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Efficient Implementation of Extended Finite Element Method

[+] Author Affiliations
Vishal Hotwani, Ashok V. Kumar

University of Florida, Gainesville, FL

Paper No. DETC2012-70893, pp. 157-163; 7 pages
doi:10.1115/DETC2012-70893
From:
  • ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 2: 32nd Computers and Information in Engineering Conference, Parts A and B
  • Chicago, Illinois, USA, August 12–15, 2012
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-4501-1
  • Copyright © 2012 by ASME

abstract

Extended finite element method (or XFEM) locally enriches the finite element solution using a priori known analytical solution. XFEM has been used extensively in fracture mechanics to compute stress concentration at crack tips. It is a mesh independent method that allows crack to be represented as an equation instead of using the mesh to approximate it. When this approach is used along with Implicit Boundary Finite Element Method (IBFEM) to apply boundary conditions, a fully mesh independent approach for studying crack tip stresses can be implemented. An efficient scheme for blending the enriched solution structure with the underlying finite element solution is presented. A ramped step function is introduced for modeling discontinuity or a crack within an element. Exact analytical solution is used as enrichment at the crack tip element to obtain the stress intensity factor (SIF) directly without any post processing or contour integral computation. Several examples are used to study the convergence and accuracy of the solution.

Copyright © 2012 by ASME

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