Application of Composite Plate Theory and the Finite Element Method to the Dynamics and Stress Analysis of Spatial Flexible Mechanical Systems

Abstract

This investigation concerns itself with the dynamic and stress analysis of thin, laminated composite plates consisting of layers of orthotropic laminae. It is assumed that the bonds between the laminae are infinitesimally thin and shear nondeformable. The finite element formulation presented is sufficiently general to accept an arbitrary number of layers and an arbitrary number of orthotropic material property sets. In the dynamic formulation presented, the laminae is assumed to undergo large arbitrary rigid body displacements and small elastic deformations. The nodal shape functions of the laminae are assumed to have rigid body modes that need to describe only large rigid body translations. Using the expressions for the kinetic and strain energies, the lamina mass and stiffness matrices are identified. The nonlinear mass matrix of the lamina is expressed in terms of a set of invariants that depend on the assumed displacement field. By summing the laminae kinetic and strain energies, the body mass and stiffness matrices are identified. It is shown that the body invariants can be expressed explicitly in terms of the invariants of its laminae. Numerical examples of a spatial RSSR mechanism are presented in order to demonstrate the use of the present formulation.