Transient stress-constrained topology optimization of structures subjected to impacts

Abstract We investigate topology optimization of the elastodynamic structures under impact loading with transient stress constraints. The impact problem is formulated as applying a prescribed loading rate to the boundary up to the maximum loading time. In contrast to existing paradigms that consider dynamic stresses, we places more emphasis on transient behavior. We minimize the volume fraction of the structure while constraining the maximum transient von Mises stress. An additional static compliance constraint is introduced to guarantee the validity of the design. The sensitivity of maximum transient von Mises stress is then derived and validated, in which the discretize-thendifferentiate method is employed for the dynamic problem. A series of benchmark problems are investigated, by which the effectiveness of the proposed method is illustrated. The evolution of the maximum stress shows the necessity of highlighting transient behavior in the topology optimization of the structures under impacts.