Comparison of SGBEM-FEM Alternating Method and XFEM Method for Determining Stress Intensity Factor for 2D Crack Problems

Abstract:

The two most promising approaches to determine Stress Intensity Factor (SIF) developedover the past decade are the Symmetric Galerkin Boundary Element Method - Finite Element Method(SGBEM-FEM) based alternating method and the Extended Finite Element (XFEM) method. Thepurpose of this paper is to determine the SIFs for a number of 2-D crack problems by the two ap-proaches and measure their relative effectiveness in terms of accuracy, speed and computational re-sources.In the SGBEM-FEM alternating method, a finite element analysis is carried out on the un-crackedbody using the externally applied loading and next a boundary element analysis is performed byreversing the stresses found on the crack location from the finite element analysis, and the residualstresses on the boundary of the finite body are determined. The steps are repeated until convergenceis achieved where the residual stresses on the boundaries and traction on the crack surfaces are closeto zero.In the XFEM method, the mesh is created without considering the topology of the crack configura-tion and the discontinuities are handled by special discontinuity enrichment functions. The enrichmentfunctions increase the degrees of freedom and the regular stiffness matrix is augmented by additionalterms corresponding to the extra degrees of freedom but the increase in computational requirement isoffset by not having the burden of remeshing the finite elements.Both SGBEM-FEM alternating method and XFEM method are used to solve a number of crackproblems and the example cases clearly show the computational efficiency of the SGBEM-FEM al-ternating method over the XFEM method.

• Periodical: Advanced Materials Research (Volumes 891-892)
• Pages: 345-350
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.891-892.345
• Online since: March 2014
• Authors: Subhasis Sarkar, Nicole Apetre, Nagaraja Iyyer, Nam Phan, Kishan Goel, Satya Atluri
• Keywords: Alternating Method, Crack Propagation, Finite Element Method (FEM), SGBEM, Stress Intensity Factor (SIF), XFEM

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