Shape Design by Integrating Shape Optimization with Topology Optimization for Multiobjective Structures. (An Approach Using Homogenization Method-and Traction Method).

Abstract

The purpose of this study is to present an optimization method to create multiobjective structures by integrating shape optimization with topology optimization. The topology optimization method used here is based on the homogenization method proposed by Bendsoe and Kikuchi. As the shape optimization method, we used the traction method proposed by Azegami. By integrating these two methods, the optimal shape with smooth boundaries considering optimal topology can be obtained. A multiobjective mean compliance minimization problem of a linear elastic structure is formulated for both topology and shape optimization using the Lagrangian multipliers and the weighted Tchebycheff norm. The integrated optimization system is developed using a general-purpose FEM code to create multiply-connected Pareto optimal shapes. An application example of an automotive component in addition to a simple example is presented to confirm the validity and the practical utility of this integration method and the system.