Finite Element Analysis of Plate Buckling Using a Mixed Variational Principle
Report Number: AFFDL TR 71-160 p. 683-705
Author(s): Allman, D. J.
Corporate Author(s): Royal Aircraft Establishment, Farnborough, UK
Date of Publication: 1973-12
Pages: 22
DoD Task:
Identifier: This paper is part of a conference proceedings. See AD0785968
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.
Provenance: Bombardier/Aero
Author(s): Allman, D. J.
Corporate Author(s): Royal Aircraft Establishment, Farnborough, UK
Date of Publication: 1973-12
Pages: 22
DoD Task:
Identifier: This paper is part of a conference proceedings. See AD0785968
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.
Provenance: Bombardier/Aero
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