T‐spline finite element method for the analysis of shell structures

A T‐spline surface is a nonuniform rational B‐spline (NURBS) surface with T‐junctions, and is defined by a control grid called T‐mesh. The T‐mesh is similar to a NURBS control mesh except that in a T‐mesh, a row or column of control points is allowed to terminate in the inner parametric space. This property of T‐splines makes local refinement possible. In the present study, shell formulation based on the T‐spline finite element method (FEM) is presented. Shell formulation based on NURBS or T‐splines has fundamental limitations because rotational DOFs, which are necessary in the shell formulation, cannot be defined on control points. In this study, the simple mapping scheme, in which every control point is mapped into one geometric point on the surface, is employed to eliminate the limitations. Using this mapping scheme, T‐spline FEM can be easily extended to the analysis of shells. The proposed shell formulation is verified through various benchmarking problems. This study is a part of the efforts by the authors for the integration of CAD–CAE processes. Copyright © 2009 John Wiley & Sons, Ltd.