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Convergence of eigenvalue solution in conforming plate bending finite elements
Author(s) -
Lynn Paul P.,
Dhillon Balaur S.
Publication year - 1972
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620040208
Subject(s) - finite element method , eigenvalues and eigenvectors , mathematics , convergence (economics) , bending of plates , plate theory , vibration , isoperimetric inequality , displacement (psychology) , mathematical analysis , rate of convergence , bending , structural engineering , computer science , boundary value problem , physics , engineering , psychology , computer network , channel (broadcasting) , quantum mechanics , economics , psychotherapist , economic growth
The convergence proof of plate eigenvalue solution from conforming displacement finite elements is presented. The analysis is based on converting a thick plate free vibration problem in to a corresponding isoperimetric variational problem. A conforming thick, plate element is used to illustrate the mathematical development. On the basis of the derived asymptotic rate of convergence of the approximate eigenvalues, the authors propose a practical method of improving the numerical solutions. Extension of the mathematical proof to cover classical thin plate finite elements is briefly discussed.