Comparing beam torsion data from Analytical, FEM and ABACUS methods

Finite element method and various other numeric methods are being used in many applications these days, so it is important to fully understand these methods and their error ranges for better usages of these methods. In this paper a simple beam torsion problem is solved by using three methods: analytical, finite element method (FEM), and ABACUS software. Since the finite element method is not efficient without the help of computers, a MATLAB code has been developed to perform required calculations. Every approach is partially described and used to solve our specific problem then the results of all three methods are compared and error percentages are provided taking the analytical method as a base for comparison. Eventually it is found that our FEM approach has a 17-20% error and the ABACUS software solution has an 8-10% error.