Modelling Convergence of Finite Element Analysis of Cantilever Beam

Abstract

Convergence studies are carried out by investigating the convergence of numerical results as the number of elements is increased. If convergence is not obtained, the engineer using the finite element method has absolutely no indication whether the results are indicative of a meaningful approximation to the correct solution. There are two major methods of mesh refinement; h-refinement and prefinement.

The cantilever beam plate was modelled using Abaqus/CAE 6.12-1, a finite element analysis tool. The geometry consists of a 300 x 100 mm beam section, spanning 3m and fixed at one end. A load of 1kN was applied at the free end. Also the model was meshed using 2D plane stress linear and quadratic quadrilaterals elements (CPS4R and CPS8), triangular elements (CPS3 and CPS6) and refined. For the linear quadrilateral element, a total of 20, 40,160 and 2560 elements were used for the coarse, medium, fine and very fine mesh respectively. Total numbers of 33, 63, 205 and 2737 nodes were generated accordingly.

The maximum bending stresses and shear stresses occurred at the fixed end. Exact stress and maximum displacement value at the mid-top fibre and free end of the beam was 100 N/mm² and-19.5122 mm respectively. Simulated results at these points were analysed using the four element types at different mesh refinement levels. The study shows that linear FE converges slower compared to quadratic elements. Also a finer mesh is required to predict accurate stresses than is needed to calculate accurate displacements.

Keywords: Cantilever beam, finite element, Abaqus, convergence, stress, strain