Une justification des équations de la thermoélasticité des poutres à section variable par des méthodes asymptotiques
RAIRO. Anal. numér., 18 4 (1984) 347-376
Published online: 2017-01-31
Articles citing this article
The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).
Cited article:
This article has been cited by the following article(s):
A new thin layer model for viscous flow between two nearby non‐static surfaces
José M. Rodríguez and Raquel Taboada‐VázquezZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 103 (12) (2023)
https://doi.org/10.1002/zamm.202200571
One-dimensional viscoelastic von Kármán theories derived from nonlinear thin-walled beams
Manuel Friedrich and Lennart MachillCalculus of Variations and Partial Differential Equations 62 (7) (2023)
https://doi.org/10.1007/s00526-023-02525-3
A numerical two-scale approach for nonlinear hyperelastic beams and beam networks
Helen Le Clézio, Claire Lestringant and Dennis M. KochmannInternational Journal of Solids and Structures 276 112307 (2023)
https://doi.org/10.1016/j.ijsolstr.2023.112307
Two New Models for Dynamic Linear Elastic Beams and Simplifications for Double Symmetric Cross-Sections
Erick PruchnickiSymmetry 14 (6) 1093 (2022)
https://doi.org/10.3390/sym14061093
Asymptotic analysis of a thin fluid layer flow between two moving surfaces
J.M. Rodríguez and R. Taboada-VázquezJournal of Mathematical Analysis and Applications 507 (1) 125735 (2022)
https://doi.org/10.1016/j.jmaa.2021.125735
A novel reduced model for a linearized anisotropic rod with doubly symmetric a cross-section: I. Theory
Erick Pruchnicki, Xiaoyi Chen and Hui-Hui DaiMathematics and Mechanics of Solids 27 (8) 1455 (2022)
https://doi.org/10.1177/10812865221094507
Derivation of a one-dimensional von Kármán theory for viscoelastic ribbons
Manuel Friedrich and Lennart MachillNonlinear Differential Equations and Applications NoDEA 29 (2) (2022)
https://doi.org/10.1007/s00030-021-00745-0
New refined model for curved linear anisotropic rods with circular cross section
Erick Pruchnicki, Xiaoyi Chen and Hui-Hui DaiApplications in Engineering Science 6 100046 (2021)
https://doi.org/10.1016/j.apples.2021.100046
Asymptotic derivation of high-order rod models from non-linear 3D elasticity
Basile Audoly and Claire LestringantJournal of the Mechanics and Physics of Solids 148 104264 (2021)
https://doi.org/10.1016/j.jmps.2020.104264
On a consistent rod theory for a linearized anisotropic elastic material: I. Asymptotic reduction method
Xiaoyi Chen, Hui-Hui Dai and Erick PruchnickiMathematics and Mechanics of Solids 26 (2) 217 (2021)
https://doi.org/10.1177/1081286520949602
Asymptotic analysis of an elastic rod with rounded ends
Sergey A. Nazarov, Andrey S. Slutskij and Jari TaskinenMathematical Methods in the Applied Sciences 43 (10) 6396 (2020)
https://doi.org/10.1002/mma.6380
New refined models for curved beams in both linear and nonlinear settings
Erick Pruchnicki and Hui-Hui DaiMathematics and Mechanics of Solids 24 (7) 2295 (2019)
https://doi.org/10.1177/1081286518825389
Contribution to beam theory based on 3-D energy principle
Erick PruchnickiMathematics and Mechanics of Solids 23 (5) 775 (2018)
https://doi.org/10.1177/1081286517691089
Pointwise error estimate for a consistent beam theory
Xiaoyi Chen, Zilong Song and Hui-Hui DaiAnalysis and Applications 16 (01) 103 (2018)
https://doi.org/10.1142/S0219530516500135
Linear viscoelastic shells: An asymptotic approach
G. Castiñeira and Á. Rodríguez-ArósAsymptotic Analysis 107 (3-4) 169 (2018)
https://doi.org/10.3233/ASY-171455
Characterization of the Bernoulli–Navier model for a rectangular section beam as the limit of the Kirchhoff–Love model for a plate
C. Ribeiro, J. M. Viaño, J. Figueiredo and Á. Rodríguez-ArósZeitschrift für angewandte Mathematik und Physik 67 (5) (2016)
https://doi.org/10.1007/s00033-016-0710-7
A model for bending and stretching of piezoelectric rods obtained by asymptotic analysis
J. M. Viaño, J. Figueiredo, C. Ribeiro and Á. Rodríguez-ArósZeitschrift für angewandte Mathematik und Physik 66 (3) 1207 (2015)
https://doi.org/10.1007/s00033-014-0438-1
Three-point bending tests-Part I: Mathematical study and asymptotic analysis
P. Quintela and M. T. SánchezMathematical Methods in the Applied Sciences 34 (10) 1211 (2011)
https://doi.org/10.1002/mma.1434
A LARGE DEFORMATION, VISCOELASTIC, THIN ROD MODEL: DERIVATION AND ANALYSIS
J. BEYROUTHY and H. LE DRETMathematical Models and Methods in Applied Sciences 19 (10) 1907 (2009)
https://doi.org/10.1142/S0218202509003954
Derivation of the model of elastic curved rods from three-dimensional micropolar elasticity
Ibrahim Aganović, Josip Tambača and Zvonimir TutekANNALI DELL'UNIVERSITA' DI FERRARA 53 (2) 109 (2007)
https://doi.org/10.1007/s11565-007-0017-x
Derivation and Justification of the Models of Rods and Plates From Linearized Three-Dimensional Micropolar Elasticity
Ibrahim Aganović, Josip Tambača and Zvonimir TutekJournal of Elasticity 84 (2) 131 (2006)
https://doi.org/10.1007/s10659-006-9060-6
Hierarchy of One-Dimensional Models in Nonlinear Elasticity
Jean-Jacques Marigo and Nicolas MeunierJournal of Elasticity 83 (1) (2006)
https://doi.org/10.1007/s10659-005-9036-y
The influence of the type of loading on the asymptotic behavior of slender elastic rings
Jean-Jacques Marigo and Kamyar MadaniJournal of Elasticity 75 (2) 91 (2005)
https://doi.org/10.1007/s10659-005-3397-0
(2004)
https://doi.org/10.1002/0470091355.ecm015
Minimal requirements on the smoothness of data preserving accuracy of a one-dimensional model of rods
S. A. NazarovJournal of Mathematical Sciences 101 (2) 2987 (2000)
https://doi.org/10.1007/BF02672182
Asymptotic analysis of torsional and stretching modes of thin rods
H. Irago, N. Kerdid and J. M. ViañoQuarterly of Applied Mathematics 58 (3) 495 (2000)
https://doi.org/10.1090/qam/1770651
One-dimensional equations of deformation of thin slightly curved rods. Asymptotical analysis and justification
S A Nazarov and A S SlutskiiIzvestiya: Mathematics 64 (3) 531 (2000)
https://doi.org/10.1070/IM2000v064n03ABEH000290
Asymptotic modelling of a nonsymmetric beam
L.J. Alvarez-Vázquez and J.M. ViañoJournal of Computational and Applied Mathematics 126 (1-2) 433 (2000)
https://doi.org/10.1016/S0377-0427(99)00370-2
Theory of Shells
Studies in Mathematics and Its Applications, Theory of Shells 29 557 (2000)https://doi.org/10.1016/S0168-2024(00)80021-1
Justification of the asymptotic theory of thin rods. Integral and pointwise estimates
S. A. NazarovJournal of Mathematical Sciences 97 (4) 4245 (1999)
https://doi.org/10.1007/BF02365044
Mathematical justification of a one-dimensional model for general elastic shallow arches
J. A. Álvarez-Dios and J. M. ViañoMathematical Methods in the Applied Sciences 21 (4) 281 (1998)
https://doi.org/10.1002/(SICI)1099-1476(19980310)21:4<281::AID-MMA951>3.0.CO;2-O
Genuinely clamped beams
L.J. Alvarez-Vázquez, A.R. Rodríguez-Rodríguez and J.M. ViañoComputer Methods in Applied Mechanics and Engineering 158 (3-4) 375 (1998)
https://doi.org/10.1016/S0045-7825(97)00265-X
New models for rods with genuinely clamped ends
L.J. Alvarez–Vazquez, A.R. Rodriguez-Rodriguez and J.M. VianoApplicable Analysis 68 (3-4) 395 (1998)
https://doi.org/10.1080/00036819808840638
Asymptotic derivation of a general linear model for thin-walled elastic rods
J.M. Rodríguez and J.M. ViañoComputer Methods in Applied Mechanics and Engineering 147 (3-4) 287 (1997)
https://doi.org/10.1016/S0045-7825(97)00019-4
Mathematical Elasticity - Volume II: Theory of Plates
Philippe G. CiarletStudies in Mathematics and Its Applications, Mathematical Elasticity - Volume II: Theory of Plates 27 xix (1997)
https://doi.org/10.1016/S0168-2024(97)80003-3
Mathematical Elasticity - Volume II: Theory of Plates
Studies in Mathematics and Its Applications, Mathematical Elasticity - Volume II: Theory of Plates 27 451 (1997)https://doi.org/10.1016/S0168-2024(97)80012-4
Quelques modèles asymptotiques pour les poutres purement encastrées
Lino J. Alvarez-Vázquez, Adela R. Rodríguez and Juan M. ViañoComptes Rendus de l'Académie des Sciences - Series I - Mathematics 324 (12) 1425 (1997)
https://doi.org/10.1016/S0764-4442(97)83587-2
Justification d'un modèle linéaire bi-dimensionnel de coques «faiblement courbées» en coordonnées curvilignes
Stéphane Busse, Philippe G. Ciarlet and Bernadette MiaraESAIM: Mathematical Modelling and Numerical Analysis 31 (3) 409 (1997)
https://doi.org/10.1051/m2an/1997310304091
Mathematical Elasticity - Volume II: Theory of Plates
Philippe G. CiarletStudies in Mathematics and Its Applications, Mathematical Elasticity - Volume II: Theory of Plates 27 3 (1997)
https://doi.org/10.1016/S0168-2024(97)80007-0
Modeling the vibrations of a multi-rod structure
N. KerdidESAIM: Mathematical Modelling and Numerical Analysis 31 (7) 891 (1997)
https://doi.org/10.1051/m2an/1997310708911
Finite Element Methods (Part 2), Numerical Methods for Solids (Part 2)
L. Trabucho and J.M. ViañoHandbook of Numerical Analysis, Finite Element Methods (Part 2), Numerical Methods for Solids (Part 2) 4 487 (1996)
https://doi.org/10.1016/S1570-8659(96)80006-8
Asymptotic analysis of linearly elastic shells. I. Justification of membrane shell equations
Philippe G. Ciarlet and Véronique LodsArchive for Rational Mechanics and Analysis 136 (2) 119 (1996)
https://doi.org/10.1007/BF02316975
Mathematical Analysis of Thin Plate Models
Philippe Destuynder and Michel SalaunMathematical Analysis of Thin Plate Models 1 (1996)
https://doi.org/10.1007/978-3-642-51761-7_1
Knowledge-based methods and smart algorithms in computational mechanics
W.W. Tworzydlo and J.T. OdenEngineering Fracture Mechanics 50 (5-6) 759 (1995)
https://doi.org/10.1016/0013-7944(94)E0060-T
A Galerkin approximation for homogeneous anisotropic elastic beams
M. F. VeigaApplicable Analysis 53 (1-2) 67 (1994)
https://doi.org/10.1080/00036819408840244
Derivation of an evolution model for nonlinearly elastic beams by asymptotic expansion methods
L Alvarez-Vazquez and J.M ViañoComputer Methods in Applied Mechanics and Engineering 115 (1-2) 53 (1994)
https://doi.org/10.1016/0045-7825(94)90186-4
Asymptotic justification of an evolution linear thermoelastic model for rods
L Alvarez-Vazquez and J.M ViañoComputer Methods in Applied Mechanics and Engineering 115 (1-2) 93 (1994)
https://doi.org/10.1016/0045-7825(94)90189-9
An asymptotic general model for linear elastic homogeneous anisotropic rods
J. A. Alvarez‐Dios and J. M. ViañoInternational Journal for Numerical Methods in Engineering 36 (18) 3067 (1993)
https://doi.org/10.1002/nme.1620361804
Towards an automated environment in computational mechanics
W.W. Tworzydlo and J.T. OdenComputer Methods in Applied Mechanics and Engineering 104 (1) 87 (1993)
https://doi.org/10.1016/0045-7825(93)90208-F
A Galerkin spectral approximation in linearized beam theory
B. Miara and L. TrabuchoESAIM: Mathematical Modelling and Numerical Analysis 26 (3) 425 (1992)
https://doi.org/10.1051/m2an/1992260304251
A new approach of Timoshenko's beam theory by asymptotic expansion method
L. Trabucho and J. M. ViañoESAIM: Mathematical Modelling and Numerical Analysis 24 (5) 651 (1990)
https://doi.org/10.1051/m2an/1990240506511
Modeling of a folded plate
H. Le DretComputational Mechanics 5 (6) 401 (1990)
https://doi.org/10.1007/BF01113445
Homogenized behaviour of a beam with a multicellular cross section
M. L. Mascarenhas and L. TrabuchoApplicable Analysis 38 (1-2) 97 (1990)
https://doi.org/10.1080/00036819008839956
Modeling and justification of eigenvalue problems for junctions between elastic structures
F Bourquin and P.G CiarletJournal of Functional Analysis 87 (2) 392 (1989)
https://doi.org/10.1016/0022-1236(89)90017-7
Folded plates revisited
H. Le DretComputational Mechanics 5 (5) 345 (1989)
https://doi.org/10.1007/BF01047051
Asymptotic theory and analysis for displacements and stress distribution in nonlinear elastic straight slender rods
A. Cimetière, G. Geymonat, H. Le Dret, A. Raoult and Z. TutekJournal of Elasticity 19 (2) 111 (1988)
https://doi.org/10.1007/BF00040890
A derivation of generalized saint venant’s torsion theory from three-dimensional elasticity by asymptotic expansion methods
L. Trabucho and J. M. ViañApplicable Analysis 31 (1-2) 129 (1988)
https://doi.org/10.1080/00036818808839820
Numerical Approximation of Partial Differential Equations, Selection of Papers Presented at the International Symposium on NumericalAnalysis held at the Polytechnic University of Madrid
Philippe G. CiarletNorth-Holland Mathematics Studies, Numerical Approximation of Partial Differential Equations, Selection of Papers Presented at the International Symposium on NumericalAnalysis held at the Polytechnic University of Madrid 133 3 (1987)
https://doi.org/10.1016/S0304-0208(08)71716-X