A new approach of Timoshenko's beam theory by asymptotic expansion method
Trabucho, L. ; Viaño, J. M.
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 24 (1990), p. 651-680 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{M2AN_1990__24_5_651_0,
     author = {Trabucho, L. and Via\~no, J. M.},
     title = {A new approach of Timoshenko's beam theory by asymptotic expansion method},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {24},
     year = {1990},
     pages = {651-680},
     mrnumber = {1076964},
     zbl = {0777.73028},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_1990__24_5_651_0}
}

Trabucho, L.; Viaño, J. M. A new approach of Timoshenko's beam theory by asymptotic expansion method. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 24 (1990) pp. 651-680. http://gdmltest.u-ga.fr/item/M2AN_1990__24_5_651_0/

[1] I. Aganovic,Z. Tutek, A justification of the one-dimensional model of elastic beam. Math. Methods in Applied Sci., 8, 1986, pp. 1-14. | MR 870989 | Zbl 0603.73056

[2] A. Bermudez,J. M. Viaño, Une justification des équations de la thermoélasticite des poutres à section variable par des méthodes asymptotiques, RAIRO, Analyse Numérique, 18, 1984, pp. 347-376. | Numdam | MR 761673 | Zbl 0572.73053

[3] F. Brezzi, On the existence uniqueness and approximation of saddle point problems arising from Lagrange multipliers. RAIRO, Analyse Numérique, Sér Rouge, 2, 1974, pp. 129-151. | Numdam | MR 365287 | Zbl 0338.90047

[4] D. Caillerie, The effect of a thin inclusion of high rigidity in a elastic body, Math. Methods in Applied Sci., 2, 1980, pp 251-270. | MR 581205 | Zbl 0446.73014

[5] P. G. Ciarlet, A justification of the von Karman equations. Arch. Rat. Mcch. Anal., 73, 1980, pp 349-389 | MR 569597 | Zbl 0443.73034

[6] P. G. Ciarlet, « Recent progress in the two-dimensional approximation of three-dimensional plate models in nonlinear elasticity» In Numerical Approximation of Partial Differential Equations E. L. Ortiz, Editor, North-Holland, Amsterdam, 1987, pp 3-19. | MR 899776 | Zbl 0612.73060

[7] P. G. Ciarlet, P. Destuynder, A justification of the two dimensional linear plate model. J. Mécanique, 18, 1979, pp 315-344. | MR 533827 | Zbl 0415.73072

[8] P. G. Ciarlet, P. Destuynder, A justification of a nonlinear model in place theory. Comp. Methods Appl. Mech. Engrg. 17/18, 1979, pp. 227-258. | MR 533827 | Zbl 0405.73050

[9] A. Cimetière, G. Geymonat,H. Ledret, A. Raoult,Z. Tutek, Une dérivation d'un modèle non lineaire de poutres à partir de l'élasticite tridimensionelle. C. R. A. S., tome 302, Sér. I, n° 19, 1986, pp. 697-700. | MR 847757 | Zbl 0593.73046

[10] P. Destuynder, Sur une justification des modèles de plaques et de coques par les méthodes asymptotiques. Thèse, Univ. P. et M. Curie, Paris, 1980.

[11] P. Destuynder, Une théorie asymptotique de plaque minces en élasticité lineaire. Masson, Paris, 1986. | MR 830660 | Zbl 0627.73064

[12] G. Duvaut,J. L. Lions, Inequalities in Mechanics and Physics. Springer-Verlag, Berlin, 1976. | MR 521262 | Zbl 0331.35002

[13] C. Dym, I. Shames, Solid Mechanics, A variational approch. McGraw-Hill, New York, 1973.

[14] B. M. Fraejis De Veubeke, A course in elasticity Applied Mathematical Sciences, Vol. 29, Springer-Verlag, Berlin, 1979. | MR 533738 | Zbl 0419.73001

[15] Y. C. Fung, Foundations of Solid Mechanics Prentice-Hall, Englewood Cliffs, N. J., 1965.

[16] I. Hlavacek, J. Necas, Mathematical Theory of Elastic and Elasto-Plastic Bodies; An Introduction Elsevier, New York, 1981. | MR 600655 | Zbl 0448.73009

[17] J. L. Lions, Perturbations singulières dans les problèmes aux limites et en contrôle optimal Lect. Notes in Math., 323, Springer-Verlag, Berlin, 1973. | MR 600331 | Zbl 0268.49001

[18] R. D. Mindlin, Influence of rotary inertia and shear on flexural motions of isotropic elastic plates. J. Appl. Mech., 18, 1951, pp. 31 38. | Zbl 0044.40101

[19] A. Raoult, Construction d'un modèle d'évolution de plaques avec terme d'inertie de rotation. Annali di Mathematica Pura ad Applicata, 139, 1985, pp. 361-400. | MR 798182 | Zbl 0596.73033

[20] A. Rigolot, Sur une théorie asymptotique des poutres. Thèse, Univ. P. et M. Curie, Paris, 1976.

[21] A. Rigolot, Sur une théorie asymtotique des poutres. J. Mécanique, 11, 1972, pp. 673-703. | MR 368552 | Zbl 0257.73013

[22] A. Rigolot, Sur la déformation due à l'effort tranchant dans les poutres droites élastiques. Ann. Inst. Techn. Bât. Trav. Publ., n° 363, 1978, pp 34-52.

[23] S. P. Timoshenko, On the correction for shear of the differential equation for transverse vibration of prismatic bars. Phil Mag, Ser 6, 41, 1921, pp 744-746.

[24] L. Trabucho,J. M. Viano, « Derivation of generalized models for linear elastic beams by asymptotic expansion methods » In Applications of Multiple Scaling to Mechanics (P. G. Ciarlet and E. Sanchez-Palencia, Editors), Masson, Paris, 1987, pp 302-315. | MR 902000 | Zbl 0646.73024

[25] L. Trabucho, J. M. Viano, Dérivation de modèles généralisés de poutres en élasticité par méthode asymptotique. C. R. Acad. Sc. Paris, tome 304, Ser I, n° 11, 1987. | MR 886729 | Zbl 0627.73015

[26] L. Trabucho,J. M. Viano , Existence and characterization of higher order terms in an asymptotic expansion method for linearized elastic beams. J. Asymptotic Analysis, 2, 1989, pp. 223-255. | MR 1020349 | Zbl 0850.73126

[27] L. Trabucho, J. M. Viaño, A dérivation of generalized Saint Venat's torsion theory from three dimensional elasticity by asymptotic expansion methods. J. Applicable Analysis, 31, 1988, pp 129-148. | MR 1017507 | Zbl 0637.73003

[28] L. Trabucho, J. M. Viaño, A justification of Vlasov s bending-torsion theory in elastic beams (to appear).

[29] L. Trabucho, J. M. Viaño, Critical cross sections in Timoshenko's beam theory (to appear).

[30] J. M. Viaño, Contribution à l'étude des modèles bidimensionels en thermoélasticité de plaques d'épaisseur non constante. Thèse, Univ. P. et M. Curie, Paris, 1983.

[31] J. M. Viaño, « Generalizacion y justificacion de modelos unilaterales en vigas elàsticas sobre fundacion » In. Actas del VIII C. E. D. Y. A., Santander, España, 1985.