A consistent control of spurious singular modes in the 9-node Lagrange element for the Laplace and Mindlin plate equations

DOI10.1016/0045-7825(84)90133-6zbMath0525.73086OpenAlexW2005715043MaRDI QIDQ593868

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

Publication date: 1984

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(84)90133-6

zbMATH Keywords

diffusionpatch test2x2 quadrature9-node Lagrangian elementavoid lockingC-o plate elementsconsistency of resulting finite difference equations not impairedcontrolled by procedure that introduces additional generalized stresses and strainsh3 convergence in L2-normMindlin plate equationsspurious singular modes

Mathematics Subject Classification ID

Plates (74K20) Finite element methods applied to problems in solid mechanics (74S05) Numerical and other methods in solid mechanics (74S99)

Related Items

Developments of Mindlin-Reissner plate elements ⋮ Automatic adaptive refinement for shell analysis using nine-node assumed strain element ⋮ The \(C^ 0\) shell plate and beam elements freed from their deficiencies ⋮ Two improvements in formulation of nine-node element MITC9 ⋮ A locking-free FEM for cavitation computation in nearly incompressible nonlinear elasticity ⋮ A perturbation method for dynamic analyses using under-integrated shell elements ⋮ Improved nine-node shell element MITC9i with reduced distortion sensitivity ⋮ A field-consistent and variationally correct representation of transverse shear strains in the nine-noded plate element ⋮ A class of simple and efficient degenerated shell elements - Analysis of global spurious-mode filtering ⋮ A diffusion equation with hourglass control in an axisymmetric geometry ⋮ On the mixed formulation of a 9-node Lagrange shell element ⋮ Finite element stabilization matrices - A unification approach ⋮ Mixed variational principles and stabilization of spurious modes in the 9-node element ⋮ Analysis of hourglass instabilities and control in underintegrated finite element methods ⋮ A consolidation of various approaches in developing naturally based quadrilaterals ⋮ An accurate and efficient a posteriori control of hourglass instabilities in underintegrated linear and nonlinear elasticity ⋮ Stress projection for membrane and shear locking in shell finite elements

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