According to the rigid body rule, for a solid member subjected to rigid body rotations, the initial forces acting on the member that form an equilibrating set must rotate following the rigid body rotations, while remaining unchanged in magnitude. Such a rule is physically intuitive and is employed in this paper to derive an approximate geometric stiffness matrix for a three-node triangular plate element (TPE) containing three translational and three rotational degrees of freedom (DOFs) at each node. An element such as this is attractive, since it can be easily used along with the 12-DOF beam element to simulate various plate and shell assemblies. Another advantage with the geometric stiffness matrix derived is that it can be explicitly given, which renders numerical integrations unnecessary. Finally, the element and procedure proposed are demonstrated to be robust in that solutions of good accuracy can always be obtained if a practically fine mesh has been used, and that the solutions converge rapidly to the exact one upon mesh refinement.
Computer methods in applied mechanics and engineering 178(3-4), pp.307-321