Geometrically exact nonlinear extended-Reissner/Mindlin Shells: Fundamentals, finite element formulation, elasticity

Extended Reissner/Mindlin shell kinematics are used to develop an exact shell that makes no further approximations on the deformation or strain. The formulation is fully tensorial. A three-dimensional isoparametric element is used as the reference configuration. The FE approximation introduces nodes on the mid-surface of the isoparametric element, with the thickness having a separately defined interpolation. The variational formulation is based on the nominal stress tensor. Isotropic linear and nonlinear elastic shells are constructed that use p-type interpolation along the director. The formulation is exact, resulting in nonlinear elements showing better characteristics in comparison to other such elements.