The Sensitivity Analysis And Shape Optimization Of Elastic Problems Using Boundary Element Method

The paper studies the application of boundary element method in shape optimization of elastic problems. The main achievements includes:1. A unified algorithm of multi-domain boundary element equation is built for planar and axisymmetric elasticity. For more accurate determination of the displacements and stresses at the points on the boundary or near the boundary, a method of introducing particular solutions to determine singular oralmost singular integrals has been developed.2. A general statement of boundary value problem and its variational formulation for sensitivity is presented. By taking material derivatives of variational identity of elasticity, the variational identity for sensitivity has been obtained.3. The algorithms developed in structural analysis, such as, multi-domain boundary element method, the determination of singular or almost singular integrals, have been extended to sensitivity analysis. The property that the order of talcing derivatives and making discretization is reversible in sensitivity analysis has been proved.4. A kind of adaptive boundary element mesh generation scheme is developed.5. Computer programs for analysis and sensitivity analysis of planar elasticity by boundary element method are made, and several computational examples have been performed. By combination usage of recursive quadratic programming and boundary element method, the optimal shapes of a polygon plate in tension, a bending cantilever, a gravity dam and a hollow gravity dam under hydrostatic and gravitational loads have been obtained.