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An energy identity in physically nonlinear elasticity and error estimates of the plate equations. (English. Russian original) Zbl 0363.73049

J. Appl. Math. Mech. 40, 291-301 (1976); translation from Prikl. Mat. Mekh. 40, 317-326 (1976).

MSC:

74S30 Other numerical methods in solid mechanics (MSC2010)
74K20 Plates
74B20 Nonlinear elasticity
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References:

[1] Prager, W.; Synge, J. L., Approximations in elasticity based on the concept of function space, Quart. Appl. Math., Vol. 5, N≗ 3 (1947) · Zbl 0029.23505
[2] Synge, J. L., The hypercircle in Mathmatical Physics (1957), Cambridge Univ. Press · Zbl 0079.13802
[3] Koiter, W. T., On the foundations of the linear theory of thin elastic shells, (Proc. Koninkl. Nederl. Acad. Wet., B, Vol. 73 (1970)), N≗ 3 · Zbl 0213.27002
[4] Koiter, W. T., On the mathematical foundation of shell theory, (Actes Congrès Internat. mathém., Vol. 3 (1971), Gautier-Villars: Gautier-Villars Paris) · Zbl 0232.73094
[5] Morgenstern, D., Herleitungeder Plattentheorie aus der dreidimensionalen Elastizitäts Theorie, Arch Rational Mech. and Analysis, Vol. 4, N≗ 2 (1959) · Zbl 0126.20605
[6] Berdichevskii, V. L., An energy inequality in the theory of plate bending, PMM, Vol. 37, N≗ 5 (1973) · Zbl 0158.46505
[7] Shoikhet, B. A., On asymptotically exact equations of thin plates of complex structure, PMM, Vol. 37, N≗ 5 (1973) · Zbl 0297.73010
[8] Kauderer, G., Nonlinear Mechanics (1961), Izd. Inostr. Lit: Izd. Inostr. Lit Moscow
[9] Ioffe, A. D.; Tikhomirov, V. M., Duality of convex functions and extremal problems, Uspekhi Matem. Nauk, Vol. 23, N≗ 6 (1968) · Zbl 0191.13101
[10] Lagenbach, A., On some nonlinear operators of elasticity theory in Hubert space, (Ser. Matem., Mekhan., Astron., N≗ 1 (1961), Vestnik Leningard Univ), Issue 1
[11] Dinca, G., Sur la monotonie d’après Minty-Browder de l’opérateur de la théorie de plasticité, C. R. Acad. Sci. Paris, Ser. A et B, Vol. 269, N≗ 13 (1969) · Zbl 0185.53604
[12] Skrypnik, I. V., Nonlinear Higher Order Elliptic Equations (1973), Naukova Dumka: Naukova Dumka Kiev · Zbl 0296.35032
[13] Vainberg, M. M., Variational Method and Method of Monotonic Operators in Nonlinear Equation Theory (1972), Nauka: Nauka Moscow
[14] Lagenbach, A., Elastisch-Plastische Deformationen von Platten, Z. angew. Math, und Mech., Vol. 41, N≗ 3 (1961) · Zbl 0104.41004
[15] Sobolev, S. L., (Applications of Functional Analysis in Mathematical Physics, Vol. N≗ 7 (1963), American Math. Society: American Math. Society Providence R. I), (English translation) · Zbl 0123.09003
[16] Nečas, J., Sur la régularité des solutions faibles des équations elliptiques non-linéaires, Comment. Math. Univ., Carolinae, Vol. 9, N≗ 3 (1968) · Zbl 0167.10904
[17] Agmon, S.; Douglis, A.; Nirenberg, L., Estimates near the Boundary of Solutions of Elliptic Partial Differential Equations with General Boundary Conditions (1962), Izd. Inostr. Lit: Izd. Inostr. Lit Moscow · Zbl 0104.32305
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