Abstract
Abstract This paper presents a comparison of geometric modeling techniques and their applicability to structural shape optimization. A method of shape definition based on intrinsic geometric quantities is then outlined. Explicit knowledge of curvature and arc length allow for a quantitative assessment of the compatibility of analysis model with the design model when using finite elements to determine structural response quantities. The compatibility condition is formalized by controlling finite element idealization error and is incorporated into the shape optimization model as simple bounds on the curvature design variables. Several examples of shape optimization problems are solved using sequential quadratic programming which proves to be an effective tool for maintaining the geometric equality constraints that arise from intrinsically defined curves.
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