Discrete-Mindlin finite element for nonlinear geometrical analysis of shell structures

A finite degenerated shell element based on Mindlin discrete approach is presented for nonlinear geometric analysis in large displacements and small deformations. The element, called DMQS (Discrete Mindlin Quadrilateral Shell) with four-nodes and 6 dof/node, includes a constant transverse displacement and rich quadratic rotations. Since the global kinematics of shell is dominated by a rigid body rotation and motion involving small displacements and rotations, an Updated Lagrangian Formulation at each Iteration is used. The tangent stiffness matrix has been treated as a sum of two parts: linear part related to the degenerated shell model (DMQS) as well as the initial stress part associated with the well-known membrane standard element. Some standard nonlinear benchmarks are presented herein, where very good results have been obtained and show better accuracy than similar quadrilateral elements.