Performance of higher order finite elements

Abstract

This study is focused on the evaluation of the performance of the higher order finite elements for the solution of basic and complex problems. Performances of higher order finite elements are compared with those of the regular order elements. Results of this comparison revealed the efficiency and accuracy of higher order finite elements. Following a brief discussion of the finite element method; isoparametric elements, higher order elements, and shape functions are explained. For the purpose of illustration, four different case studies are investigated in a comparative fashion.Firstly, a cantilever deep beam under a concentrated force at the tip is selected as a plane stress problem and is analyzed using five different types of finite elements and in each case the mesh size is gradually decreased. Second problem consists of a circular plate, which is analyzed using two different types of regular and higher order finite elements. The third and the fourth plate bending problems are the fixed boundary square plates, under uniform and central point loads, modeled by the same four different types of finite elements. The analyses of all these four problems are handled by the LUSAS package program. The purpose of utilizing higher order finite elements is to obtain as accurate solutions as possible, with as little number of degrees of freedom as possible. It is demonstrated in all four case studies that the accuracies of higher order finite element were much superior than those of the regular finite elements.