Previous studies on topology optimization subject to stress constraints usually considered von Mises or Drucker–Prager criterion. In some engineering applications, e.g., the design of concrete structures, the maximum first principal stress (FPS) must be controlled in order to prevent concrete from cracking under tensile stress. This paper presents an effective approach to dealing with this issue. The approach is integrated with the bi-directional evolutionary structural optimization (BESO) technique. The p-norm function is adopted to relax the local stress constraint into a global one. Numerical examples of compliance minimization problems are used to demonstrate the effectiveness of the proposed algorithm. The results show that the optimized design obtained by the method has slightly higher compliance but significantly lower stress level than the solution without considering the FPS constraint. The present methodology will be useful for designing concrete structures.

以前在应力约束下进行拓扑优化的研究通常被视为von Mises或Drucker-Prager准则。在某些工程应用中，例如混凝土结构的设计，必须控制最大第一主应力（FPS），以防止混凝土在拉伸应力下开裂。本文提出了一种解决此问题的有效方法。该方法与双向进化结构优化（BESO）技术集成在一起。该p-norm函数用于将局部应力约束放宽为整体约束。法规遵从性最小化问题的数值示例用于证明所提出算法的有效性。结果表明，与该方法相比，在不考虑FPS约束的情况下，通过该方法获得的优化设计具有更高的柔度，但应力水平却大大降低。本方法学对于设计混凝土结构将是有用的。