Analysis of free‐edge effects by boundary finite element method

Abstract

AbstractThe scaled boundary finite element method is a novel semi‐analytical analysis technique that combines the advantages of the finite element method and the boundary element method. Only a part of the boundary of the considered domain has to be discretized but nevertheless the method is solely finite element based. The governing equations are solved in the so‐called scaling direction analytically, whereas a finite element approximation of the solution is performed in the circumferential directions, which form the boundary of the considered domain. Thus, the numerical effort can be reduced considerably when handling stress concentration problems such as e.g. the free‐edge effect in laminated plates. In order to analyze the free‐edge effect in a semi‐infinite half plane, some kinematic coupling equations have to be introduced, that not only couple the degrees of freedom on the boundary, but also within the non‐discretized domain. The implementation of kinematic coupling equations within the method is presented. Finally, the efficiency of the new approach is shown in some benchmark examples. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)