A level set based method for the optimization of 3D structures with the extrusion constraint

Abstract

An extrudable structure is formed via the extrusion process in which materials are squeezed through a die with pre-specified shape. Then, we obtain the long and straight metal parts with the fixed cross sections. The key of implementing the extrusion process is that the cross sections are perpendicular to the specified direction should be kept constant. To this end, this paper proposes a level set based optimization method for 3D structures with the extrusion constraint. The compactly supported radial basis functions (CS-RBFs) are introduced to convert the conventional level set method to a parametric one. The cross section projection strategy is applied to reduce the design variables and satisfy the extrusion constraint. Several 3D numerical examples are also provided.