# 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

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topHlaváček, 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

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