Controlling the maximum first principal stress in topology optimization

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.