Shape optimization based on traction method using Voxel-FEM

Abstract

Using a voxel finite element method that allows us to integrate modeling and analysis of a complicated three-dimensional structure, a new numerical method for shape optimization problem was proposed here based on the traction method. A minimization problem of stress nonuniformity in the domain was formulated for a three-dimensional linear elastic structure. In this method, a domain variation that was obtained as a velocity field from a shape gradient function was accomplished by removal and addition of the voxel elements on the domain surface. A case study for cantilevers subjected to uniformly distributed forces demonstrated that the minimization of the stress nonuniformity was achieved by changing the domain shape. In addition, a possibility of the topological change as well as shape change was suggested using the proposed method.