Some applications of the singular perturbation method to the bending problems of thin plates and shells

1984 ◽  
Vol 5 (4) ◽  
pp. 1449-1457 ◽  
Author(s):  
Chou Huan-wen
Keyword(s):  
Singular Perturbation ◽  
Perturbation Method ◽  
Thin Plates ◽  
Singular Perturbation Method ◽  
Plates And Shells ◽  
Bending Problems ◽  
Thin Plates And Shells

A New Rate Principle Suitable for Analysis of Inelastic Deformation of Plates and Shells

1985 ◽  
Vol 52 (3) ◽  
pp. 533-535 ◽  
Author(s):  
S. Mukherjee ◽  
F. G. Kollmann
Keyword(s):  
Variational Principle ◽  
Linear Elasticity ◽  
Inelastic Deformation ◽  
Thin Plates ◽  
Independent Functions ◽  
Rate Form ◽  
Plates And Shells ◽  
Thin Plates And Shells

A variational principle for linear elasticity, using displacements and strains as independent functions, is presented in this paper. An extension of this principle in rate form is claimed to be extremely useful for the analysis of inelastic deformation of thin plates and shells.

Radiation conditions for a semi-infinite elastic strip

2005 ◽  
Vol 461 (2056) ◽  
pp. 1163-1179 ◽  
Author(s):  
E Babenkova ◽  
J Kaplunov
Keyword(s):  
High Frequency ◽  
Thin Plates ◽  
Elastic Strip ◽  
Resonance Frequencies ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Plates And Shells ◽  
High Frequency Vibrations ◽  
Thin Plates And Shells ◽  
Radiation Conditions

High-frequency vibrations of a semi-infinite elastic strip with traction-free faces are considered. The conditions on end data that are derived do not allow non-radiating in Sommerfeld's sense of polynomial modes at thickness resonance frequencies. These represent a high-frequency analogue of the well-known decay conditions in statics that agree with the classical Saint-Venant principle. The proposed radiation conditions are applied to the construction of boundary conditions in the theories of high-frequency long-wave vibrations describing slow-varying motions in the vicinity of thickness resonance frequencies. The derivation is based on the Laplace transform technique along with the asymptotic methodology that is typical for thin plates and shells.

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