Remesh-free shape optimization using the wavelet-Galerkin method

Abstract

The objective of this investigation is to develop a new remesh-free shape optimization method based on the adaptive wavelet-Galerkin analysis. To avoid cumbersome remeshing processes, we embed the original analysis design domain inside a simple fictitious domain and use the predetermined analysis grid points. For efficient adaptive analysis, we utilize the multiscale multiresolution characteristics of the hat interpolation wavelets that are associated with predetermined grid points. Furthermore, we approximate the design boundary curve by oblique lines that do not necessarily pass through the analysis grid points and develop an accurate stress evaluation technique based on the proposed boundary approximation. The validity of the proposed remesh-free shape optimization formulation based on the wavelet-Galerkin method is verified through benchmark shape optimization problems.