Transient stress-constrained topology optimization of impacted structures

• Published in: Structural and multidisciplinary optimization Vol. 66; no. 4; p. 94
• Main Authors: Wang, Chao, Zhou, E. L., Wu, Yi, Li, Eric, Huang, Y. Y.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2023; Springer Nature B.V
• Subjects: Computational Mathematics and Numerical Analysis; Constraints; Elastodynamics; Engineering; Engineering Design; Impact loads; Loading rate; Optimization; Research Paper; Theoretical and Applied Mechanics; Time dependence; Topology optimization; Traction force; Transient analysis; Topology optimization; Transient stress constraint; Elastodynamics; Impact problem; SIMP
• ISSN: 1615-147X; 1615-1488
• DOI: 10.1007/s00158-023-03558-0

We investigate topology optimization of the elastodynamic structures under impact loading with transient stress constraints. In contrast to existing methods that apply a time-dependent prescribed traction force, we model the impact problem by directly imposing a prescribed loading rate on the boundary over time. It allows us to carry out topology optimization for impacted structures with strongly acyclic and transient characteristics. 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 transient analysis-based design. The sensitivity of maximum transient von Mises stress is then derived and validated, in which the discretize-then-differentiate 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 significance of highlighting transient behavior in the topology optimization of impacted structures.