A Comparative Study of Isogeometric Analysis for Topology Optimzation Based on the Level Set and the Phase Field Methods

This work presents a comparative study on the application of isogeometric analysis in boundary variation methods based topology optimization problems. Level set and phase field are two boundary variation methods gaining in popularity in topology optimization research community. Among different formulations on update methods, this work employs reaction-diffusion and Allen-Cahn update equations for level set and phase field methods respectively. The application of the isogeometric analysis method for these two update equations is new in the literature. The work explores the effect of different parameters, like basis function order, diffusion coefficient, and mesh size on three benchmark topology optimization problems. Our results indicate that quadratic NURBS-basis functions are adequate to solve compliance minimization problems, and increasing order leads to an increase of computation time without much change in accuracy. We found that whereas the phase field method allows a range of diffusion coefficients, the reaction-diffusion-based level set method was able to converge only for a narrow range of diffusion coefficients. Both methods faced convergence problems when the mesh size is increased for higher order basis functions. This study can provide guidance to new users interested in the application of isogeometric analysis in boundary variation methods for topology optimization.