Derivation of Non-dimensional Equation of Motion for Thin Plate in Absolute Nodal Coordinate Formulation

Abstract

The absolute nodal coordinate formulation was developed in the mid- 1990s to express large deformations and large rotations in flexible multi-body dynamics. It is a non-incremental finite-element procedure wherein the mass matrix is expressed as a constant while the stiffnessmatrix carries highly nonlinear features. The formulation for a thin plate can be developed on the basis of continuum or structural mechanics similar to that for a beam. Absolute nodal coordinate formulation necessarily uses the global slope vector, and this results in an increase in the degree of freedom. In this study, to reduce analysis time, the non-dimensional equation of motion of a thin plate is derived from the dimensional equation of motion using non-dimensional variables. An example of a thin cantilever plate is used to present the improved efficiency of analysis due to the non-dimensional equation of motion, and the simulations are shown with various numbers of elements. The non-dimensional equation of motion is thus verified by demonstrating the similarities of the solutions for both the dimensional and non-dimensional equations of motion.