Combination of the phase field method and BESO method for topology optimization

In this paper, the phase field method and the BESO (bidirectional evolutionary structural optimization) are combined to solve the topology optimization problems. The phase field function is used to represent the structure, and a time-dependent reaction diffusion equation called the Allen–Cahn equation is used to update the phase field function. In the sensitivity of Lagrange function, the Lagrange multiplier is replaced by the product of the Lagrange multiplier and the phase field function for fairing. The material removal scheme of the BESO which is easy to implement is employed to nucleate holes in the phase field method–based topology optimization. For a given target volume in each iterative step, a threshold of sensitivity is used to determine which elements should be removed; then, the structure is updated to match the target volume. Several numerical examples based on a two-dimensional minimum compliance problem are studied to demonstrate the effectiveness of this method.