A simple nonlinear triangular plate element and strategies of computation for nonlinear analysis

According to the rigid body rule, for a solid member subjected to rigid bod y rotations, the initial forces acting on the member Chat form an equilibra ting set must rotate following the rigid body rotations, while remaining un changed in magnitude. Such a rule is physically intuitive and is employed i n this paper to derive an approximate geometric stiffness matrix for a thre e-node triangular plate element (TPE) containing three translational and th ree rotational degrees of freedom (DOFs) at each node. An element such as t his is attractive, since it can be easily used along with the 12-DOF beam e lement to simulate various plate and shell assemblies. Another advantage wi th the geometric stiffness matrix derived is that it can be explicitly give n, which renders numerical integrations unnecessary. Finally, the element a nd procedure proposed are demonstrated to be robust in that solutions of go od 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 refine ment. (C) 1999 Elsevier Science S.A. All rights reserved.