Effects of element distortions on the performance of isoparametric elements

DOI10.1002/nme.1620362009zbMath0800.73465OpenAlexW1992266968MaRDI QIDQ4285118

Publication date: 24 March 1994

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

Full work available at URL: https://doi.org/10.1002/nme.1620362009

Mathematics Subject Classification ID

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

Related Items (89)

A set of pathological test to validate new finite elements ⋮ New superconvergent points of the 8‐node serendipity plane element for patch recovery ⋮ Direct serendipity and mixed finite elements on convex quadrilaterals ⋮ A new enhanced assumed strain quadrilateral membrane element with drilling degree of freedom and modified shape functions ⋮ Moving least-squares in finite strain analysis with tetrahedra support ⋮ A quadratic plane triangular element immune to quadratic mesh distortions under quadratic displacement fields ⋮ Galerkin-based finite strain analysis with enriched radial basis interpolation ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Two 8-node quadrilateral spline elements by B-net method ⋮ Hexahedral volume coordinate method (HVCM) and improvements on 3D Wilson hexahedral element ⋮ A shape-free 8-node plane element unsymmetric analytical trial function method ⋮ An effective membrane element based on analytical solution ⋮ Construct `FE-meshfree' Quad4 using mean value coordinates ⋮ A novel numerical manifold method with derivative degrees of freedom and without linear dependence ⋮ A partition-of-unity based `FE-meshfree' triangular element with radial-polynomial basis functions for static and free vibration analysis ⋮ Free and forced vibration analyses using the four-node quadrilateral element with continuous nodal stress ⋮ Application of the `FE-meshfree' Quad4 with continuous nodal stress using radial-polynomial basis functions for vibration and geometric nonlinear analyses ⋮ Construction of \(n\)-sided polygonal spline element using area coordinates and B-net method ⋮ A linear smoothed higher-order CS-FEM for the analysis of notched laminated composites ⋮ A novel twice-interpolation finite element method for solid mechanics problems ⋮ A concave-admissible quadrilateral quasi-conforming plane element using B-net method ⋮ Finite-strain low order shell using least-squares strains and two-parameter thickness extensibility ⋮ Numerical analysis of plane stress free vibration in severely distorted mesh by generalized finite element method ⋮ Four-Node Quadrilateral Element with Continuous Nodal Stress for Geometrical Nonlinear Analysis ⋮ A Three-Node Triangular Element with Continuous Nodal Stress (Trig3-CNS) for Geometry Nonlinear Solid Mechanics Problems ⋮ Asymmetric quadrilateral shell elements for finite strains ⋮ A numerical approach based on the meshless collocation method in elastodynamics ⋮ Four-node generalized conforming membrane elements with drilling DOFs using quadrilateral area coordinate methods ⋮ Automatic adaptive refinement for shell analysis using nine-node assumed strain element ⋮ The quadrilateral Mindlin plate elements using the spline interpolation bases ⋮ Application of the quadrilateral area coordinate method: a new element for laminated composite plate bending problems ⋮ Generalized modal element method. I: Theory and its application to eight-node asymmetric and symmetric solid elements in linear analysis ⋮ A 3D pyramid spline element ⋮ Two improvements in formulation of nine-node element MITC9 ⋮ Distortion-immune nine-node displacement-based quadrilateral thick plate finite elements that satisfy constant-bending patch test ⋮ Two 8‐node quadrilateral unsymmetric elements with different incompatible modes immune to severe distortion ⋮ An unsymmetric 4-node, 8-DOF plane membrane element perfectly breaking through MacNeal's theorem ⋮ Virtual and smoothed finite elements: A connection and its application to polygonal/polyhedral finite element methods ⋮ Reformulation of dynamic crack propagation using the numerical manifold method ⋮ Three‐dimensional spline scaled boundary finite elements with high‐order completeness ⋮ Construction of generalized shape functions over arbitrary polytopes based on scaled boundary finite element method's solution of Poisson's equation ⋮ Multiscale modeling of linear elastic heterogeneous structures via localized model order reduction ⋮ A 3D triangular prism spline element using B-net method ⋮ Extension of the unsymmetric 8‐node hexahedral solid element <scp>US‐ATFH8</scp> to <scp>3D</scp> hyper‐elastic finite deformation analysis ⋮ Three-component volume coordinate system for constructing high performance elements ⋮ Construction of a new class of quadrilateral spline elements based on the scaled boundary coordinates ⋮ Unnamed Item ⋮ An unsymmetric 8-node hexahedral solid-shell element based on ANS and incompatible concepts for thin shell analysis ⋮ A subdivision-stabilized B-Spline mixed material point method ⋮ Subdomain-based error techniques for generalized finite element approximations of problems with singular stress fields ⋮ On the condition number of high order finite element methods: influence of \(p\)-refinement and mesh distortion ⋮ A technique to develop mesh-distortion immune finite elements ⋮ Shape-free finite element method: another way between mesh and mesh-free methods ⋮ A new cloud-based \(hp\) finite element method ⋮ Quadratic maximum-entropy serendipity shape functions for arbitrary planar polygons ⋮ General complete Lagrange family for the cube in finite element interpolations ⋮ 8- and 12-node plane hybrid stress-function elements immune to severely distorted mesh containing elements with concave shapes ⋮ Finite element linear and nonlinear, static and dynamic analysis of structural elements: a bibliography (1992‐1995) ⋮ Modification of the 8-node serendipity element ⋮ Iterative correction to enhance the mesh distortion tolerance of isoparametric QUAD8 element ⋮ On the Factors Affecting the Accuracy and Robustness of Smoothed-Radial Point Interpolation Method ⋮ Analytical trial function method for development of new 8‐node plane element based on the variational principle containing Airy stress function ⋮ Improved nine-node shell element MITC9i with reduced distortion sensitivity ⋮ FINITE ELEMENT MODELING OF ACOUSTICS USING HIGHER ORDER ELEMENTS PART I: NONUNIFORM DUCT PROPAGATION ⋮ On the consistency of finite element models in thermoelastic analysis. ⋮ General complete Lagrange interpolations with applications to three-dimensional finite element analysis ⋮ A direct mixed-enriched Galerkin method on quadrilaterals for two-phase Darcy flow ⋮ A 17-node quadrilateral spline finite element using the triangular area coordinates ⋮ Extension of unsymmetric finite elements US‐QUAD8 and US‐HEXA20 for geometric nonlinear analyses ⋮ Smoothed FE-meshfree method for solid mechanics problems ⋮ 8-node quasi-conforming plane element by using Bernstein basis functions ⋮ 8-node unsymmetric distortion-immune element based on Airy stress solutions for plane orthotropic problems ⋮ A mixed three-node triangular element with continuous nodal stress for fully dynamic consolidation of porous media ⋮ α-Finite Element Method for Frictionless and Frictional Contact Including Large Deformation ⋮ Generalized higher order layerwise theory for the dynamic study of anisotropic doubly-curved shells with a mapped geometry ⋮ Quadrilateral-area-coordinate-based numerical manifold method accommodating static and dynamic analysis ⋮ A finite-strain solid-shell using local Löwdin frames and least-squares strains ⋮ High order transition elements: the \(x\boldsymbol{N}y\)-element concept. I: Statics ⋮ High-order polygonal discontinuous Petrov-Galerkin (PolyDPG) methods using ultraweak formulations ⋮ Quadrilateral membrane element family formulated by the quadrilateral area coordinate method ⋮ Development of User Element Routine (UEL) for Cell-Based Smoothed Finite Element Method (CSFEM) in Abaqus ⋮ A high-order three dimensional numerical manifold method with continuous stress/strain field ⋮ Modeling unconfined seepage flow in soil-rock mixtures using the numerical manifold method ⋮ Stability analysis of soil-rock-mixture slopes using the numerical manifold method ⋮ Mesh-distortion immunity assessment of QUAD8 elements by strong-form patch tests ⋮ A semi-implicit finite strain shell algorithm using in-plane strains based on least-squares ⋮ On the regularity and uniformness conditions on quadrilateral grids

This page was built for publication: Effects of element distortions on the performance of isoparametric elements