A Geometry-Based Parameterization Method for Shape Design of Elastic Solids*

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Abstract
One of the major difficulties in structural shape optimal design is to create a design model by parameterizing a geometric model. Shape design parameterization is more complicated and difficult to handle than sizing design parameterization. First, the optimum shape is highly dependent on the design parameterization selected. An inappropriate design parameterization may result in an impractical design. On the other hand, changing the geometric shape of the design model to reflect successive changes in design parameters is a tedious, complicated, and inefficient process. Manual updates of geometric shape and finite element meshes are quite impractical. In this paper, a shape design parameterization method that is built on the geometric modeler PATRAN is presented. Using this method, a number of geometric entities that represent structural design boundaries are parameterized, and a design parameter linking process can be performed to create geometric features from geometric entities. To support the proposed method in structural shape design, a unified velocity computation method using geometric parametric mapping and an elliptic equation solver is developed for shape design sensitivity computation. The design parameterization and associated velocity Held computation methods are general enough to handle a broad range of engineering applications. Finally, automatic finite element mesh and geometric shape update methods are presented, which can be used to easily perform design changes.

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