The use of 2D enriched elements with bubble functions for finite element analysis

In this paper, the concept that adds the interior nodes of the Lagrange elements to the serendipity elements is described and a family of enriched elements is presented to improve the accuracy of finite element analysis. By the use of the static condensation technique at the element level, the extra computation time in using these elements can be ignored. Plane stress problems are used as examples in this paper. The numerical results show that these enriched elements are more accurate than the traditional serendipity elements. The convergence rate of the proposed elements is the same as the traditional serendipity elements. The error norm of the second and third order proposed elements can be reduced from 40% to 60% when compared with the use of the traditional serendipity elements. In the numerical examples, the use of the second and third order proposed elements not only give an improvement in element accuracy but also save computation time, when the precondition conjugate gradient method is used to solve the system of equations. The saving of computation time is due to the decrease of iteration number in iteration method.