Mixed variational principles and stabilization of spurious modes in the 9-node element

DOI10.1016/0045-7825(87)90063-6zbMath0614.73072OpenAlexW2074898594MaRDI QIDQ1820007

Ted Beltytschko, Jame Shau-Jen Ong, Wing Kam Liu

Publication date: 1987

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

Full work available at URL: https://doi.org/10.1016/0045-7825(87)90063-6

zbMATH Keywords

stabilization matrixHu-Washizu principlemixed variational principles9-node plane stress elementcontrol of spurious modesframe invariant formulationgama-projection operatorLagrange continuum elementsuppression of appropriate stressesunderintegrated 9-node element

Mathematics Subject Classification ID

Related Items (10)

Mixed finite element formulations and related limitation principles: A general treatment ⋮ Numerical analysis of plane stress free vibration in severely distorted mesh by generalized finite element method ⋮ Physical stabilization of the 4-node shell element with one point quadrature ⋮ An explicit hybrid-stabilized 9-node Lagrangian shell element ⋮ The \(C^ 0\) shell plate and beam elements freed from their deficiencies ⋮ Generalized mixed variational principles and solutions of ill-conditioned problems in computational mechanics. II: Shear locking. ⋮ Quadrilateral with high coarse-mesh accuracy for solid mechanics in axisymmetric geometry ⋮ A class of simple and efficient degenerated shell elements - Analysis of global spurious-mode filtering ⋮ Unnamed Item ⋮ A stabilized co-rotational curved quadrilateral composite shell element

Cites Work

• Unnamed Item
• A consistent control of spurious singular modes in the 9-node Lagrange element for the Laplace and Mindlin plate equations
• Development and testing of stable, invariant, isoparametric curvilinear 2- and 3-D hybrid-stress elements
• Analysis of hourglass instabilities and control in underintegrated finite element methods
• Hourglass control in linear and nonlinear problems
• Efficient implementation of quadrilaterals with high coarse-mesh accuracy
• Stress projection for membrane and shear locking in shell finite elements
• Rational approach for assumed stress finite elements
• Control of zero-energy modes in 9-node plane element
• A Curved C0 Shell Element Based on Assumed Natural-Coordinate Strains
• The patch test—a condition for assessing FEM convergence
• A uniform strain hexahedron and quadrilateral with orthogonal hourglass control
• Control of spurious modes in the nine-node quadrilateral element

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