A level set method for structural shape and topology optimization using Radial Basis Function

Abstract

In order to address the efficient issue of the topological shape optimization problem, this paper presents a parametric level set method for the problem of continuum structures by using the Radial Basis Functions (RBFs). The level set-based method is introduced to implicitly represent the free boundary of a structure. To evolve the level set front, the Wu's compactly supported radial basis function (CSRBF) with C4 smoothness is applied. Then, the Hamilton-Jacobi partial differential equation (PDE) is transformed into a relatively easier ordinary differential equation (ODE). Furthermore, a self-adaptive moving limit scheme is incorporated into the optimality criteria to achieve a better optimal result. Finally, the numerical ex-ample is provided to show the effectiveness of the proposed method.