Adaptive multiscale wavelet-Galerkin analysis for plane elasticity problems and its applications to multiscale topology design optimization

The multiscale Galerkin formulation of two-dimensional elasticity problems is presented. For easy interpolation and boundary handlings as well as efficient adaptive analysis, two-dimensional interpolation wavelets are used as the multiscale trial functions in the Galerkin formulation. After the validity of the present multiscale adaptive method is verified with some benchmark problems, the present wavelet-based method is applied to the multiscale topology optimization that progresses design resolution levels dyadically from low to high levels. By this application, we show the potential of the multiscale method and the possibility of developing a fully integrated analysis and topology design optimization in the multiscale multiresolution setting.