Linear approximation in Continuum Mechanics

Giuseppe Grioli

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1994)

  • Volume: 5, Issue: 3, page 273-281
  • ISSN: 1120-6330

Abstract

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Some critical remarks are made about the theory of Linear Elasticity, questioning on its validity in general. An alternative linear approximation of the exact theory is proposed.

How to cite

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Grioli, Giuseppe. "Linear approximation in Continuum Mechanics." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 5.3 (1994): 273-281. <http://eudml.org/doc/244326>.

@article{Grioli1994,
abstract = {Some critical remarks are made about the theory of Linear Elasticity, questioning on its validity in general. An alternative linear approximation of the exact theory is proposed.},
author = {Grioli, Giuseppe},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Continuum mechanics; Mathematical theory of elasticity; Mathematical physics},
language = {eng},
month = {9},
number = {3},
pages = {273-281},
publisher = {Accademia Nazionale dei Lincei},
title = {Linear approximation in Continuum Mechanics},
url = {http://eudml.org/doc/244326},
volume = {5},
year = {1994},
}

TY - JOUR
AU - Grioli, Giuseppe
TI - Linear approximation in Continuum Mechanics
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1994/9//
PB - Accademia Nazionale dei Lincei
VL - 5
IS - 3
SP - 273
EP - 281
AB - Some critical remarks are made about the theory of Linear Elasticity, questioning on its validity in general. An alternative linear approximation of the exact theory is proposed.
LA - eng
KW - Continuum mechanics; Mathematical theory of elasticity; Mathematical physics
UR - http://eudml.org/doc/244326
ER -

References

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  1. SIGNORINI, A., Sulle deformazioni termoelastiche finite. Proc. 3rd Int. Cong. Appl. Mech., 2, 1930, 80-89. Zbl0003.03203JFM57.1080.05
  2. SIGNORINI, A., Trasformazioni termoelastiche finite. Ann. Mat. Pura e Applicata, IV, 30, 1949, 1-72. Zbl0036.39502MR35616
  3. STOPPELLI, F., Sulla sviluppabilità in serie di potenze di un parametro delle soluzioni delle equazioni dell'elastostatica isoterma. Ricerche Mat., 4, 1955, 58-73. Zbl0067.41503MR75761
  4. GRIOLI, G., Mathematical Theory of Elastic Equilibrium (Recent Results). Springer-Verlag, 1962. Zbl0102.17004MR154463
  5. CAPRIZ, G. - PODIO GUIDUGLI, P., On Signorini's perturbation method in finite elasticity. Arch. Rational Mech. An., 57, 1974, 1-30. Zbl0315.73062MR368543
  6. BARATHA, S. - LEVINSON, M., Signorini's perturbation scheme for a general reference configuration in finite elastostatics. Arch. Rational Mech. An., 67, 1977, 365-394. Zbl0389.73022
  7. BRILLA, J., The Compatible Perturbation Method in Viscoelasticity. Symposium at Kozubnik, Poland, Pitman, 1977 
  8. CAPRIZ, G. - PODIO GUIDUGLI, P., The role of Fredholm conditions in Signorini's perturbation method. Arch. Rational Mech. An., 70, 1979, 261-288. Zbl0433.73035MR553619DOI10.1007/BF00280537
  9. GRIOLI, G., Mathematical problems in elastic equilibrium with finite deformation. Applicable Analysis, 1983. Zbl0497.73042MR710189DOI10.1080/00036818308839445
  10. GRIOLI, G., Asymptotic structures and internal constraints in continuum mechanics. In: P. E. RICCI (ed.), Atti del Simposio Intemazionale: Problemi attuali dell'Analisi e della Fisica Matematica (Taormina, 15-17 ottobre 1992). Dip. di Mat. Univ. di Roma «La Sapienza»1993. Zbl0796.73017MR1249091

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