Shape design sensitivity analysis in elasticity using the boundary element method

Abstract

This paper deals with sensitivity analysis of the different functionals appearing in optimum shape design in elasticity using boundary element method (BEM). First, a general review concerning sensitivity analysis of the most usual functionals in elasticity is presented, based on the continuum approach. The accuracy in sensitivity analysis depends on the accuracy in evaluating strains and stresses on the boundary. A general procedure for strain calculation based upon some results of differential geometry of surfaces is shown. Another essential aspect in sensitivity analysis is the definition of the design velocity on the boundary, which defines the change in the geometry of the elastic solid. A computational treatment independent of the design variables used is presented, defining nodal values of the design velocity and taking advantage of the boundary element approximation. Finally, the feasibility and accuracy of the proposed procedures are assessed through several example problems.