Derivation of non-classical variational principles in the theory of elasticity

Ivan Hlaváček

Aplikace matematiky (1967)

  • Volume: 12, Issue: 1, page 15-29
  • ISSN: 0862-7940

Abstract

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Generalized variational principles, suggested by Hu Hai-Chang and Washizu or Hellinger and Reissner respectively, are derived on the base of complementary energy respectively. Besides, a short survey of further variational theorems, which follow from the fundamental principles, and the proof of the convergence for a method based on one of them, are presented.

How to cite

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Hlaváček, Ivan. "Derivation of non-classical variational principles in the theory of elasticity." Aplikace matematiky 12.1 (1967): 15-29. <http://eudml.org/doc/14447>.

@article{Hlaváček1967,
abstract = {Generalized variational principles, suggested by Hu Hai-Chang and Washizu or Hellinger and Reissner respectively, are derived on the base of complementary energy respectively. Besides, a short survey of further variational theorems, which follow from the fundamental principles, and the proof of the convergence for a method based on one of them, are presented.},
author = {Hlaváček, Ivan},
journal = {Aplikace matematiky},
keywords = {mechanics of solids},
language = {eng},
number = {1},
pages = {15-29},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Derivation of non-classical variational principles in the theory of elasticity},
url = {http://eudml.org/doc/14447},
volume = {12},
year = {1967},
}

TY - JOUR
AU - Hlaváček, Ivan
TI - Derivation of non-classical variational principles in the theory of elasticity
JO - Aplikace matematiky
PY - 1967
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 12
IS - 1
SP - 15
EP - 29
AB - Generalized variational principles, suggested by Hu Hai-Chang and Washizu or Hellinger and Reissner respectively, are derived on the base of complementary energy respectively. Besides, a short survey of further variational theorems, which follow from the fundamental principles, and the proof of the convergence for a method based on one of them, are presented.
LA - eng
KW - mechanics of solids
UR - http://eudml.org/doc/14447
ER -

References

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  1. Courant-Hilbert, Methoden der Mathematischen Physik I Zbl0156.23201
  2. P. Funk, Variationsrechnung und ihre Anwendung in Physik und Technik, Springer 1962, pp. 515-520. (1962) Zbl0119.09101MR0152914
  3. С. Г. Михлин, Вариационные методы в математической физике, Москва 1957. (1957) Zbl0995.90594
  4. I. Hlaváček, Sur quelques theorémes variationelles dans la théorie du fluage linéaire, Aplikace matematiky 11 (1966), 4, 283-295. (1966) Zbl0158.21406
  5. W. Prager J. L. Synge, Approximations in elasticity based on the concept of function space, Quart. Appl. Math. 5, 3 (1947), 241-269. (1947) Zbl0029.23505MR0025902
  6. Hu Hai-Chang, On some variational principles in the theory of elasticity and the theory of plasticity, Scientia Sinica 4 (1955), 1, 33-55. (1955) Zbl0066.17903
  7. K. Washizu, On the variational principles of elasticity and plasticity, ASRL TR 25-18. Massachusetts Inst. of Techn. 1955. (1955) Zbl0064.37703
  8. E. Reissner, On some variational theorems in elasticity, Problems of Continuum Mechanics, 370-381. Contributions in honor of 70th birthday of N. I. Muschelišvili, 1961. (1961) MR0122087
  9. И. H. Слезингер, Принцип Кастильяно в нелинейной теории упругости, Прикладна механіка5(1959), 1,38-44. (1959) Zbl1047.90504MR0102945
  10. Л. Айнола, О вариационной задаче Кастильяно динамики нелинейной теории упругости, Изв. АН Эстон. CCP 10 (1961), 1, сер. физ.-мат., 22-27. (1961) Zbl1160.68305
  11. С. Г. Михлин, Проблема минимума квадратного функционала, Гостехиздат 1952. (1952) Zbl1145.11324

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, Some variational principles for nonlinear elastodynamics
  3. Ivan Hlaváček, Variational principles in the linear theory of elasticity for general boundary conditions
  4. Ivan Hlaváček, Variational principles for parabolic equations
  5. Ivan Hlaváček, On Reissner's variational theorem for boundary values in linear elasticity

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