Shell Finite Element Analysis with Exact Geometric Quantities from NURBS Surface

Abstract

‡In this study a framework that directly links a general tensor -based shell finite element to NURBS(Non -Uniform Rational B -Spline ) geometric modeling is implemented. The geometrically exact shell element for analysis has been developed and the accuracy and efficiency were demonstrated in our previous work s. Generally, in the CAD systems, surfaces are represented by the NURBS which is the industry standard tool for the representation and design of surface geometry. Here, NURBS blending functions are composed by two parameters in the parametric domain. A general tensor -based shell element also has a two -parameter representation in the surfaces, and all the computations of geometric quantities which are needed in shell finite element analysis such as normal vector and derivatives of the surface at a specific point on the surface can be performed in local surface patch. Because these quan tities are calculated directly from the NURBS equations without any interpolation of nodal values, the geometry errors can be dramatically decreased. Naturally, the geometric modeling based on NURBS technology can be directly linked to the shell analysis. A t rimmed surface which is often encountered during modeling process in the CAD systems is also presented in this study. The performance of the developed geometrically exact shell element integrated with the exact geometric representations by the NURBS eq uation is compared to those of the previous reported shell elements in the selected benchmark problems. In addition we developed six -node triangular shell element for automatic mesh generation of complex shape surfaces for more practical application.