A geometric representation scheme suitable for shape optimization

A geometric representation scheme is outlined which utilizes the natural design variable concept. A base configuration with distinct topological features is created. This configuration is then deformed to define components with similar topology but different geometry. The values of the deforming loads are the geometric entities used in the shape representation. The representation can be used for all geometric design studies; it is demonstrated here for structural optimization. This technique can be used in parametric design studies, where the system response is defined as functions of geometric entities. It can also be used in shape optimization, where the geometric entities of an original design are modified to maximize performance and satisfy constraints. Two example problems are provided. A cantilever beam is elongated to meet new design specifications and then optimized to reduce volume and satisfy stress constraints. A similar optimization problem is presented for an automobile crankshaft section. The finite element method is used to perform the analyses.