Abstract
This paper presents a geometry based approach for coupling CAD with finite element methods. Non uniform rational B-splines (NURBs), known from computer aided geometric design, are used to describe the shape of a structure. NURB curves and surfaces and Gordon surfaces defined by NURB curves are introduced for design description. These geometries are used directly for the mapping of finite elements and for parameterization for the optimization of the structural shape. The cross-sectional torsion problem is employed to demonstrate the proposed mapping techniques for finite elements. Solid and thin walled cross-sectional shapes are treated differently. Hierarchical shape functions will be used for the approximation of the warping function to solve the torsion problem. The proposed mapping techniques are applied to shape optimization. A sensitivity analysis using NURB defined geometries is developed. Two optimization solutions are given to complete the presentation.
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