A Geometric Representation Scheme Suitable for Shape Optimization* †

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Abstract
A geometric representation scheme that utilizes the natural design variable concept is outlined. A base configuration with distinct topological features is created. This configuration is then deformed to define components with similar topologies and different geometries. The values of the deforming loads are the geometric entities used in shape representation. The representation can be used for various geometric design studies. In this paper, it is demonstrated 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. To perform the shape change analysis, a total-Lagrangian approach is used to reduce computational requirements, nonlinear multi-point constraints are used to retain geometric features, and thermal loads are applied to locally deform the structure. Two examples 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.

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