A nurbs finite element method for product shape design

Abstract

In a design of industrial product, its shape that influences the rigidity and vibratory characteristics as well as productivity is determined by trial-and-error-based experimentation or simulation. The NURBS representation is used widely in computer-aided design/computer-aided manufacturing (CAD/CAM) systems because it offers good capabilities for representation of sculptured surfaces, reduction of the amount of numerical control data, and control of the cutter pass and cutting speed. Thereby, it realizes a smooth surface and high efficiency of manufacturing. Therefore, once a finite element method based on the NURBS representation is established, we may integrate it into a comprehensive CAD/CAM/computer-aided engineering tool for product design. From that point of view, this study addresses the formulation of a finite shell element that perfectly forms the product shape represented by the NURBS surface. The NURBS surface, which is originally defined by a control point scheme, is represented by interpolating the nodal points on the surface. The function for this interpolation is used for the shape function. The explicit derivation of the shape function also allows formation of a mass matrix to solve dynamic problems. The method presented here is applied to several bending analyses of plates and shells to demonstrate the effectiveness and good accuracy of the method. Results suggest that this method offers a useful tool for product shape design.

Keywords:

• Product design
• Computer-aided design/computer-aided manufacturing
• Computer-aided engineering