Stress-based topology optimization and nonlinear structural topology optimization is gaining increasing attention in order to make topology optimization more realistic. Thus, this paper extends current concepts of topology optimization to the design of structures made of nonlinear materials. An extended bi-directional evolutionary structural optimization (BESO) method for stress minimization topology optimization of material nonlinear structures is proposed in this work. BESO method based on discrete variables can effectively avoid the well-known singularity problem in density-based methods with low-density elements. The maximum von Mises stress is approximated by the p-norm global stress. The sensitivity information for designing variable updates is derived in detail by adjoint method. As for the highly nonlinear stress behavior, the updated scheme takes advantages from two filters respectively of the sensitivity and topological variables to improve convergence. Moreover, the filtered sensitivity numbers are combined with their historical sensitivity information to further stabilize the optimization process. The effectiveness of the proposed method is demonstrated by several 2D benchmark design problems.

基于应力的拓扑优化和非线性结构拓扑优化正越来越引起人们的注意，以使拓扑优化更加现实。因此，本文将当前拓扑优化的概念扩展到了由非线性材料制成的结构的设计中。本文提出了一种扩展的双向演化结构优化（BESO）方法，用于材料非线性结构的应力最小化拓扑优化。基于离散变量的BESO方法可以有效避免基于密度的低密度元素方法中众所周知的奇点问题。von Mises最大应力由p近似-规范全球压力。通过伴随方法详细推导了用于设计变量更新的敏感性信息。对于高度非线性的应力行为，该更新方案利用了两个滤波器分别的敏感度和拓扑变量的优势来提高收敛性。此外，将滤波后的灵敏度数字与其历史灵敏度信息相结合，以进一步稳定优化过程。几个2D基准测试设计问题证明了该方法的有效性。