Fracture strength topology optimization of structural specific position using a bi-directional evolutionary structural optimization method

A new topology optimization procedure based on the extended finite element method (XFEM) for enhancing the fracture strength of structural specific position is proposed. The XFEM is used as an approach for the description of discontinuity states in the design domain, such as cracks, voids and inclusions, by employing the enrichment shape function with discontinuous properties. Based on linear elastic fracture mechanics and the bi-directional evolutionary structural optimization (BESO) method, the J integral, as a criterion for predicting crack growth, is considered to prevent crack propagation and enhance the fracture strength of the structure. Several typical examples are provided to verify the effectiveness of the present method by considering different situations of length and location of the crack, and the interactions between crack, void and inclusion. The results suggest that combining the XFEM with BESO is a promising approach for optimizing the anti-fracturing mechanical properties of structures.