Finite Element Method for Large Deflection Analysis of Free Horizontally Sliding Supported Beam

Abstract

This research presents a large deflection analysis of beams with moveable support subjected to self-weight and compression at beam tip. A mathematical model of beams has been developed based on virtual work principle. The study used a non-linear Finite Element Method (FEM) combined with the Newton-Raphson iterative method to obtain numerical solutions. In addition, a system of first order non-linear differential equations, which is obtained by considering the force and moment equilibrium of the beam segment is used for calculation the internal force of the beam. The computer program for implementing the finite element algorithm is developed by Fortran 90. The numerical verification revealed that the result obtained from the finite element method were consistent with the result from the shooting method. The result also showed that the beam self-weight and the compressive force acting on the support cause the support movement, which induce large deflection, and instability of the beam.