A stabilization matrix for the bilinear mindlin plate element

T. Belytschko; C. S. Tsay; W. K. Liu

doi:10.1016/0045-7825(81)90048-7

A stabilization matrix for the bilinear mindlin plate element

T. Belytschko^*, C. S. Tsay, W. K. Liu

^*Corresponding author for this work

Mechanical Engineering

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

113 Scopus citations

Abstract

The reduced integration of the four node quadrilateral plate element based on Mindlin theory results in zero energy modes other than the rigid body modes. These modes present difficulties in certain situations. In this paper we suggest a method to remove these zero-energy (kinematic) modes by perturbing the stiffness by a stabilization matrix. This approach eliminates the element's kinematic modes without inducing locking and thus does not affect its convergence.

Original language	English (US)
Pages (from-to)	313-327
Number of pages	15
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	29
Issue number	3
DOIs	https://doi.org/10.1016/0045-7825(81)90048-7
State	Published - Dec 1981

ASJC Scopus subject areas

Computational Mechanics
Mechanics of Materials
Mechanical Engineering
Physics and Astronomy(all)
Computer Science Applications

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10.1016/0045-7825(81)90048-7

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title = "A stabilization matrix for the bilinear mindlin plate element",

abstract = "The reduced integration of the four node quadrilateral plate element based on Mindlin theory results in zero energy modes other than the rigid body modes. These modes present difficulties in certain situations. In this paper we suggest a method to remove these zero-energy (kinematic) modes by perturbing the stiffness by a stabilization matrix. This approach eliminates the element's kinematic modes without inducing locking and thus does not affect its convergence.",

author = "T. Belytschko and Tsay, {C. S.} and Liu, {W. K.}",

note = "Funding Information: The partial support of EPRI gratefully acknowledged. Funding Information: and the National Science Foundation to",

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AU - Belytschko, T.

AU - Tsay, C. S.

AU - Liu, W. K.

N1 - Funding Information: The partial support of EPRI gratefully acknowledged. Funding Information: and the National Science Foundation to

PY - 1981/12

Y1 - 1981/12

N2 - The reduced integration of the four node quadrilateral plate element based on Mindlin theory results in zero energy modes other than the rigid body modes. These modes present difficulties in certain situations. In this paper we suggest a method to remove these zero-energy (kinematic) modes by perturbing the stiffness by a stabilization matrix. This approach eliminates the element's kinematic modes without inducing locking and thus does not affect its convergence.

AB - The reduced integration of the four node quadrilateral plate element based on Mindlin theory results in zero energy modes other than the rigid body modes. These modes present difficulties in certain situations. In this paper we suggest a method to remove these zero-energy (kinematic) modes by perturbing the stiffness by a stabilization matrix. This approach eliminates the element's kinematic modes without inducing locking and thus does not affect its convergence.

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A stabilization matrix for the bilinear mindlin plate element

Abstract

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