Structural Optimization Based on the Phase Field Method and Sensitivity Analysis

Abstract

This paper discusses a structural optimization method that achieves optimum shape and topology based on the phase field method. The proposed method has the same functional capabilities as a structural optimization method based on the level set method. Since the proposed method does not require extra operations such as re-initialization of the level set function or smoothing of sensitivities, the computational cost is lower than that of typical level set methods. Structural shapes are represented by the phase field function defined in the design domain and optimization of this function is performed by solving a time-dependent reaction diffusion equation. The artificial double-well potential function used in the equation is derived from sensitivity analysis. The proposed method is applied toa two-dimensional linear elastic problem. The provided numerical examples illustrate the convergence of the compliance minimization problem.