Preliminary Results for an Isogeometric Shell

Piecewise continuous Lagrangian polynomials are the traditional interpolation functions used in the finite element method. They work well for many applications, but they also have shortcomings for many important applications. For example, in metal forming, the dies are designed using CAD programs and their geometry is defined in terms of NURBS (non-uniform rational B-splines) which can not be exactly replicated with a piecewise continuous Lagrangian polynomial in all cases. Therefore, there is a geometric incompatibility between the desired shape and the kinematic range of the blank modeled with traditional finite elements. This paper presents initial results for a shell element formulation based on NURBS.