Effect of Number of Node on the Deflection of a Simply Supported Beam Using Finite Element Analysis

Abstract

The effect of the numbers of nodes for a simply supported beam is considered under a pointed load (e.g., vehicle moving on a bridge) using the finite element method and Lagrange polynomial shape function. The deflection problem of the beam was solved analytically and compared with that of the finite element method. The number of nodes considers is 3, 5, 10, 15, 20, and 30. The results of the analytical and finite element method show a very close agreement and have an identical profile. The error became more stable as the numbers of nodes increase, as shown on the graph, that from 30 numbers of nodes the error is very minimal and stable. This error exhibit an exponential function for the deflection of a simply supported beam.