| In this study, applications of the boundary element method for two- and three-dimensional structural shape optimization are presented. The displacements and stresses of the structure are computed using the boundary element method and substructuring analysis. The boundary element method provides the capability and advantages of modeling the varied shape of the boundaries during the optimization process. The substructuring analysis of the boundary element method produces better accuracy of the solution and reduces the computer time. The corresponding nonlinear programming problem for the optimization is solved by the generalized reduced gradient method (OPT program, Gabriele, Ragsdell, 1976). The Bezier and B-spline curves or surfaces are introduced to describe the shape of the design. The control points on these curves or surfaces are considered as design variables. The number of design variables is smaller than the number of the nodal points of the boundary element mesh. The optimal design objective is to minimize weight or peak stress of the structural element and to determine an optimum shape for the structure, subject to geometrical and stress constraints. The optimization method has been successfully applied to the structural shape optimization of plain stress, plain strain and three-dimensional elasticity problems. |
