Geodesic
On Reissner's variational theorem for boundary values in linear elasticity
Applications of Mathematics, Tome 16 (1971) no. 2, pp. 109-124
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E. Reissner suggested a variational theorem for the theory of elasticity, related closely to the well-known Trefftz method. In the present paper, the Reissner's theorem is discussed within the range of linear anisotropic and non-homogeneous elasticity. For the traction boundary-value problem, the minimal property of the functional and the convergence of any minimizing sequence are proved. For the displacement boundary-value problem and sime mixed problems, it is shown that a modification is necessary. Then, in case of the displacement problem, the maximal property of the functional on the modified class of admissible functions and the convergence of maximizing sequence are proved.
E. Reissner suggested a variational theorem for the theory of elasticity, related closely to the well-known Trefftz method. In the present paper, the Reissner's theorem is discussed within the range of linear anisotropic and non-homogeneous elasticity. For the traction boundary-value problem, the minimal property of the functional and the convergence of any minimizing sequence are proved. For the displacement boundary-value problem and sime mixed problems, it is shown that a modification is necessary. Then, in case of the displacement problem, the maximal property of the functional on the modified class of admissible functions and the convergence of maximizing sequence are proved.
DOI : 10.21136/AM.1971.103335
Classification : 74B05, 74B99, 74H99, 74P10, 74S30 
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Hlaváček, Ivan. On Reissner's variational theorem for boundary values in linear elasticity. Applications of Mathematics, Tome 16 (1971) no. 2, pp. 109-124. doi: 10.21136/AM.1971.103335

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[4] I. Hlaváček: Derivation of non-classical variational principles in the theory of elasticity. Aplikace matematiky 12, 1967, 1, 15-29. | MR

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[6] I. Hlaváček J. Nečas: On inequalities of Korn's type. II. Applications to linear elasticity. Archive for Ratl. Mech. Anal. 36, 1970, 312-334. | DOI | MR

[7] С. Г. Михлин: Проблема минимума квадратичного функционала. Гостехиздат, 1952. | Zbl

[8] С. Г. Михлин: Вариационные методы в математической физике. Москва 1957. | Zbl

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