Variational principles in the linear theory of elasticity for general boundary conditions

Ivan Hlaváček

Aplikace matematiky (1967)

  • Volume: 12, Issue: 6, page 425-448
  • ISSN: 0862-7940

Abstract

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Mixed boundary-value problem of the classical theory of elasticity is considered, where not only displacements and tractions are prescribed on some parts of the boundary, but also conditions of contact and elastic supports for normal and tangential directions to the boundary surface separately. Classical variational principles are derived using functional analysis methods, especially methods of Hilbert space. Furthermore, generalized variational principles and bilateral estimates of errors are suggested.

How to cite

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Hlaváček, Ivan. "Variational principles in the linear theory of elasticity for general boundary conditions." Aplikace matematiky 12.6 (1967): 425-448. <http://eudml.org/doc/14503>.

@article{Hlaváček1967,
abstract = {Mixed boundary-value problem of the classical theory of elasticity is considered, where not only displacements and tractions are prescribed on some parts of the boundary, but also conditions of contact and elastic supports for normal and tangential directions to the boundary surface separately. Classical variational principles are derived using functional analysis methods, especially methods of Hilbert space. Furthermore, generalized variational principles and bilateral estimates of errors are suggested.},
author = {Hlaváček, Ivan},
journal = {Aplikace matematiky},
keywords = {mechanics of solids},
language = {eng},
number = {6},
pages = {425-448},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Variational principles in the linear theory of elasticity for general boundary conditions},
url = {http://eudml.org/doc/14503},
volume = {12},
year = {1967},
}

TY - JOUR
AU - Hlaváček, Ivan
TI - Variational principles in the linear theory of elasticity for general boundary conditions
JO - Aplikace matematiky
PY - 1967
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 12
IS - 6
SP - 425
EP - 448
AB - Mixed boundary-value problem of the classical theory of elasticity is considered, where not only displacements and tractions are prescribed on some parts of the boundary, but also conditions of contact and elastic supports for normal and tangential directions to the boundary surface separately. Classical variational principles are derived using functional analysis methods, especially methods of Hilbert space. Furthermore, generalized variational principles and bilateral estimates of errors are suggested.
LA - eng
KW - mechanics of solids
UR - http://eudml.org/doc/14503
ER -

References

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  1. E. Reissner, Some variational principles in elasticity, О некоторых вариационных теоремах теории упругости. Проблемы механики сплошной среды, Издат. АН СССР, 1961, 328-337. (1961) MR0096419
  2. К. Ф. Черных, Линейная теория оболочек, ч. II., гл. IX. Издат. Ленингр. унив., 1964. (1964) Zbl1117.65300
  3. С. Г. Михлин, Проблема минимума квадратичного функционала, Москва 1952, гл. IV. (1952) Zbl1145.11324
  4. С. Г. Михлин, Вариационные методы в математической физике, Москва 1957. (1957) Zbl0995.90594
  5. W. S. Dorn A. Schild, A converse to the virtual work theorem for deformable solids, Quart. Appl. Math., 14 (1956), 209-213. (1956) Zbl0074.19201MR0079418
  6. M. E. Gurtin, 10.1007/BF01262691, Arch. Ratl. Mech. Anal., 13 (1963), 3, 179-191. (1963) Zbl0123.40803MR0214321DOI10.1007/BF01262691
  7. O. D. Kellog, Foundations of Potential Theory, Springer, Berlin 1929. (1929) MR0222317
  8. Hu Hai-Chang, On some variational principles in the theory of elasticity and the theory of plasticity, Sci. Sinica 4 (1955) 1, 33. (1955) Zbl0066.17903
  9. J. Nečas, Les méthodes directes en théorie des équations elliptiques, Academia, Prague 1967. (1967) MR0227584
  10. J. Nečas, Sur les normes équivalentes dans W p ( k ) ( Ω ) et sur la coercitivité des formes formellement positives, Les presses de l'Université de Montreal, Janvier 1966, 102-128. (1966) 
  11. I. Hlaváček, Derivation of nonclassical variational principles in the theory of elasticity, Aplikace matematiky 12 (1967), 1, 15 - 29. (1967) Zbl0163.19201MR0214324
  12. J. Nečas I. Hlaváček, On inequalities of Korn's type. I. General theory. II. Applications in elasticity, To appear in Arch. Ratl. Mech. Anal. Zbl0193.39002

Citations in EuDML Documents

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  1. Ivan Hlaváček, Miroslav Hlaváček, On the existence and uniqueness of solution and some variational principles in linear theories of elasticity with couple-stresses. I: Cosserat continuum
  2. Ivan Hlaváček, Variational principles for parabolic equations
  3. Rolf Hünlich, Joachim Naumann, On general boundary value problems and duality in linear elasticity. II
  4. Ivan Hlaváček, On Reissner's variational theorem for boundary values in linear elasticity
  5. Rolf Hünlich, Joachim Naumann, On general boundary value problems and duality in linear elasticity. I
  6. Ivan Hlaváček, Convergence of an equilibrium finite element model for plane elastostatics
  7. Jaroslav Haslinger, Ivan Hlaváček, Convergence of a finite element method based on the dual variational formulation
  8. Miroslav Vondrák, Slab analogy in theory and practice of conforming equilibrium stress models for finite element analysis of plane elastostatics

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