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mechanics of solids
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.
[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 0250537
[2] Mindlin R. D.: Microstructure in linear elasticity. Arch. Ratl. Mech. and Analysis, 16 (1964), 51-78. DOI 10.1007/BF00248490 | MR 0160356
[3] Toupin R. A.: Theories of elasticity with couple-stresses. Arch. Ratl. Mech. and Analysis, 17 (1964), 85-112. DOI 10.1007/BF00253050 | MR 0169425
[4] Ломакин В. А.: Вопросы обобщенной моментной теории упругости. Вестник Моск. университета, Сер. 1, 1967, 1, 82-88. Zbl 1103.35360
[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 0166.20601
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