Generalized Gaussian quadrature rules for discontinuities and crack singularities in the extended finite element method

DOI10.1016/j.cma.2010.06.031zbMath1225.74099OpenAlexW2010549663MaRDI QIDQ643888

Publication date: 2 November 2011

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cma.2010.06.031

zbMATH Keywords

numerical integration crack growth discontinuous functions generalized duffy transformation node elimination algorithm partition-of-unity enrichment weakly singular functions

Mathematics Subject Classification ID

Brittle fracture (74R10) Stress concentrations, singularities in solid mechanics (74G70) Finite element methods applied to problems in solid mechanics (74S05)

Related Items

An XFEM method for modeling geometrically elaborate crack propagation in brittle materials, Numerical integration of discontinuities on arbitrary domains based on moment fitting, The finite cell method: a review in the context of higher-order structural analysis of CAD and image-based geometric models, Efficient evaluation of integrals with kernel \(1/r^\chi\) for quadrilateral elements with irregular shape, Adaptively weighted numerical integration over arbitrary domains, Adaptive concurrent multiscale model for fracture and crack propagation in heterogeneous media, About the use of standard integration schemes for X-FEM in solid mechanics plasticity, An accurate semi-analytical method for an arbitrarily oriented edge or interior crack in an anisotropic homogeneous elastic solid, A unified enrichment approach addressing blending and conditioning issues in enriched finite elements, Selective enrichment of moment fitting and application to cut finite elements and cells, A computational framework for well production simulation: coupling steady state Darcy flow and channel flow by SGBEM-FEM, Simple multidimensional integration of discontinuous functions with application to level set methods, Three-dimensional integration strategies of singular functions introduced by the XFEM in the LEFM, Higher-order extended FEM for weak discontinuities - level set representation, quadrature and application to magneto-mechanical problems, Highly accurate surface and volume integration on implicit domains by means of moment-fitting, Representation of singular fields without asymptotic enrichment in the extended finite element method, New strategies for some issues of numerical manifold method in simulation of crack propagation, A conformal decomposition finite element method for arbitrary discontinuities on moving interfaces, Accuracy of three-dimensional analysis of regularized singularities, Equivalent polynomials for quadrature in Heaviside function enriched elements, Some numerical issues on the use of XFEM for ductile fracture, New anisotropic crack-tip enrichment functions for the extended finite element method, A new technique for numerical simulation of dendritic solidification using a meshfree interface finite element method, Adaptive quadrature/cubature rule: application to polytopes, Improved XFEM for multiple crack analysis: accurate and efficient implementations for stress intensity factors, Generalizations of the finite element method, Combined visibility and surrounding triangles method for simulation of crack discontinuities in meshless methods, Cover refinement of numerical manifold method for crack propagation simulation, Quadrature schemes for arbitrary convex/concave volumes and integration of weak form in enriched partition of unity methods, Variationally consistent eXtended FE model for 3D planar and curved imperfect interfaces, An Extended Discontinuous Galerkin Framework for Multiphase Flows, ILS-MPM: an implicit level-set-based material point method for frictional particulate contact mechanics of deformable particles, Higher-order extended finite elements with harmonic enrichment functions for complex crack problems, Efficient integration of crack singularities in the extended finite element method: Duffy-distance transformation and conformal preconditioning strategy, A four-way enhanced numerical manifold method for crack propagation and failure analysis of rock slopes, Harmonic enrichment functions: A unified treatment of multiple, intersecting and branched cracks in the extended finite element method, Numerical integration of polynomials and discontinuous functions on irregular convex polygons and polyhedrons, Numerical Integration of On-the-Fly-Computed Enrichment Functions in the PUM, A new method for numerical integration of singular functions on the plane, Some investigations on 3D homogenization of nano-composite/nano-porous materials with surface effect by FEM/XFEM methods combined with level-set technique, Phase field modeling of frictional slip with slip weakening/strengthening under non-isothermal conditions, An accurate, robust, and easy-to-implement method for integration over arbitrary polyhedra: application to embedded interface methods, Adaptively weighted numerical integration in the finite cell method, A local crack-tracking strategy to model three-dimensional crack propagation with embedded methods, Stable 3D extended finite elements with higher order enrichment for accurate non planar fracture, A general algorithm for numerical integration of three-dimensional crack singularities in PU-based numerical methods, Shape aware quadratures, Static and dynamic analysis of plane elasticity using complex Fourier manifold method based on numerical improvement of Gauss-Legendre quadrature techniques, Adaptive Integration of Cut Finite Elements and Cells for Nonlinear Structural Analysis

Uses Software

Cites Work