Three-dimensional shape design optimization of holes and cavities using the boundary element method

Three-dimensional shape design optimization of holes and cavities under linear elastostatic conditions is presented. The shape optimization technique used is the normal movement approach, whose use has previously been confined to two dimensions, and the technique of stress analysis employed is the boundary element method (BEM) using quadratic surface elements. The normal movement approach is founded on the idea that the optimum boundary shape can be determined by moving points that define the boundary in directions that lie along the local normals to the boundary surface at the points concerned. The amount of movement at each iteration of the process is determined by the local level of stress in the surface. The main advantage of the approach is that no design sensitivity analysis is required, which is computationally more efficient, and many more design variables defining the geometry can be used. The BEM for stress analysis is particularly appropriate because it simplifies the mesh regeneration that is generally required during the optimization process. The quality of this re-meshing is crucial to the success of the technique. The overall method is applied to problems of holes and cavities in engineering components and structures.