Differential geometry management of higher order 2D boundary elements

Abstract

This paper addresses the use of higher order elements in boundary element analysis concerning accuracy and implementation techniques. It is shown that the generation of values of higher order shape functions for elements of any order, as well as for their derivatives, can be accomplished in a simple way through the use of Lagrange polynomials, avoiding the difficulties regarding the explicit deduction and coding of the equations. To this end, an effective computational scheme is given and the generalization of the intrinsic space is discussed within two-dimensional stress analysis. Finally, numerical experiments with slender components subjected to bending are carried out for studies on convergence. The results obtained showed that the appropriate order of the element to be used may depends directly on the nature of the problem being analyzed.