Systematic shape parameterization in design optimization

The shape design problem requires a parameterization of the shape design space to be amenable to numerical solution. Existing shape design parameterizations entail the hazards of shape design space bias and/or difficulty in maintaining shape integrity. Here, we address the problem of systematically defining a finite dimensional space of allowable shapes which insures the physical integrity of the optimal shape and does not bias the design space. The new shape definition is based on a geometric abstraction - the skeleton- which forms a canonical representation of the shape. We demonstrate the efficacy of this shape representation on a model problem defined as maximizing the moment of inertia of a shape of constant volume.