Some variational principles for nonlinear elastodynamics

Ivan Hlaváček

Aplikace matematiky (1967)

  • Volume: 12, Issue: 2, page 107-118
  • ISSN: 0862-7940

Abstract

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Three variational principles of linear elastodynamics for two initial conditions, recentrly established by M. R. Gurtin, are extended to nonlinear problems with large elastic deformations.

How to cite

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Hlaváček, Ivan. "Some variational principles for nonlinear elastodynamics." Aplikace matematiky 12.2 (1967): 107-118. <http://eudml.org/doc/14459>.

@article{Hlaváček1967,
abstract = {Three variational principles of linear elastodynamics for two initial conditions, recentrly established by M. R. Gurtin, are extended to nonlinear problems with large elastic deformations.},
author = {Hlaváček, Ivan},
journal = {Aplikace matematiky},
keywords = {mechanics of solids},
language = {eng},
number = {2},
pages = {107-118},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some variational principles for nonlinear elastodynamics},
url = {http://eudml.org/doc/14459},
volume = {12},
year = {1967},
}

TY - JOUR
AU - Hlaváček, Ivan
TI - Some variational principles for nonlinear elastodynamics
JO - Aplikace matematiky
PY - 1967
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 12
IS - 2
SP - 107
EP - 118
AB - Three variational principles of linear elastodynamics for two initial conditions, recentrly established by M. R. Gurtin, are extended to nonlinear problems with large elastic deformations.
LA - eng
KW - mechanics of solids
UR - http://eudml.org/doc/14459
ER -

References

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  1. M. E. Gurtin, Variational Principles for Linear Elastodynamics, Archive for Rat. Mech. Anal. 16, 1, 34-50 (1964). (1964) Zbl0124.40001MR0214322
  2. W. Prager, Einführung in die Kontinuumsmechanik, Birkhäuser Verlag 1961. (1961) Zbl0094.18601MR0126973
  3. Л. Aйнола, О вариционной задаче Кастильяно динамики нелинейной теории упругости, Изв. АН Эстон. CCP, т. X, сер. физ.-мат н. 1, 22-27 (1961). (1961) Zbl0995.90569
  4. Yi Yuan Yu, 10.1121/1.1918921, J. Acoust. Soc. America, 36, 1, 111-120 (1964). (1964) MR0164502DOI10.1121/1.1918921
  5. O. D. Kellog, Foundations of Potential Theory, Springer, Berlin 1929. (1929) MR0222317
  6. Л. M. Качанов, Теория ползучести, Москва 1960. (1960) Zbl1004.90500
  7. Нu Hai Chang, On some variational principles in the theory of elasticity and plasticity, Scientia Sinica 4, 1, 33 (1955). (1955) 
  8. K. Washizu, On the variational principles of elasticity and plasticity, ASRL TR 25 - 18. Massachusetts Institute of Technology (1955). (1955) Zbl0064.37703
  9. E. Reissner, О некоторых вариационных теоремах теории упругости, Проблемы механики сплошной среды (к 70-летию ак. H. И. Мусхелишвили), Москва 1961, 328 - 337. (1961) Zbl0134.44402
  10. E. Hellinger, Die allgemeinen Ansätze der Mechanik der Kontinua, Enzyklopädie der Mathematischen Wissenschaften, 4, parts 4 & 5 (1914). (1914) Zbl45.1012.01
  11. I. Hlaváček, Derivation of non-classical variational principles in the theory of elasticity, Aplikace matematiky 12 (1967), 1, 15 - 29. (1967) Zbl0163.19201MR0214324

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