The coupled dual boundary element-scaled boundary finite element method for efficient fracture mechanics

Abstract

A novel numerical method is presented for applications to general fracture mechanics problems in engineering. The coupled dual boundary element-scaled boundary finite element method (DBE-SBFEM) incorporates the numerical accuracy of the SBFEM and the geometric versatility of the DBEM. Background theory, detailed derivations and literature reviews accompany the extensions made to the methods constituents necessary for their coupling as part of the present work. The coupled DBE-SBFEM, its constituent components and their application to linear elastic fracture mechanics are critically assessed and presented with numerical examples to demonstrate both method convergence and improvements over previous work. Further, a proof of concept demonstrates an alternative formation of the DBEM that both negates the need for hyper-singular integration and lends itself to a wider variety of imposed boundary conditions. Conclusions to this work are drawn and further recommendations for research in this area are made.