Finite Element Analysis of Plate Buckling Using a Mixed Variational Principle

Item

Title
Finite Element Analysis of Plate Buckling Using a Mixed Variational Principle
Description
A (mixed) variational principle for stresses and displacements is presented from which the governing differential equations of the bifurcational buckling of thin 'elastic plates. are derived. Subsequent finite element analysis, using a linear approximation for the bending moments and a cubic approximation for the displacements within each element, leads to the familiar linear eigenvalue problem for determining the critical intensities of in-plane loading. Numerical solutions are given to a number of simple examples involving square plates using a recently published eigenvalue algorithm which takes advantage of the banded properties of the final matrix formulation. Comparisons are made, where possible, with results from the finite element analyses of other authors and with exact or classical Rayleigh-Ritz solutions.
Creator
Allman, D. J.
Abstract
A (mixed) variational principle for stresses and displacements is presented from which the governing differential equations of the bifurcational buckling of thin 'elastic plates. are derived. Subsequent finite element analysis, using a linear approximation for the bending moments and a cubic approximation for the displacements within each element, leads to the familiar linear eigenvalue problem for determining the critical intensities of in-plane loading. Numerical solutions are given to a number of simple examples involving square plates using a recently published eigenvalue algorithm which takes advantage of the banded properties of the final matrix formulation. Comparisons are made, where possible, with results from the finite element analyses of other authors and with exact or classical Rayleigh-Ritz solutions.
Corporate Author
Royal Aircraft Establishment, Farnborough, UK
Report Number
AFFDL TR 71-160 p. 683-705
Report Availability
Full text available
Publisher
Wright-Patterson Air Force Base, OH : Air Force Flight Dynamics Laboratory, Air Force Systems Command and Air Force Institute of Technology, Air University
Date
1973
Type
article
Date Issued
1973-12
Provenance
Bombardier/Aero
Distribution Classification
1
Distribution Conflict
No
DTIC Record Exists
No
Format
1 online resource (22 pages) : ill.
Extent
22
Identifier
AD0785968
Is Part Of
Proceedings of the Third Conference on Matrix Methods in Structural Mechanics: Proceedings of the Conference held at Wright-Patterson Air Force Base, Ohio 19-21 October 1971
Media
AFFDLTR71-160article23.pdf

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Items with "Has Part: Finite Element Analysis of Plate Buckling Using a Mixed Variational Principle"
Title Class
Proceedings of the Third Conference on Matrix Methods in Structural Mechanics: Proceedings of the Conference held at Wright-Patterson Air Force Base, Ohio 19-21 October 1971