MESH REFINEMENT FOR SHAPE OPTIMIZATION

The numerical solution of shape optimization problems is considered. T he algorithm of successive optimization based on finite element techni ques and design sensitivity analysis is applied. Mesh refinement is us ed to improve the quality of finite element analysis and the computed numerical solution. The norm of the variation of the Lagrange augmente d functional with respect to boundary variation (residuals in necessar y optimality conditions) is taken as an a posteriori error estimator f or optimality conditions and the Zienkiewicz-Zhu error estimator is us ed to improve the quality of structural analysis. The examples present ed show meaningful effects obtained by means of mesh refinement with a new error estimator.