About DML-CZ | FAQ | Conditions of Use | Math Archives | Contact Us
  Previous |  Up |  Next

Article

First Page Preview
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. (English). Aplikace matematiky, vol. 14 (1969), issue 5, pp. 411-427
MSC: 73-35 | MR 0250538 | Zbl 0195.27003 | DOI: 10.21136/AM.1969.103249
Keywords:
mechanics of solids
Summary:
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.
Related articles:
On the existence and uniqueness of solution and some variational principles in linear theories of elasticity with couple-stresses. I: Cosserat continuum
References:
[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
Partner of
EuDML logo