ACCURACY IMPROVEMENT OF SEMI-ANALYTIC AL DESIGN SENSITIVITIES BY LAPLACIAN SMOOTHING

Sensitivity analysis by means of the semianalytical method often results in severe accuracy problems for shape design variables. It turns out that the method used to generate the perturbed meshes has an important effect on the accuracy of the design sensitivities. In the present paper it will be shown that the accuracy of the design sensitivities can be improved by using Laplacian smoothing instead of a boundary node approach. When Laplacian smoothing is used design perturbations are distributed more equally over the finite element mesh. Implementation of the method is easy in an existing preprocessor. The proposed method is applied to semi-analytic al and refined semi-analytical design sensitivities. In both cases more accurate design sensitivities are obtained. The accuracy of the design sensitivities has been studied by means of an analytical beam example and several numerical examples.