New Formula of Geometrically Exact Shell Element Undergoing Large Deformation and Finite Rotation

The paper develops a new geometrically exact shell element that allows large deformation and finite rotation. The new element is based on the Reissner–Mindlin shell theory, where the shell is considered as a surface with oriented directors. Accordingly, an incremental description for rotational fields of oriented directors is given. The description takes advantage of two rotational variables of the pseudo-rotation vector to avoid the vectorial parameterizations of rotation tensor. With the application of Mixed Interpolation of Tensorial Components (MITC), the shell is shear-locking free, features second-order accuracy, and contains nine nodes. Each node has five degrees of freedom, three for translations and two for rotations. Finally, numerical simulations show these new shell elements have the ability of dealing with large deformations and finite rotations with high efficiency and good accuracy.