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

Abstract

This paper describes a numerical analysis method for multiobjective shape optimization problems of linear elastic structures. For an example, we treat a multiloading mean compliance minimization problem with a volume constraint. The presented method is based on the traction method that was proposed as a solution to the domain optimization problems by one of the authors. The traction method is implemented to analyze the speed field, which represents the domain variation, with regard to the deformation field of the linear elastic continuum formed in the objective domain applying the force in proportion to the shape gradient function. To scalarize the multiobjective functionals we employ the weighted lp-norm method with four types of norms. The shape gradient functions for each scalarized objective functional are obtained using the Lagrange multiplier method. For the numerical analyses we used a general-purpose finite-element code. Numerical results to a multiply connected plate problem and to a solid structure problem under the multiloading conditions show the validity of the present method to obtain practical Pareto solutions.