Controlling the maximum stress in structural stiffness topology optimization of geometrical and material nonlinear structures

Structural topology optimization for nonlinear structures and stress-based design problems have been well developed and extensively studied. However, topology optimization of Simultaneous Geometrical and Material Nonlinear (SGMN) structures under stress constraints, requires significant investigation. Hence, based on an extended Bi-directional Evolutionary Structural Optimization (BESO) method, this work proposes a novel topology optimization method to maximize the stiffness of SGMN structures subject to both volume fraction and maximum von Mises stress constraints. The extended BESO method based on discrete variables can avoid the stress singularity problem. The global von Mises stress is established with the p-norm function, and the adjoint sensitivity analysis is derived. The nonlinear finite element equations are established by the Lagrangian method and the large deformation problem is solved by the Total Lagrangian method. A series of comparison studies have been conducted to validate the effectiveness and practicability of the method on several benchmark design problems. It concludes that the proposed approach can well control the stress level and efficiently solve the stress concentration effect at the critical stress areas of SGMN structures.