data collection, modeling, analysis and original draft was prepared by Kaelin azariah d King. The idea, conceptualization, supervision, reviewing and editing, overall administration of the research work, final approval of the manuscript was performed by Haniyeh (Ramona) Fayazfar. The reviewing, editing and final approval of manuscript were also performed by Saumang Swarup, Ankit Sahai and Rahul Swarup Sharma.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eS. Shahbazi, C. J\u0026ouml;nsson, M. Wiktorsson, M. Kurdve, and M. Bjelkemyr, \u0026ldquo;Material efficiency measurements in manufacturing: Swedish case studies,\u0026rdquo; \u003cem\u003eJournal of Cleaner Production\u003c/em\u003e, vol. 181, pp. 17\u0026ndash;32, 2018. doi:10.1016/j.jclepro.2018.01.215 \u003c/li\u003e\n\u003cli\u003eO. Sigmund and K. Maute, \u0026ldquo;Topology Optimization approaches,\u0026rdquo; \u003cem\u003eStructural and Multidisciplinary Optimization\u003c/em\u003e, vol. 48, no. 6, pp. 1031\u0026ndash;1055, 2013. doi:10.1007/s00158-013-0978-6 \u003c/li\u003e\n\u003cli\u003eT. Kumar and K. Suresh, \u0026ldquo;A density-and-strain-based K-clustering approach to microstructural topology optimization,\u0026rdquo; \u003cem\u003eStructural and Multidisciplinary Optimization\u003c/em\u003e, vol. 61, no. 4, pp. 1399\u0026ndash;1415, 2019. doi:10.1007/s00158-019-02422-4 \u003c/li\u003e\n\u003cli\u003eG. I. N. Rozvany, \u0026ldquo;Aims, scope, methods, history and unified terminology of computer-aided topology optimization in structural mechanics,\u0026rdquo; \u003cem\u003eStructural and Multidisciplinary Optimization\u003c/em\u003e, vol. 21, no. 2, pp. 90\u0026ndash;108, 2001. doi:10.1007/s001580050174 \u003c/li\u003e\n\u003cli\u003eI. Ntintakis, G. E. Stavroulakis, and N. Plakia, \u0026ldquo;Topology optimization by the use of 3D printing technology in the product design process,\u0026rdquo; \u003cem\u003eHighTech and Innovation Journal\u003c/em\u003e, vol. 1, no. 4, pp. 161\u0026ndash;171, 2020. doi:10.28991/hij-2020-01-04-03 \u003c/li\u003e\n\u003cli\u003eQ. Hu \u003cem\u003eet al.\u003c/em\u003e, \u0026ldquo;Research into topology optimization and the FDM method for a space cracked membrane,\u0026rdquo; \u003cem\u003eActa Astronautica\u003c/em\u003e, vol. 136, pp. 443\u0026ndash;449, 2017. doi:10.1016/j.actaastro.2017.03.033 \u003c/li\u003e\n\u003cli\u003eH. Yin \u003cem\u003eet al.\u003c/em\u003e, \u0026ldquo;Review on lattice structures for energy absorption properties,\u0026rdquo; \u003cem\u003eComposite Structures\u003c/em\u003e, vol. 304, p. 116397, 2023. doi:10.1016/j.compstruct.2022.116397 \u003c/li\u003e\n\u003cli\u003eY. Feng Zhou, R. Fa Wang, and Ao Deng, \u0026ldquo;Topology optimization design of Biology Wooden Furniture,\u0026rdquo; \u003cem\u003eInternational Journal of Advanced Engineering and Management Research\u003c/em\u003e, vol. 08, no. 02, pp. 81\u0026ndash;87, 2023. doi:10.51505/ijaemr.2023.8208\u003c/li\u003e\n\u003cli\u003eD. Jubinville, J. Sharifi, T. H. Mekonnen, and H. 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H. Azman, and S. Abdullah, \u0026ldquo;A review on integration of lightweight gradient lattice structures in additive manufacturing parts,\u0026rdquo; \u003cem\u003eAdvances in Mechanical Engineering\u003c/em\u003e, vol. 12, no. 6, p. 168781402091695, 2020. doi:10.1177/1687814020916951 \u003c/li\u003e\n\u003cli\u003eC. Beyer and D. Figueroa, \u0026ldquo;Design and analysis of lattice structures for additive manufacturing,\u0026rdquo; \u003cem\u003eJournal of Manufacturing Science and Engineering\u003c/em\u003e, vol. 138, no. 12, 2016. doi:10.1115/1.4033957 \u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"the-international-journal-of-advanced-manufacturing-technology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jamt","sideBox":"Learn more about [The International Journal of Advanced Manufacturing Technology](https://www.springer.com/journal/170)","snPcode":"170","submissionUrl":"https://submission.nature.com/new-submission/170/3","title":"The International Journal of Advanced Manufacturing Technology","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Topology Optimization (TO), Additive Manufacturing, Wood Composite Lattice Structures, Sustainable Materials","lastPublishedDoi":"10.21203/rs.3.rs-7178669/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7178669/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study provides a theoretical investigation into the union of topology optimization (TO), additive manufacturing and composite materials for the manufacturing industry. Additionally, the added weight saving and structural performance enhancement benefits of lattice structures are examined. In this study, a single-seater chair made of both Polylactic acid (PLA) and a PLA/Wood composite material was subjected to a TO study in efforts of reducing the overall material usage and enhancing its structural performance. A static analysis was used to conduct comparative analyses to examine the behavior of TO technology to change in material properties, to highlight the superiority of computational TO when compared to design- based optimization, as well as to examine the added benefit of lattice structures. Through this study, a composite lattice structure was created in efforts of defining a unified lattice structure that provided optimal structural reinforcement of the multi-mode deforming chair. It was found that the TO technology was largely dependent on material characterization as it relates to the aggressiveness of material penalization. In addition, the composite lattice structure was highlighted for its superior weight-saving property while still maintaining competitive mechanical performance over the FCC and Diamond TPMS lattice models.\u003c/p\u003e","manuscriptTitle":"An Investigation into Topology Optimization for Weight Saving and Mechanical Property Enhancement of FDM 3D Printed Objects","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-08-12 13:25:06","doi":"10.21203/rs.3.rs-7178669/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Major Revisions Needed","date":"2025-09-16T09:01:57+00:00","index":"","fulltext":""},{"type":"reviewerAgreed","content":"","date":"2025-08-01T13:18:26+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-08-01T13:17:18+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-08-01T03:26:48+00:00","index":"","fulltext":""},{"type":"submitted","content":"The International Journal of Advanced Manufacturing Technology","date":"2025-07-30T09:42:40+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"the-international-journal-of-advanced-manufacturing-technology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jamt","sideBox":"Learn more about [The International Journal of Advanced Manufacturing Technology](https://www.springer.com/journal/170)","snPcode":"170","submissionUrl":"https://submission.nature.com/new-submission/170/3","title":"The International Journal of Advanced Manufacturing Technology","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"d5060f28-9253-447c-8bf7-101e9617f8bd","owner":[],"postedDate":"August 12th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-12-15T16:05:50+00:00","versionOfRecord":{"articleIdentity":"rs-7178669","link":"https://doi.org/10.1007/s00170-025-16983-w","journal":{"identity":"the-international-journal-of-advanced-manufacturing-technology","isVorOnly":false,"title":"The International Journal of Advanced Manufacturing Technology"},"publishedOn":"2025-12-10 15:59:18","publishedOnDateReadable":"December 10th, 2025"},"versionCreatedAt":"2025-08-12 13:25:06","video":"","vorDoi":"10.1007/s00170-025-16983-w","vorDoiUrl":"https://doi.org/10.1007/s00170-025-16983-w","workflowStages":[]},"version":"v1","identity":"rs-7178669","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7178669","identity":"rs-7178669","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}