Integration of singular enrichment functions in the generalized/extended finite element method for three‐dimensional problems

By Kyoungsoo Park, J. Pereira, Carlos Armando Duarte, Glaucio H. Paulino. 2009

98 citations recorded by the source corpus.

Subfields: Computational Mechanics, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/0dff54deb89d722aeb88fcdc35acae2c249443ed

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In Computational Mechanics

In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

Analysis of three‐dimensional fracture mechanics problems: A two‐scale approach using coarse‐generalized FEM meshes (2010, background): “Special quadrature rules, such as those proposed in [ 55 ], may be used at local elements enriched with singular functions.”
Generalized Gaussian Quadrature Rules for Discontinuities and Crack Singularities in the Extended Finite Element Method (2010, methodology): “[55] use the mapping of Nagarajan and Mukherjee [56] and generalize it to three dimensions for crack problems.”
Equivalent polynomials for quadrature in Heaviside function enriched elements (2015, methodology): “A third mapping method was introduced in [17], where a generalization of Nagarajan and Mukherjee mapping [18] to three dimensions for crack problems was introduced.”
Generalized Duffy transformation for integrating vertex singularities (2009, methodology): “[53] generalize this transformation to three-dimensional tetrahedral elements and use it to integrate singular enrichment bases for crack problems within the generalized finite element method.”
Unstructured polygonal meshes with adaptive refinement for the numerical simulation of dynamic cohesive fracture (2014, background): “The cohesive elements are inserted on the fly, where and when needed, and follow the constitutive response of the extrinsic Park–Paulino– Roesler (PPR) cohesive model (Park et al. 2009).”
Domain integral formulation for 3-D curved and non-planar cracks with the extended finite element method (2013, unknown): “The elements including the crack front are subdivided and integrated using a quasi polar rule introduced in [16].”
The extended/generalized finite element method: An overview of the method and its applications (2010, background): “[141] which is also applicable to three dimensions.”
A stable and optimally convergent generalized FEM (SGFEM) for linear elastic fracture mechanics (2013, methodology): “These meshes also ensure accurate integration of singular enrichment functions using the quadrature rules presented in [29].”
Three-dimensional crack growth with hp-generalized finite element and face offsetting methods (2010, unknown): “A detailed study of numerical integration and computational performance of these functions is presented in [ 48 ].”
Extended finite element method with global enrichment (2015, methodology): “Other drawbacks of the method include blending problems between the enriched and the standard part of the approximation for which several solutions have been given [27,28,29,30,31,32] and problems in numerical integration which can be dealt with by using techniques such as element partitioning and s”