Structural optimization based on the phase field method (validation of perimeter constraint effect and extension to compliant mechanism design problem and eigen frequency maximization problem)

This paper discusses a structural optimization method that optimizes 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 incorporating perimeter control functions. 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 to two-dimensional linear elastic and vibration optimization problems such as the minimum compliance problem, a compliant mechanism design problem and the eigenfrequency maximization problem. The numerical examples provided illustrate the convergence of the various objective function and the effect that perimeter control has on the optimal configurations.