Multiscale Multiresolution Topology Optimization in General Design Domains Using a Subdivision Method

摘要

The purpose of this paper is to extend the multiscale multiresolution topology optimization [1] for arbitrary-shaped design domains including two-dimensional curved surfaces and multiply-connected regions. To achieve this goal, we propose to employ a subdivision method. If the geometric information of a design domain is given by CAD data or randomly sampled data, a lowest-resolution model, call the control model, is generated. Then by means of the multiscale subdivision scheme commonly employed in the computer graphics community, the control mesh is repeatedly subdivided until a desired resolution level is reached. In the present topology design optimization problem, not only the mesh but also the design variables must be decomposed in multiscales. To this end, the geometry data are subdivided by interpolation wavelets, but the design variables by the Haar wavelets. In this work, the present strategy is illustrated in a design domain discretized by arbitrarily-shaped quadrilateral finite elements, though it is equally applied for a design domain discretized by triangular finite elements. Specific numerical examples include optimization in a shell geometry and a two-dimensional plane region.