A Fourier analysis of spurious mechanisms and locking in the finite element method

DOI10.1016/0045-7825(84)90129-4zbMath0538.73097OpenAlexW2035363901MaRDI QIDQ793569

N. E. Zubov

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)90129-4

zbMATH Keywords

characteristic equationsdiscrete filter conceptselement locking phenomenaFourier analysis techniquespurious mechanismsspurious mode carrieruncoupled discrete Fourier operatorsvibration of Timoshenko beamviolating unlocking conditionwave propagation in bar

Mathematics Subject Classification ID

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

Related Items (16)

Nodally exact Ritz discretizations of 1D diffusion-absorption and Helmholtz equations by variational FIC and modified equation methods ⋮ A multigrid method for the membrane problem ⋮ Mass matrix templates: general description and 1D examples ⋮ Complex wave-number dispersion analysis of Galerkin and Galerkin least-squares methods for fluid-loaded plates ⋮ Design of Galerkin generalized least squares methods for Timoshenko beams ⋮ Grid dispersion analysis of plane square biquadratic serendipity finite elements in transient elastodynamics ⋮ Dispersion and transient analyses of Hermite reproducing kernel Galerkin meshfree method with sub-domain stabilized conforming integration for thin beam and plate structures ⋮ Fourier analysis of membrane locking and unlocking ⋮ The influence of the mass matrix on the dispersive nature of the semi-discrete, second-order wave equation ⋮ Customizing the mass and geometric stiffness of plane beam elements by Fourier methods ⋮ Residual-based methods for fluid-loaded beams ⋮ Error estimates in 2-node shear-flexible beam elements ⋮ A priori identification of shear locking and stiffening in triangular Mindlin elements ⋮ A symbolic Fourier synthesis of a one-point integrated quadrilateral plate element ⋮ Complex wavenumber Fourier analysis of the \(p\)-version finite element method ⋮ Stress projection for membrane and shear locking in shell finite elements

Cites Work

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• Finite Elements Based Upon Mindlin Plate Theory With Particular Reference to the Four-Node Bilinear Isoparametric Element
• A uniform strain hexahedron and quadrilateral with orthogonal hourglass control
• A note on locking in a shear flexible triangular plate bending element
• A simple and efficient finite element for plate bending
• A simple quadrilateral shell element
• Spurious reflection of elastic waves due to gradually changing finite element size
• Fourier Analysis of the Finite Element Method in Ritz‐Galerkin Theory
• Improved numerical integration of thick shell finite elements
• Reduced integration technique in general analysis of plates and shells

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