DYNAMIC ANALYSIS OF PLANAR FLEXIBLE MECHANISMS BY COROTATIONAL FORMULATION

Abstract

A co-rotational formulation of beam element and numerical procedure for the dynamic analysis of planar flexible mechanisms is presented. The nodal coordinates, velocities, accelerations, incremental displacements and rotations, and equations of motion of the system are defined in terms of fixed global coordinates, while the total strains in the beam element are measured in an element coordinate system which rotates and translates with the element but does not deform with the element. The element equations are constructed using the small deflection beam theory with the inclusion of the effect of axial force first in the element coordinate system, and then transformed to the global coordinate system using a standard procedure. In the proposed approach the resulting equations of motion are the same as those typically arising in nonlinear structural dynamics. An incremental-iterative method based on the Newmark direct integration method and the Newton-Raphson method is employed here for numerical studies. Numerical examples are presented to demonstrate the accuracy and efficiency of the present method.