The application of geometrically exact shell elements to B-spline surfaces
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 HellingerReissner 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.
shell finite element geometric modeling ans b-spline function