Stress-based bi-directional evolutionary structural topology optimization considering nonlinear continuum damage

This paper proposes a new methodology for structural topology optimization that is capable of stress minimization design considering nonlinear continuum damage. A quasi-static non-local damage model is integrated into a linear finite element analysis for modeling the structural damage. The Bi-directional Evolutionary Structural Optimization (BESO) method is adopted to circumvent the singularity issue. To cope with large scale constraints, the maximal von Mises stress is measured by the global p-norm stress aggregation approach. The density filter BESO method is developed while the sensitivity expressions of proposed indices with respect to design variables are derived. Influences of varying damage threshold and p-norm parameter on final designs are investigated through 2D and 3D numerical tests. The effectiveness of the proposed method is further validated in comparison with the stiffness maximization design. It is revealed that the smaller value of the damage threshold results in higher strength while the damage in the majority of solid material increases. The results demonstrate that the proposed approach can achieve stress minimization design by simultaneously considering nonlinear continuum damage.