Three-dimensional shape optimization with variational geometry

The unification of computer aided design (CAD) and the finite element method (FEM) has greatly enhanced the engineer's ability to evaluate potential designs (Finnigan et al. 1989). However, analysis alone is not the answer to design, and thus shape optimization methods have become increasingly popular, particularly for structural problems (Yang et al. 1992; Botkin 1992). However, for shape optimization methods to be fully accepted by the engineering community they must first be integrated with CAD systems. To date, the difficulty of integrating CAD and shape optimization is the inability to relate the finite element nodal coordinates to the CAD solid model dimensions. Here, the critical link between these CAD and FEM data is developed within an industry standard feature-based modelling environment. A three-dimensional connecting rod model is optimized to exemplify the method.