Direct Continuum Approach to Three‐Dimensional Sensitivity Analysis

Abstract

A direct continuum approach for shape‐design sensitivity of three‐dimensional elastic components is presented. By analyzing the shape‐design perturbation process, the shape change can be represented by a boundary loading on the design boundary. Therefore, the design sensitivity can be obtained by solving a boundary‐value problem, which has an identical geometry with the original problem, but with different loads. This approach does not involve the perturbed geometry, and is independent of the perturbation step. The total design sensitivity is obtained by using the material derivative concept. The direct continuum approach is implemented using the boundary‐element method, and the terms corresponding to the stress variation on the design boundary are expressed using the boundary information only. Three numerical examples are used to study the accuracy of the approach with respect to different boundary‐element meshes. The numerical results indicate that the direct continuum approach can provide good sensitivity results, and a proper mesh distribution on the design boundary is essential for sensitivity analysis.