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

Ted Belytschko; Shau-Jen Ong Jame Shau-Jen Ong; Kam Liu Wing Kam Liu

doi:10.1016/0045-7825(84)90133-6

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

Ted Belytschko^*, Shau-Jen Ong Jame Shau-Jen Ong, Kam Liu Wing Kam Liu

^*Corresponding author for this work

Mechanical Engineering

Research output: Contribution to journal › Article › peer-review

65 Scopus citations

Abstract

When 2 × 2 quadrature is used with the 9-node Lagrange element, which is essential in C⁰ plate elements to avoid locking, spurious singular modes appear on the element level which can lead to singularity or near-singularity of the global equations. Here these modes are controlled by a procedure that introduces additional generalized stresses and strains so that the spurious modes are eliminated and the consistency of the resulting finite difference equations is not impaired; hence the procedure passes the patch test. Applications to the diffusion and Mindlin plate equations are presented. Results show that h³ convergence in the L₂-norm is almost retained.

Original language	English (US)
Pages (from-to)	269-295
Number of pages	27
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	44
Issue number	3
DOIs	https://doi.org/10.1016/0045-7825(84)90133-6
State	Published - Aug 1984

Funding

*The research was supported by the Air Force Oflice of Scientific Research under Grant F-4%2~~g2-K-~13.

ASJC Scopus subject areas

Computational Mechanics
Mechanics of Materials
Mechanical Engineering
General Physics and Astronomy
Computer Science Applications

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10.1016/0045-7825(84)90133-6

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title = "A consistent control of spurious singular modes in the 9-node Lagrange element for the laplace and mindlin plate equations",

abstract = "When 2 × 2 quadrature is used with the 9-node Lagrange element, which is essential in C0 plate elements to avoid locking, spurious singular modes appear on the element level which can lead to singularity or near-singularity of the global equations. Here these modes are controlled by a procedure that introduces additional generalized stresses and strains so that the spurious modes are eliminated and the consistency of the resulting finite difference equations is not impaired; hence the procedure passes the patch test. Applications to the diffusion and Mindlin plate equations are presented. Results show that h3 convergence in the L2-norm is almost retained.",

author = "Ted Belytschko and {Jame Shau-Jen Ong}, {Shau-Jen Ong} and {Wing Kam Liu}, {Kam Liu}",

note = "Funding Information: *The research was supported by the Air Force Oflice of Scientific Research under Grant F-4%2~~g2-K-~13.",

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T1 - A consistent control of spurious singular modes in the 9-node Lagrange element for the laplace and mindlin plate equations

AU - Belytschko, Ted

AU - Jame Shau-Jen Ong, Shau-Jen Ong

AU - Wing Kam Liu, Kam Liu

N1 - Funding Information: *The research was supported by the Air Force Oflice of Scientific Research under Grant F-4%2~~g2-K-~13.

PY - 1984/8

Y1 - 1984/8

N2 - When 2 × 2 quadrature is used with the 9-node Lagrange element, which is essential in C0 plate elements to avoid locking, spurious singular modes appear on the element level which can lead to singularity or near-singularity of the global equations. Here these modes are controlled by a procedure that introduces additional generalized stresses and strains so that the spurious modes are eliminated and the consistency of the resulting finite difference equations is not impaired; hence the procedure passes the patch test. Applications to the diffusion and Mindlin plate equations are presented. Results show that h3 convergence in the L2-norm is almost retained.

AB - When 2 × 2 quadrature is used with the 9-node Lagrange element, which is essential in C0 plate elements to avoid locking, spurious singular modes appear on the element level which can lead to singularity or near-singularity of the global equations. Here these modes are controlled by a procedure that introduces additional generalized stresses and strains so that the spurious modes are eliminated and the consistency of the resulting finite difference equations is not impaired; hence the procedure passes the patch test. Applications to the diffusion and Mindlin plate equations are presented. Results show that h3 convergence in the L2-norm is almost retained.

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

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