Stress-hybrid virtual element method on six-noded triangular meshes for compressible and nearly-incompressible linear elasticity

DOI10.1016/j.cma.2024.116971zbMath1539.74425MaRDI QIDQ6550124

N. Sukumar, Joseph E. Bishop, Alvin Chen

Publication date: 4 June 2024

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

zbMATH Keywords

volumetric lockingshear lockingtriangular meshesHellinger-Reissner variational principlehexagonal meshesstabilization-free virtual element method

Mathematics Subject Classification ID

Classical linear elasticity (74B05) Linear elasticity with initial stresses (74B10) Finite element methods applied to problems in solid mechanics (74S05)

Cites Work

• Fifteen node tetrahedral elements for explicit methods in nonlinear solid dynamics
• 8- and 12-node plane hybrid stress-function elements immune to severely distorted mesh containing elements with concave shapes
• On optimization approaches of hybrid stress elements
• A macro-element for incompressible finite deformations based on a volume-averaged deformation gradient
• Efficient implementation of quadrilaterals with high coarse-mesh accuracy
• Assumed strain stabilization of the 4-node quadrilateral with 1-point quadrature for nonlinear problems
• Mixed finite element methods - reduced and selective integration techniques: a unification of concepts
• Computational modelling of impact damage in brittle materials
• A mixed virtual element method for a pseudostress-based formulation of linear elasticity
• Higher-order hybrid stress triangular Mindlin plate element
• Efficient virtual element formulations for compressible and incompressible finite deformations
• Improved versions of assumed enhanced strain tri-linear elements for 3D finite deformation problems
• A family of virtual element methods for plane elasticity problems based on the Hellinger-Reissner principle
• Polytopal composite finite elements
• Solution of nearly incompressible field problems using a generalized finite element approach
• An enhanced VEM formulation for plane elasticity
• Unlocking the secrets of locking: finite element analysis in planar linear elasticity
• Scaled boundary cubature scheme for numerical integration over planar regions with affine and curved boundaries
• Refined 18-DOF triangular hybrid stress element for couple stress theory
• Stabilization-free serendipity virtual element method for plane elasticity
• Displacement and equilibrium models in the finite element method by B. Fraeijs de Veubeke, Chapter 9, Pages 145–197 of Stress Analysis, Edited by O. C. Zienkiewicz and G. S. Holister, Published by John Wiley & Sons, 1965
• Virtual Elements for Linear Elasticity Problems
• A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: a dynamic variational multiscale approach
• Rational approach for assumed stress finite elements
• On the Variational Foundations of Assumed Strain Methods
• Relations between incompatible displacement model and hybrid stress model
• A rational approach for choosing stress terms for hybrid finite element formulations
• Improved hybrid-stress axisymmetric elements includng behaviour for nearly incompressible materials
• Plane isoparametric hybrid-stress elements: Invariance and optimal sampling
• A systematic construction of B-bar functions for linear and non-linear mixed-enhanced finite elements for plane elasticity problems
• Patch recovery based on superconvergent derivatives and equilibrium
• Superconvergent patch recovery with equilibrium and conjoint interpolant enhancements
• Voronoi cell finite elements
• Tetrahedral composite finite elements
• A 3D brick element based on Hu-Washizu variational principle for mesh distortion
• A Simple Mesh Generator in MATLAB
• A plane hybrid element with rotational d.o.f. and adjustable stiffness
• BASIC PRINCIPLES OF VIRTUAL ELEMENT METHODS
• On immunizing five-beta hybrid-stress element models from ?trapezoidal locking? in practical analyses
• A dual hybrid virtual element method for plane elasticity problems
• Hybridization of the virtual element method for linear elasticity problems
• The Hitchhiker's Guide to the Virtual Element Method
• A class of mixed assumed strain methods and the method of incompatible modes
• Non-linear analysis of structures using high performance hybrid elements
• Penalty-equilibrating approach and an innovative formulation of 4-noded hybrid stress elements
• F‐bar‐based linear triangles and tetrahedra for finite strain analysis of nearly incompressible solids. Part I: formulation and benchmarking
• A Hu-Washizu variational approach to self-stabilized virtual elements: 2D linear elastostatics
• Airy stress function for proposed thermoelastic triangular elements
• Stabilization-free virtual element method for plane elasticity
• B-bar virtual element method for nearly incompressible and compressible materials
• An equilibrium-based stress recovery procedure for the VEM
• Novel quadratic Bézier triangular and tetrahedral elements using existing mesh generators: applications to linear nearly incompressible elastostatics and implicit and explicit elastodynamics
• Extending a 10-node composite tetrahedral finite element for solid mechanics
• Stress-hybrid virtual element method on quadrilateral meshes for compressible and nearly-incompressible linear elasticity
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