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.

非线性结构和基于应力的设计问题的结构拓扑优化已经得到很好的发展和广泛的研究。然而，在应力约束下同时进行几何和材料非线性 (SGMN) 结构的拓扑优化需要大量研究。因此，基于扩展的双向演化结构优化 (BESO) 方法，这项工作提出了一种新的拓扑优化方法，以最大化受体积分数和最大 von Mises 应力约束的 SGMN 结构的刚度。基于离散变量的扩展BESO方法可以避免应力奇异问题。全局 von Mises 应力由p建立-norm 函数，并导出伴随敏感性分析。采用拉格朗日法建立非线性有限元方程，采用全拉格朗日法求解大变形问题。已经进行了一系列比较研究，以验证该方法在几个基准设计问题上的有效性和实用性。得出的结论是，所提出的方法可以很好地控制应力水平，有效地解决SGMN结构临界应力区域的应力集中效应。