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Some remarks on Saint‐Venant's principle
Author(s) -
Levine H. A.,
Quintanilla R.,
Payne L. E.
Publication year - 1989
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670110105
Subject(s) - mathematics , hyperelastic material , exponential function , exponential growth , exponential decay , exponential stability , cylinder , mathematical analysis , calculus (dental) , geometry , physics , thermodynamics , finite element method , medicine , nonlinear system , quantum mechanics , nuclear physics , dentistry
Abstract We consider a three‐dimensional hyperelastic cylinder in Ω = D × [0, ∞]. We study the asymptotic behaviour of the deformations of the cross‐sections in an equilibrium state. In this case we show that the solutions either have exponential decay or exponential growth. We give some initial conditions such that the latter case occurs.