A Large Deformation Plate Element for Multibody Applications

Abstract

095 REPORT DOCUMENTATION PAGEThe views, opinions and/or findings contained in this report are those of the author(s) and should not be construed as an official Department of the Army position, policy or decision, unless so designated by other documentation. a. DISTRIBUTION / AVAILABILITY STATEMENTApproved for public release; distribution unlimited. 12 b. DISTRIBUTION CODE 13. ABSTRACT l In this investigation, a method for the finite rotation and large deformation analysis of plates is presented. The method, which is based on the absolute nodal coordinate formulation, leads to an isoparametric plate element capable of representing exact rigid body motion. In this method, continuity conditions on all the displacement gradients are imposed. Therefore, non-smoothness of the plate mid-surface at the nodal points is avoided. Unlike other existing finite element formulations that lead to a highly nonlinear inertial forces for three-dimensional elements, the proposed formulation leads to a constant mass matrix, and as a result, the centrifugal and Coriolis forces are identically equal to zero. Furthermore, the method relaxes some of the assumptions used in the classical and Mindlin plate theories. By using a general continuum mechanics approach, a relatively simple expression for the elastic forces is obtained. By developing such an isoparametric plate element, the development of three-dimensional shell elements becomes straightforward. Numerical results are presented in order to demonstrate the use of the proposed method in the large rotating and deformation analysis of plates. ABSTRACTIn this investigation, a method for the finite rotation and large deformation analysis of plates is presented. The method, which is based on the absolute nodal coordinate formulation, leads to an isoparametric plate element capable of representing exact rigid body motion. In this method, continuity conditions on all the displacement gradients are imposed. Therefore, non-smoothness of the plate mid-surface at the nodal points is avoided. Unlike other existing finite element formulations that lead to a highly nonlinear inertial forces for three-dimensional elements, the proposed formulation leads to a constant mass matrix, and as a result, the centrifugal and Coriolis forces are identically equal to zero. Furthermore, the method relaxes some of the assumptions used in the classical and Mindlin plate theories. By using a general continuum mechanics approach, a relatively simple expression for the elastic forces is obtained. By developing such an isoparametric plate element, the development of three-dimensional shell elements becomes straightforward. Numerical results are presented in order to demonstrate the use of the proposed method in the large rotating and deformation analysis of plates.

Research status and prospect of plate elements in absolute nodal coordinate formulation

“…Subsequently, in a report by Mikkola and Shabana, 20 a fully parameterized plate element (No. 4443) was proposed, and the node definition and shape function of this fully parameterized quadrilateral plate element were systematically given.…”

Multibody System Modeling of Leaf Springs

“…Here, I is a 3 8 3 identity matrix, J is the matrix of the displacement gradients, and J 0 is the Jacobian matrix of the element in the reference configuration. Both the matrix of displacement gradients and the Jacobian matrix can be simply evaluated using the absolute nodal coordinate formulation as described in Mikkola and Shabana (2000). Equation ( 55) leads to a general expression for the elastic forces that takes into account all geometric nonlinearities and the effect of shear deformation.…”