Computational efficiency aspects in boundary element based structural shape optimization

The paper examines the use of boundary element methods in optimal shape synthesis from the standpoint of an integrated formulation. A set of linear equations obtained from the boundary element analysis are treated as equality constraints in the mathematical programming optimization problem. Requirements of computational efficiency mandate the inclusion of grid refinement and grid adaptation in boundary element analysis, which in the present formulation is treated as a nested optimization problem. Two strategies for the solution of this optimization problem, one based on a variational approach and another employing non-linear programming methods, are presented in the paper. The use of non-linear programming methods in grid definition allows greater flexibility in selecting the form and relative importance of criteria employed for grid adaptation and refinement.