Topology optimization using bi-directional evolutionary structural optimization based on the element-free Galerkin method

In this article, the bi-directional evolutionary structural optimization (BESO) method based on the element-free Galerkin (EFG) method is presented for topology optimization of continuum structures. 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 EFG method is used to derive the shape functions using the moving least squares approximation. The essential boundary conditions are enforced by the method of Lagrange multipliers. Several topology optimization problems are presented to show the effectiveness of the proposed method. Many issues related to topology optimization of continuum structures, such as chequerboard patterns and mesh dependency, are studied in the examples.