Stable generalized finite element methods for elasticity crack problems

DOI10.1002/NME.6347zbMATH Open1548.74784MaRDI QIDQ6553469

Qinghui Zhang, Cu Cui

Publication date: 11 June 2024

Published in: International Journal for Numerical Methods in Engineering (Search for Journal in Brave)

zbMATH Keywords

convergenceprincipal component analysiscondition numberGFEM/XFEMSGFEM

Mathematics Subject Classification ID

Classical linear elasticity (74B05) Brittle fracture (74R10) Finite element methods applied to problems in solid mechanics (74S05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Cites Work

• A note on the conditioning of a class of generalized finite element methods
• Stable generalized finite element method (SGFEM)
• A simple and efficient preconditioning scheme for Heaviside enriched XFEM
• Stable enrichment and local preconditioning in the particle-partition of unity method
• Higher order stable generalized finite element method
• An \(h\)-\(p\) adaptive method using clouds
• The partition of unity finite element method: basic theory and applications
• A computational approach to handle complex microstructure geometries.
• Stable GFEM (SGFEM): improved conditioning and accuracy of GFEM/XFEM for three-dimensional fracture mechanics
• Principal component analysis.
• The design and analysis of the generalized finite element method
• Three-dimensional improved XFEM (IXFEM) for static crack problems
• Strongly stable generalized finite element method (SSGFEM) for a non-smooth interface problem
• A stable generalized/extended FEM with discontinuous interpolants for fracture mechanics
• Improving the conditioning of XFEM/GFEM for fracture mechanics problems through enrichment quasi-orthogonalization
• The stable XFEM for two-phase flows
• A unified enrichment approach addressing blending and conditioning issues in enriched finite elements
• On the use of singular functions with finite element approximations
• Robustness in stable generalized finite element methods (SGFEM) applied to Poisson problems with crack singularities
• A stable generalized finite element method (SGFEM) of degree two for interface problems
• Strongly stable generalized finite element method: application to interface problems
• Stable generalized finite element method (SGFEM) for parabolic interface problems
• Stable generalized finite element method and associated iterative schemes; application to interface problems
• A stable and optimally convergent generalized FEM (SGFEM) for linear elastic fracture mechanics
• A finite element method dealing the singular points with a cut-off function
• A stabilization technique for the regularization of nearly singular extended finite elements
• A particle-partition of unity method. II: Efficient cover construction and reliable integration
• Optimal convergence analysis for the extended finite element method
• A robust preconditioning technique for the extended finite element method
• The extended/generalized finite element method: An overview of the method and its applications
• Improved implementation and robustness study of the X-FEM for stress analysis around cracks
• Multiscale Finite Element Methods
• Integrating strong and weak discontinuities without integration subcells and example applications in an XFEM/GFEM framework
• A corrected XFEM approximation without problems in blending elements
• Elastic crack growth in finite elements with minimal remeshing
• THE PARTITION OF UNITY METHOD
• Survey of meshless and generalized finite element methods: A unified approach
• Arbitrary branched and intersecting cracks with the extended finite element method
• A finite element method for crack growth without remeshing
• High-order extended finite element method for cracked domains
• GENERALIZED FINITE ELEMENT METHODS — MAIN IDEAS, RESULTS AND PERSPECTIVE
• DOF‐gathering stable generalized finite element methods for crack problems
• Material-dependent crack-tip enrichment functions in XFEM for modeling interfacial cracks in bimaterials

Related Items (2)

Unfitted generalized finite element methods for Dirichlet problems without penalty or stabilization ⋮ Mass lumping of stable generalized finite element methods for parabolic interface problems

This page was built for publication: Stable generalized finite element methods for elasticity crack problems

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6553469)