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. First, a case study for a plate with fillets under compression verified that the desired velocity field based on stress nonuniformity was successfully expressed by the discretized domain variation using voxel finite elements. Second, case studies for cantilevers subjected to a concentrated and 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.