Accuracy of semi-analytic sensitivity analysis

Abstract

The integration of FEM, CAD and optimization is becoming an important area of research in the field of computational mechanics. Implementing the integration, one of the main difficulties encountered is to perform a sensitivity analysis for the structural response with respect to any design variable. It has been shown in the literature that the semi-analytic sensitivity analysis method provides an ideal tool to solve this difficulty. Nevertheless, the accuracy of the method remains to be studied. The present paper addresses the accuracy problem. Structures composed of beam elements, 3-node constant plane stress triangular elements, 4-node plane stress isoparametric elements, 8-node plane stress isoparametric elements, 8-node solid elements, and 3-node triangular bending elements are studied. It is found that for beam and plate elements, whose nodal degrees of freedom have non-uniform dimensions, the error caused by the semi-analytic sensitivity analysis method is almost proportional to the square of the number of elements. An alternative forward-backward finite difference scheme solves the problem nicely. For the other elements, the accuracy of the semi-analytic sensitivity analysis is acceptable. The results obtained in the present paper justify the usage of the semi-analytic sensitivity analysis method.