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

Ivan Hlaváček; Miroslav Hlaváček

Aplikace matematiky (1969)

  • Volume: 14, Issue: 5, page 411-427
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Hlaváček, Ivan, and 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." Aplikace matematiky 14.5 (1969): 411-427. <http://eudml.org/doc/14615>.

@article{Hlaváček1969,
abstract = {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.},
author = {Hlaváček, Ivan, Hlaváček, Miroslav},
journal = {Aplikace matematiky},
keywords = {mechanics of solids},
language = {eng},
number = {5},
pages = {411-427},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
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},
url = {http://eudml.org/doc/14615},
volume = {14},
year = {1969},
}

TY - JOUR
AU - Hlaváček, Ivan
AU - Hlaváček, Miroslav
TI - 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
JO - Aplikace matematiky
PY - 1969
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 14
IS - 5
SP - 411
EP - 427
AB - 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.
LA - eng
KW - mechanics of solids
UR - http://eudml.org/doc/14615
ER -

References

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  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). (1969) MR0250537
  2. Mindlin R. D., Microstructure in linear elasticity, Arch. Ratl. Mech. and Analysis, 16 (1964), 51-78. (1964) MR0160356
  3. Toupin R. A., Theories of elasticity with couple-stresses, Arch. Ratl. Mech. and Analysis, 17 (1964), 85-112. (1964) MR0169425
  4. Ломакин В. А., Вопросы обобщенной моментной теории упругости, Вестник Моск. университета, Сер. 1, 1967, 1, 82-88. (1967) Zbl1103.35360
  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. (1968) Zbl0166.20601

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