Multiobjective Shape Optimization of Linear Elastic Structures Considering Multiple Loading Conditions : Dealing with Mean Compliance Minimization problems

Abstract

We describe numerical analysis methods for multiobjective shape optimization of linear elastic structures. As an example, we consider a multiloading mean compliance minimization problem with a volume constraint. The methods presented here are based on the traction method, in which the speed field representing the domain variation is analyzed. A weighted lp-norm method with four types of norm is employed to scalarize the multiobjective functionals. The shape gradient functions for each scalarized objective functional are obtained using the Lagrange multiplier method. A general-purpose finite element code is used to perform the numerical analyses. Numerical analysis results for a multiply connected plate problem and a solid structure problem under multiloading conditions are presented to demonstrate the validity of the traction method in obtaining Pareto optimal solutions.