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On the existence and uniqueness of solution and some variational principles in linear theories of elasticity with couple-stresses. II. Mindlin's elasticity with microstructure and the first strain-gradient theory
Applications of Mathematics, Tome 14 (1969) no. 5, pp. 411-427
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A weak solution to the boundary-value problems both in the Mindlin's theory of elasticity with microstructure and in the first strain-gradient theory is defined for the statical loading of bounded, inhomogeneous and anisotropic bodies. Its existence, uniqueness and continuous dependence upon the given data is proved and the principles of minimum potential energy and minimum complementary energy are establshed.
A weak solution to the boundary-value problems both in the Mindlin's theory of elasticity with microstructure and in the first strain-gradient theory is defined for the statical loading of bounded, inhomogeneous and anisotropic bodies. Its existence, uniqueness and continuous dependence upon the given data is proved and the principles of minimum potential energy and minimum complementary energy are establshed.
DOI : 10.21136/AM.1969.103249
Classification : 73-35
Keywords: mechanics of solids 
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     title = {On the existence and uniqueness of solution and some variational principles in linear theories of elasticity with couple-stresses. {II.} {Mindlin's} elasticity with microstructure and the first strain-gradient theory},
     journal = {Applications of Mathematics},
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Hlaváček, Ivan; Hlaváček, Miroslav. On the existence and uniqueness of solution and some variational principles in linear theories of elasticity with couple-stresses. II. Mindlin's elasticity with microstructure and the first strain-gradient theory. Applications of Mathematics, Tome 14 (1969) no. 5, pp. 411-427. doi: 10.21136/AM.1969.103249

[1] Hlaváček I.., Hlaváček M.: On the existence and uniqueness of solution and some variational principles in linear theories of elasticity with couple-stresses. I. Cosserat continuum. Aplikace matematiky 14 (1969). | MR

[2] Mindlin R. D.: Microstructure in linear elasticity. Arch. Ratl. Mech. and Analysis, 16 (1964), 51-78. | DOI | MR

[3] Toupin R. A.: Theories of elasticity with couple-stresses. Arch. Ratl. Mech. and Analysis, 17 (1964), 85-112. | DOI | MR

[4] Ломакин В. А.: Вопросы обобщенной моментной теории упругости. Вестник Моск. университета, Сер. 1, 1967, 1, 82-88. | Zbl

[5] Mindlin R. D., Eshel N. N.: On first strain-gradient theories in linear elasticity. Int. Jour. Solids and Structures, 4 (1968), 1, 75-95. | Zbl

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