| Summary: | 碩士 === 國立交通大學 === 機械工程系 === 91 === A simple and effective consistent co-rotational total Lagrangian finite element formulation and a numerical procedure are proposed to investigate the geometric nonlinear dynamic response of sliding beam. To exactly predict the dynamic response of the sliding beam, the total length of the sliding beam is considered. The motion of the beam element is not restrained when it is outside the prismatic joint. The lateral motion of the beam is fully restrained when it is inside the prismatic joint. The ordinary beam element is used here when it is inside or outside the prismatic joint. A transition beam element developed here when it is partially housed inside the prismatic joint. The total undeformed length of the transition element is constant. However, the undeformed length housed inside the prismatic joint is time dependent. The kinematics, deformations, and equations of motion of the transition beam element are defined in terms of two element coordinate systems constructed at the current configuration of the deformed beam element. The principle of virtual work, d’Alembert principle and the consistent second order linearization of the fully geometrically nonlinear beam theory are used to derive the deformation nodal force and inertia nodal force of the beam element. In element nodal forces, all coupling between bending and stretching deformations of the beam element is considered. An incremental-iterative method based on the Newmark direct integration method and the Newton-Raphson method is employed for the solution of nonlinear dynamic equilibrium equations. Numerical examples are presented to demonstrate the accuracy and efficiency of the proposed method.
|
|---|
