Une justification des équations de la thermoélasticité des poutres à section variable par des méthodes asymptotiques

Bermúdez, Alfredo; Viaño, J. M.

doi:10.1051/m2an/1984180403471

Cited by 79 publications

(51 citation statements)

References 2 publications

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“…Applications of this method in solid mechanics were done, for example, by Caillerie [4], Ciarlet-Destuynder [7,8], Destuynder [10,11], Raoult [19] and Viaiio [30] in order to justify the classical models in plate bending. The study of the linearized theory of beam bending by this method, was already introduced in Rigolot [20,21] and it was continued in Bermudez-Viano [2], Aganovic-Tutek [1] and Viano [31] using a mixed variational formulation. In these works the classical Bernoulli-Euler-Navier theory is justifïed but the stress components of p , in the first term of the asymptotic expansion (3.11) are not uniquely determined.…”

Section: The Asymptotic Expansion Methodsmentioning

confidence: 99%

“…This method is used in Trabucho-Viano [24,25,26] in order to calculate the higher order terms in the asymptotic expansion introduced in Bermudez-Viano [2] for the linear case. This allows us to dérive and justify the most well known beam théories both in bending and torsion including Bernoulli-Euler-Navier (see Bermudez-Viano [2]), Saint Venant, Timoshenko and Vlasov (see 26,27,28]).…”

Section: The Asymptotic Expansion Methodsmentioning

confidence: 99%

“…This allows us to dérive and justify the most well known beam théories both in bending and torsion including Bernoulli-Euler-Navier (see Bermudez-Viano [2]), Saint Venant, Timoshenko and Vlasov (see 26,27,28]). …”

Section: The Asymptotic Expansion Methodsmentioning

confidence: 99%

“…Let w e be an open bounded, simply connected, subset of the plane <9xfxf with a sufficiently smooth boundary, whose area is A (o> e ) = meas co e = s 2 . In what follows, we shall consider a beam occupying volume fT = o> F x (0, L), L > 0, and we shall write : 7 £ -3a> 8 ?…”

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confidence: 99%

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A new approach of Timoshenko's beam theory by asymptotic expansion method

Trabucho¹,

Viaño²

1990

ESAIM: M2AN

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( 2 ) Communicated by P G CIARLET Abstract -In this work we obtain a gênerahzation of Timoshenko s beam theory by applying the asymptotic expansion method to a mixed vanational formulation of the three dimensional hneanzed elasticity model A classical subject of major discussion in this model is the proper définition of the so called Timoshenko s constants taking into account the f act that the shear stresses vary on each cross section Due to the technique employed we shall be able to define these constants in a clear way and show its dependence on the geometty of the cross section and on Poisson s ratio Finally we present several numencal examples showing the relationship between the classical and the new constants for different geometnes Resumé -En appliquant la methode des développements asymptotiques a un modèle variationnel mixte de l élasticité linéarisée on obtient une généralisation de la theorie de poutres de Timoshenko Associées a cette généralisation on obtient aussi une définition et une généralisation des constantes de Timoshenko tenant en compte la flexion additionnelle due a l effort tranchant La technique employee permet de demontier sa dependance par rapport a la geometrie et au coefficient de Poisson Finalement différents exemples numériques sont traites montrant la relation entre les nouvelles constantes et les constantes classiques pour différentes geometties NOTATIONSIn this work the summation convention on repeated indexes is used Latin indexes such as z, y, k, take values on the set {1,2,3} while Greek indexes such as a, (3, y, take values on the set {1,2}

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Section: The Asymptotic Expansion Methodsmentioning

confidence: 99%

Section: The Asymptotic Expansion Methodsmentioning

confidence: 99%

Section: The Asymptotic Expansion Methodsmentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

A new approach of Timoshenko's beam theory by asymptotic expansion method

Trabucho¹,

Viaño²

1990

ESAIM: M2AN

Self Cite

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“…Pour les coques « générales », c'est-à-dire dont la surface moyenne est indépendante de l'épaisseur, voir les travaux « de pionnier » de Destuynder [1980Destuynder [ , 1985 et Sanchez- Palencia [1990], ainsi que Caillerie & Sanchez-Palencia [1995], Miara & Sanchez-Palencia [1995], Ciarlet & Lods [1996a, Ciarlet, Lods & Miara [1996], et Ciarlet [1998]. Pour les poutres droites, voir Bermudez & Viano [1984], Geymonat, Krasucki & Marigo [1987], Le Dret [1995], Trabucho & Viafio [1996] ; signalons enfin Alvarez-Dios & Viafio [1995], qui viennent de justifier un modèle de poutre «faiblement courbée » en coordonnées cartésiennes. On se reportera à Ciarlet [1990Ciarlet [ , 1997Ciarlet [ , 1998] pour des bibliographies beaucoup plus complètes sur le sujet, en ce qui concerne notamment l'analyse asymptotique dans le cas non linéaire.…”

Section: Introductionunclassified