Non‑intrusive polynomial chaos expansion for robust topology optimization of truss-like continua under random loads

This paper dedicates to presenting an uncertain analysis framework for robust topology optimization (RTO) based on truss-like material model that integrates non-intrusive polynomial chaos expansion (PCE) approach. In this framework, the RTO problem is formulated as a bi-objective optimization one to simultaneously minimize the expectancy and its standard deviation of structural compliance with volume constraints. The magnitude and direction of load uncertainty are assumed to follow a Gaussian distribution independently. A standard non-intrusive PCE requires a large number of multivariate integrals to calculate the expansion coefficient. Therefore, response metrics such as structural compliance are efficiently characterized using the decoupling techniques based on the expansions of the uncertain parameters. The mechanical analysis and uncertainty analysis are separated, so that the number of simulations in the original PCE procedure is greatly reduced for linear structures by means of superposition. The optimization is achieved by gradient-based methods. The appreciable accuracy and efficiency are validated by the brutal Monte Carlo simulation. Three numerical examples are provided to demonstrate that the proposed method can lead to designs with completely different topologies and superior robustness.