Numerical study of some approaches to shape design sensitivity analysis using boundary elements

Abstract

A numerical study is made of analytical differentiation (AD) and finite difference (FD) approaches to the computation of sensitivity derivatives required in shape design optimization problems. Based on the boundary element method for linear elastostatics, numerical solutions for response and sensitivity analysis are illustrated for the AD technique and the FD schemes with different step sizes. By solving the problem of an annular disc under internal pressure (for which analytical solutions are available), an indication of the absolute level of accuracy achievable by the FD procedure can be obtained. As there are advantages in using the FD technique for shape optimization, it is desirable to check its accuracy and effectiveness compared to the AD approach. An optimization problem based on the annular disc is then formulated and solved using the various analytical, AD and FD sensitivity values to show how the differing accuracies of the derivatives will affect the efficiency and performance of the optimization process, and whether the FD values used are sufficiently accurate for converging upon the correct optimum solution.