The topology optimization design for cracked structures

In this paper, the element free Galerkin method (EFG) is proposed for topology optimization of cracked structures using the bi-directional evolutionary structural optimization method (BESO). The mathematical formulation of the topology optimization is developed considering the nodal strain energy as the design variable and the minimization of compliance as the objective function. The element free Galerkin method is enriched by the crack-tip enrichment functions to increase the approximation accuracy near the crack-tip. The Lagrange multiplier method is employed to enforce the essential boundary conditions. Several numerical examples are presented to show the effectiveness of the proposed method. Many issues related to topology optimization of cracked structures such as the effects of crack size and location on the optimal topology are addressed in the examples. The common numerical instabilities do not exist in the results.