The application of geometrically exact shell elements to B-spline surfaces

Abstract

In the present study, we propose a framework that directly links a general tensor-based geometrically exact shell finite element to B-spline surface geometric modeling. Four-node and 9-node assumed strain elements based on the partial mixed Hellinger–Reissner variational functional and a 4-node assumed natural strain (ANS) element are implemented in B-spline surface representation. Bubble functions are included in the basis functions to improve the performance of the developed elements. The bi-cubic rectangular B-spline tensor patch is employed to generate the general form of parameterized shell surfaces. By using the B-spline function, the present general tensor-based shell elements can handle the arbitrary geometry of the free-form surfaces. Numerical results demonstrate the efficient linkage concept between surface modeling of computer aided geometric design (CAGD) and finite element shell analysis in static and dynamic examples.