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Keywords:
deformation theory of plasticity; physically nonlinear elasticity; uncertain data
deformation theory of plasticity; physically nonlinear elasticity; uncertain data
Summary:
Maximization problems are formulated for a class of quasistatic problems in the deformation theory of plasticity with respect to an uncertainty in the material function. Approximate problems are introduced on the basis of cubic Hermite splines and finite elements. The solvability of both continuous and approximate problems is proved and some convergence analysis presented.
References:
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[2] Hlaváček, I.: Reliable solutions of elliptic boundary value problems with respect to uncertain data. (to appear). MR 1602891
[3] Kačanov, L. M.: Mechanics of plastic materials. Moscow, 1948. (Russian)
[4] Langenbach, A.: Monotone Potentialoperatoren in Theorie und Anwendung. VEB Deutscher Verlag der Wissenschaften, Berlin, 1976. MR 0495530 | Zbl 0387.47037
[5] Nečas, J. – Hlaváček, I.: Mathematical Theory of Elastic and Elasto-Plastic Bodies: An Introduction. Elsevier, Amsterdam, 1981.
[6] Nečas, J. – Hlaváček, I.: Solution of Signorini’s contact problem in the deformation theory of plasticity by secant modules method. Apl. Mat. 28 (1983), 199–214. MR 0701739
[7] Nečas, J.: Les méthodes directes en théorie des équations elliptiques. Academia, Prague, 1967. MR 0227584
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