Structural topology optimization using an enhanced level set method

Abstract

This paper proposes an effective algorithm based on the Level Set Method (LSM) to solve the problem of topology optimization. The Hamilton–Jacobi Partial Differential Equation (H-J PDE), level set equation, is modified to increase the performance. We combine the topological derivative with nonlinear LSM to create a remedy against premature convergence and strong dependency of the optimal topology on the initial design. The magnitude of the gradient in the LS equation was replaced by several Delta functions and the results were explored. Instead of the explicit scheme, which is commonly used in conventional LSM, a semi-implicit additive operator splitting scheme was carried out in our study to solve the LS equation. A truncation strategy was implemented to limit maximum and minimum values in the design domain. Finally, several numerical examples were provided to confirm the validity of the method and show its accuracy, as well as convergence speed.