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

• Published in: Structural and multidisciplinary optimization Vol. 64; no. 6; pp. 3971 - 3998
• Main Authors: Han, Yongsheng, Xu, Bin, Duan, Zunyi, Huang, Xiaodong
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2021; Springer Nature B.V
• Subjects: Computational Mathematics and Numerical Analysis; Engineering; Engineering Design; Optimization; Research Paper; Sensitivity analysis; Stiffness; Stress concentration; Theoretical and Applied Mechanics; Topology optimization; Topology optimization; Adjoint sensitivity analysis; Material nonlinear; BESO method; Stress constraints; Geometrical nonlinear
• ISSN: 1615-147X; 1615-1488
• DOI: 10.1007/s00158-021-03072-1

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.