A Level Set-Based Topology Optimization Method Using the Boundary Element Method in Three Dimension

Abstract

Level set-based shape and topology optimization methods get attention as a new type of structural optimization. However, the structural optimization methods cannot treat explicitly a design dependent load, such as pressure load, because the finite elements for solving the equilibrium equation are fixed during the optimization process. On the other hand, Boundary Element Method (BEM) is only required boundary elements to solve a boundary value problem. Therefore, some complicated numerical techniques for re-meshing process are not required. This paper presents a level set-based topology optimization method using the BEM for three-dimensional problems. First, we briefly discuss BEM for three-dimensional elastic problems and the topology optimization method using the level set method and the Tikhonov regularization method. Second, the minimum mean compliance problem with volume constraint is formulated. Next, an optimization algorithm and numerical implementation for generating boundary elements based on the level set boundary expressions are shown. Finally, we show some three-dimensional numerical examples including design dependent load problem and discuss effectiveness and adequacy of proposed method.