Effect of member initial curvature on a flexible mechanism response

Abstract

A co-rotational finite element formulation of slender curved beam element is presented to investigate the effect of member initial curvature on the dynamic behaviour of planar flexible mechanisms. The Euler-Bernoulli hypothesis and the initial curvature are properly considered for the kinematics of curved beam. The nodal co-ordinates, incremental displacements and rotations, velocities, accelerations and the equations of motion of the system are defined in terms of a fixed global co-ordinate system, while the total strains in the beam element are measured in element co-ordinates which are constructed at the current configuration of the beam element. The element equations are constructed first in the element co-ordinate system and then transformed to the global co-ordinate system by using standard procedures. Both the deformation nodal forces and the inertia nodal forces of the beam element are systematically derived by consistent linearization of the non-linear beam theory in the element co-ordinates. An incremental-iterative method based on the Newmark direct integration method and the Newton-Raphson method is employed here for the solution of the non-linear dynamic equilibrium equations. Numerical examples are presented to demonstrate the effectiveness of the proposed element and to investigate the effect of the initial curvature on the dynamic response of the flexible mechanisms. (C) 1996 Academic Press Limited