I³MS - Klinkel Seminar
Prof. Dr. Sven Klinkel - A Reissner-Mindlin Shell Formulation for Isogemetric Analysis Accounting for Large Rotations
Institute for Structural Mechanics, RWTH Aachen University
The work is concerned with the interpolation of the director vector in the context of an isogeometric shell formulation. In the frame of a NURBS-based formulation the director vector as well as the nodal coordinate system is defined at the control points. The kinematic description of shells necessitates the director vector at the shell reference surface. This is realized by an interpolation and leads to an approximation of the director. The approximated director violates basic kinematic assumptions in the shell theory. In this contribution a method to overcome this problem is presented. A geometrically exact Reissner-Mindlin shell formulation is provided. The nodal degrees of freedom are three displacements and two rotations. The accuracy of the director is improved to be as close as possible to the exact directions in all integration points. This is achieved by a manipulation of the director at the control points. Due to the loss of orthonormality the variation of the director vector has to be altered. The isogeometric implementation is tested with standard benchmark problems. The results show a clear improvement for NURBS of higher order and monotone convergence of deformations.