Structural topology optimization with design-dependent pressure loads

Abstract

One way to solve topology optimization of continuum structures under design-dependent pressure loads is to recover the loading surface at each step of the minimization process. During the topology evolution, the intermediate topologies obtained by using the SIMP (Solid Isotropic Material with Penalization) method actually can be regarded as gray scale images, for which the paper proposes a new material boundary identification scheme based on image segmentation technique. The Distance Regularized Level Set Evolution (DRLSE) method proposed by Li et al., IEEE Trans Image Process 19(12):3243---3254 (2010) is utilized to detect the image edge. Then the pressure boundary is represented as the zero level contour of a level set function (LSF). Inheriting the merits of the level set method, the current scheme can handle the topological change of the pressure boundary efficiently and be easily extended to the three-dimensional problems. In addition, the scheme is more stable compared with the conventional loading surface searching methods since it works well for the intermediate topologies with local scattered densities. A new optimization framework is also proposed to avoid the load sensitivity analysis. Four numerical examples are presented to show the validity and advantages of the proposed scheme.