Beam bending problems on a Pasternak foundation using reciprocal variational inequalities
Author:
Noboru Kikuchi
Journal:
Quart. Appl. Math. 38 (1980), 91-108
MSC:
Primary 73T05; Secondary 49A29, 58E30, 73C20, 73K25
DOI:
https://doi.org/10.1090/qam/575834
MathSciNet review:
575834
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Abstract: The present study is concerned with a class of two-body contact problems in linear elasticity. The model problem is a bending problem of the beam resting unilaterally upon a Pasternak foundation. A variational formulation is given by the mini-max principle of the functional, and proof of the existence of saddle points is given by the compatibility condition for applied forces and moments on the beam. It has been found that the compatibility condition for equilibrium of the beam and foundation can be achieved by arguments of coerciveness of the functional on the admissible set. An approximation and example of the problem by finite element methods and a numerical method for its solution are also introduced.
- Ivar Ekeland and Roger Temam, Analyse convexe et problèmes variationnels, Dunod; Gauthier-Villars, Paris-Brussels-Montreal, Que., 1974 (French). Collection Études Mathématiques. MR 0463993
M. Fremond, Solid resting on a stratified medium, in Variational methods in engineering II, University of Southampton, 1972, pp. 8/80–8/86
- M. Boucher, Signorini’s problem in viscoelasticity, The mechanics of the contact between deformable bodies (Proc. Sympos. Internat. Union of Theoret. and Appl. Mech. (IUTAM), Enschede, 1974) Delft Univ. Press, Delft, 1975, pp. 41–53. MR 0452027
Y. C. Fung, Foundations of solid mechanics, Prentice-Hall, 1975
J. Nečas, Les méthodes directes en theorie de equations elliptiques, Masson, Paris, 1967
A. C. Keer, Elastic and viscoelastic foundation models, J, of Appl. Mech., ASME, 491–498 (1964)
I. Ekeland and R. Temam, Convex analysis and variational problems, North-Holland, American Elsevier, New York, 1976
M. Fremond, Solid resting on a stratified medium, in Variational methods in engineering II, University of Southampton, 1972, pp. 8/80–8/86
M. Boucher, Signorini’s problem in viscoelasticity, in The mechanics of the contact between deformable bodies, ed. Pater and Kalker, Delft University Press, 1975, p. 41–53
Y. C. Fung, Foundations of solid mechanics, Prentice-Hall, 1975
J. Nečas, Les méthodes directes en theorie de equations elliptiques, Masson, Paris, 1967
A. C. Keer, Elastic and viscoelastic foundation models, J, of Appl. Mech., ASME, 491–498 (1964)
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Article copyright:
© Copyright 1980
American Mathematical Society
