On the extreme variational principles for nonlinear elastic plates
Author:
Yang Gao
Journal:
Quart. Appl. Math. 48 (1990), 361-370
MSC:
Primary 73V25; Secondary 73C50, 73G05, 73K10
DOI:
https://doi.org/10.1090/qam/1052141
MathSciNet review:
MR1052141
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Abstract: The min-maximum variational principles for Von Karman plates are formulated by using the theory of convex analysis. It is shown that the global extremum criteria for both the total potential and complementary variational functional is directly related to a so-called dual gap function. The existence and uniqueness of the variational solutions are proved. And the saddle point condition of the generalized variational principle is also discussed.
- Satya N. Atluri, Alternate stress and conjugate strain measures, and mixed variational formulations involving rigid rotations, for computational analyses of finitely deformed solids, with application to plates and shells. I. Theory, Comput. & Structures 18 (1984), no. 1, 93–116. MR 721721, DOI https://doi.org/10.1016/0045-7949%2884%2990085-3
- W. R. Bielski and J. J. Telega, A note on duality for von Kármán plates in the case of the obstacle problem, Arch. Mech. (Arch. Mech. Stos.) 37 (1985), no. 1-2, 135–141. MR 829830
- Philippe G. Ciarlet and Patrick Rabier, Les équations de von Kármán, Lecture Notes in Mathematics, vol. 826, Springer, Berlin, 1980 (French). MR 595326
- Yang Gao and Gilbert Strang, Geometric nonlinearity: potential energy, complementary energy, and the gap function, Quart. Appl. Math. 47 (1989), no. 3, 487–504. MR 1012271, DOI https://doi.org/10.1090/qam/1012271
- Yang Gao and Gilbert Strang, Dual extremum principles in finite deformation elastoplastic analysis, Acta Appl. Math. 17 (1989), no. 3, 257–267. MR 1040379, DOI https://doi.org/10.1007/BF00047073
- Yang Gao, Opposite principles in nonlinear conservative systems, Adv. in Appl. Math. 10 (1989), no. 3, 370–377. MR 1008563, DOI https://doi.org/10.1016/0196-8858%2889%2990021-3
- Yang Gao and Y. K. Cheung, On the extremum complementary energy principles for nonlinear elastic shells, Internat. J. Solids Structures 26 (1990), no. 5-6, 683–693. MR 1049287, DOI https://doi.org/10.1016/0020-7683%2890%2990039-X
- Ivar Ekeland and Roger Temam, Analyse convexe et problèmes variationnels, Dunod; Gauthier-Villars, Paris-Brussels-Montreal, Que., 1974 (French). Collection Études Mathématiques. MR 0463993
- Yang Gao and Tomasz Wierzbicki, Bounding theorem in finite plasticity with hardening effect, Quart. Appl. Math. 47 (1989), no. 3, 395–403. MR 1012265, DOI https://doi.org/10.1090/qam/1012265
S. N. Atluri, Alternate stress and conjugate strain measures and mixed variational formulations involving rigid rotations, for computational analysis of finitely deformed solids, with applications to plates and shells. I, Comput. & Structures 18 (1), 93–116 (1983)
W. R. Bielski and J. J. Telega, A note on duality for Von Kármán plates in the case of the obstacle problem, Arch. Mech. 37 (1), 135–141 (1985)
P. G. Ciarlet and P. Rabier, Les Equations de Von Kármán, Lecture Notes in Mathematics, Vol. 826, Springer—Verlag, Berlin, 1980
Yang Gao and Gilbert Strang, Geometrical nonlinearity: Potential energy, complementary energy and the gap function, 17th IUTAM, Grenoble, France, 1988, Quart. Appl. Math. 47 (3), 487–504 (1989)
Yang Gao and Gilbert Strang, Dual extremum principles in finite deformation elastoplatic analysis, to appear in Acta Appl. Math., (1990)
Yang Gao, Opposite principles in nonlinear conservative systems, Adv. in Appl. Math. 10 (3), 370–377 (1989)
Yang Gao and Y. K. Cheung, On the extremum complementary energy principles for nonlinear elastic shells, Internat. J. Solids and Structures 26 (1990)
I. Ekeland and R. Temam, Convex Analysis and Variational Problems, North-Holland, Amsterdam, 1976
Yang Gao and T. Wierzbicki, Bounding theorem in finite plasticity with hardening effect, Quart. Appl. Math. 47 (3), 395–403 (1989)
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Article copyright:
© Copyright 1990
American Mathematical Society