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Buckling‐Bending Problem for Circular Plate
Author(s) -
Marko Lubomir
Publication year - 2005
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200510100
Subject(s) - buckling , bending , bending of plates , eigenvalues and eigenvectors , thrust , enhanced data rates for gsm evolution , pure bending , geometry , structural engineering , plate theory , mathematics , materials science , physics , mathematical analysis , boundary value problem , engineering , telecommunications , quantum mechanics , thermodynamics
Abstract We consider radially symmetric deformation of a thin flat elastic circular plate of constant thickness clamped at its edge. The plate is under the action of a uniform compressive thrust along its edge in the midplane of the plate. The thrust is proportional to a real parameter λ. The plate is also subjected to a radially symmetric load, normal to its midplane. The equilibrium states of the given buckling‐bending problem are the solutions of von Kármán equations. Let λ 1 < λ 2 be the first and the second eigenvalue of the linearized problem. If λ ≤ λ 1 the buckling‐bending problem has unique solution for any normal load. If λ ∈ (λ 1 , λ c ), where λ 1 < λ c < λ 2 the buckling‐bending problem has one or three solutions depending on the normal load. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)