A modified corotational framework for triangular shell elements

The corotational framework for triangular shell elements has been presented by different authors (see the Introduction). The purpose of this paper is to introduce three modifications in this approach. The first one is a simplified definition of the local rotations. The second one is a reduction of the number of local degrees of freedom from 18 to 15. The third and principal one concerns the parameterisation of the global finite rotations. A new approach based on Euler parameters (quaternion) is proposed. In particular, it is shown that only three parameters are required. The purpose of these three modifications is to obtain a formulation which gives the same numerical results but which is computationally more efficient than the original one. This aspect is illustrated in several numerical examples.