On the existence and uniqueness of solution and some variational principles in linear theories of elasticity with couple-stresses. I: Cosserat continuum

Ivan Hlaváček; Miroslav Hlaváček

Aplikace matematiky (1969)

  • Volume: 14, Issue: 5, page 387-410
  • ISSN: 0862-7940

Abstract

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A weak (generalized) solution to the boundary-value problems in Cosserat continuum is defined. Its existence, uniqueness and continuous dependence upon the given data is proved for the statical loading of bounded, inhomogeneous and anisotropic bodies. Principles of minimum potential energy, of minimum complementary energy and some generalized variational principles are established.

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. I: Cosserat continuum." Aplikace matematiky 14.5 (1969): 387-410. <http://eudml.org/doc/14614>.

@article{Hlaváček1969,
abstract = {A weak (generalized) solution to the boundary-value problems in Cosserat continuum is defined. Its existence, uniqueness and continuous dependence upon the given data is proved for the statical loading of bounded, inhomogeneous and anisotropic bodies. Principles of minimum potential energy, of minimum complementary energy and some generalized variational principles are established.},
author = {Hlaváček, Ivan, Hlaváček, Miroslav},
journal = {Aplikace matematiky},
keywords = {mechanics of solids},
language = {eng},
number = {5},
pages = {387-410},
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. I: Cosserat continuum},
url = {http://eudml.org/doc/14614},
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. I: Cosserat continuum
JO - Aplikace matematiky
PY - 1969
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 14
IS - 5
SP - 387
EP - 410
AB - A weak (generalized) solution to the boundary-value problems in Cosserat continuum is defined. Its existence, uniqueness and continuous dependence upon the given data is proved for the statical loading of bounded, inhomogeneous and anisotropic bodies. Principles of minimum potential energy, of minimum complementary energy and some generalized variational principles are established.
LA - eng
KW - mechanics of solids
UR - http://eudml.org/doc/14614
ER -

References

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  1. Nečas J., Les méthodes directes en théorie des equations elliptiques, Academia, Prague 1967. (1967) MR0227584
  2. Hlaváček I., Nečas J., On inequalities of Korn's type, (to appear in Arch. Ratl. Mech. Anal. (1969)). (1969) 
  3. Hlaváček I., Derivation of non-classical variational principles in the theory of elasticity, Aplikace matematiky 12 (1967), 1, 15 - 29. (1967) MR0214324
  4. Hlaváček I., Variational principles in the linear theory of elasticity for general boundary conditions, Aplikace matematiky 12 (1967), 6, 425 - 448. (1967) MR0231575
  5. Eringen A. C., Linear theory of micropolar elasticity, Jour. Math. and Mech., 15 (1966), 6, 909-923. (1966) Zbl0145.21302MR0198744
  6. Палмов В. А., Основные уравнения теории несимметричной упругости, Приклад, мат. мех., 28 (1964), 3, 401. (1964) Zbl1117.65300
  7. Neuber H., On the general solution of linear-elastic problems in isotropic and anisotropic Cosserat continua, Applied Mechanics, Proceedings of the 11-th international congress of Appl. Mech., Munich, 1964. (1964) 

Citations in EuDML Documents

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  1. D. Ieșan, On the second boundary value problem in the linear ștheory of micropolar elasticity
  2. Ivan Hlaváček, Miroslav Hlaváček, 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
  3. Josip Tambača, Igor Velčić, Semicontinuity theorem in the micropolar elasticity
  4. Ivan Hlaváček, Michal Křížek, On a superconvergent finite element scheme for elliptic systems. I. Dirichlet boundary condition
  5. Josip Tambača, Igor Velčić, Existence theorem for nonlinear micropolar elasticity

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