O. Ahmed, D. Van-gemert, and L. Vandewalle, Improved model for plate-end shear of CFRP strengthened RC beams, Cement and Concrete Composites, vol.23, issue.1, pp.3-19, 2001.
DOI : 10.1016/S0958-9465(00)00051-2

M. Aitali, M. Pinglot, and M. Lorrain, Mod??lisation du comportement en flexion statique des sections rectangulaires en b??ton arm??, Materials and Structures, vol.69, issue.ST 7, pp.207-213, 1993.
DOI : 10.1007/BF02472613

C. A. Anderson and R. Shield, A class of complete solutions for bending of perfectly-plastic beams, International Journal of Solids and Structures, vol.3, issue.6, pp.935-950, 1967.
DOI : 10.1016/0020-7683(67)90020-0

M. Artola and G. Duvaut, Homogénéisation d'une plaque renforcée, 1977.

R. Ball and S. L. Lee, On the effect of uniform surface load upon the plastic yielding of simply supported beams, Journal of the Mechanics and Physics of Solids, vol.10, issue.2, pp.151-163, 1962.
DOI : 10.1016/0022-5096(62)90018-2

A. Bensoussan, J. L. Lions, and G. Papanicolaou, Asymtotic Analysis For Periodic Structures, 1978.

G. Bouchitté, Convergence et relaxation de fonctionnelles du calcul des variationsà variationsà croissance linéaire. apllicationàapllicationà l'homogénéisation en plasticité, pp.7-36, 1986.

S. Bourgeois, Modélisation numérique des panneaux structuraux légers, 1997.

S. Bourgeois, Homogenization of periodic beams : limit of the expansions. Comptesrendus de l, Académie des Science, vol.10, pp.719-725, 2000.
URL : https://hal.archives-ouvertes.fr/hal-01296586

S. Bourgeois, O. Débordes, and P. Patou, Homog??n??isation et plasticit?? de plaques minces, Revue Europ??enne des ??l??ments Finis, vol.7, issue.1-3, pp.39-54, 1998.
DOI : 10.1080/12506559.1998.11690464

C. Boutin, Microstructural effects in elastic composites, International Journal of Solids and Structures, vol.33, issue.7, pp.1023-1051, 1996.
DOI : 10.1016/0020-7683(95)00089-5

URL : https://hal.archives-ouvertes.fr/hal-00940462

N. Buanic and P. Cartraud, Higher-order effective modeling of periodic heterogeneous beams. I. Asymptotic expansion method, International Journal of Solids and Structures, vol.38, issue.40-41, pp.7139-7161, 2001.
DOI : 10.1016/S0020-7683(00)00422-4

F. Buyle-bodin, E. David, and E. Rangneau, Finite element modelling of flexural behaviour of externally bonded CFRP reinforced concrete structures, Engineering Structures, vol.24, issue.11, pp.1423-1429, 2002.
DOI : 10.1016/S0141-0296(02)00085-8

URL : https://hal.archives-ouvertes.fr/hal-00139953

D. Caillerie, Thin elastic and periodic plates, Mathematical Methods in the Applied Sciences, vol.2, issue.18, pp.159-191, 1984.
DOI : 10.1002/mma.1670060112

J. Calgaro and R. Lacroix, Maintenance et réparations des ponts, 1997.

J. F. Caron, A. Diaz-diaz, R. Carreira, A. Chabot, and A. Ehrlacher, Multi-particle modelling for the prediction of delamination in multi-layered materials, Composites Science and Technology, vol.66, issue.6, pp.755-765, 2006.
DOI : 10.1016/j.compscitech.2004.12.022

J. Caron and K. Sab, Un nouveau mod??le de plaque multicouche ??paisse, Comptes Rendus de l'Acad??mie des Sciences - Series IIB - Mechanics, vol.329, issue.8, pp.595-600, 2001.
DOI : 10.1016/S1620-7742(01)01372-1

R. Carreira, Validation parélémentsparéléments finis des modèles multiparticulaires pour matériaux multicouches, 1998.

R. Carreira, J. Caron, and A. Diaz-diaz, Model of multilayered materials for interface stresses estimation and validation by finite element calculations, Mechanics of Materials, vol.34, issue.4, pp.217-230, 2002.
DOI : 10.1016/S0167-6636(02)00102-3

URL : https://hal.archives-ouvertes.fr/hal-00401790

A. Cecchi and K. Sab, A homogenized Reissner???Mindlin model for orthotropic periodic plates: Application to brickwork panels, International Journal of Solids and Structures, vol.44, issue.18-19, pp.6055-6079, 2007.
DOI : 10.1016/j.ijsolstr.2007.02.009

A. Chabot, Analyse des effortsàeffortsà l'interface entre les couches de matériaux compositesà compositesà l'aide de modèles de matériaux multiparticulaires multicouches, 1997.

P. Ciarlet and P. Destuynder, Justification of the 2-dimensional linear plate model, Journal de Mécanique, vol.18, issue.2, pp.315-344, 1979.

A. Cimetì-ere, G. Geymonat, H. Ledret, A. Raoult, and Z. Tutek, Asymptotic theory and analysis for displacements and stress distribution in nonlinear elastic straight slender rods, Journal of Elasticity, vol.18, issue.18, pp.111-161, 1988.
DOI : 10.1007/BF00040890

D. Cioranescu and J. Saint-paulin, Homogenization of Reticulated Structures, Applied Mechanics Reviews, vol.54, issue.4, 1999.
DOI : 10.1115/1.1383678

L. Corradi and P. Vena, Limit analysis of orthotropic plates??????Partial results were presented at the Plasticity '00 Symposium, Whistler, BC, 16???20 July 2000., International Journal of Plasticity, vol.19, issue.10, pp.1543-1566, 2003.
DOI : 10.1016/S0749-6419(02)00021-9

J. Dallot and K. Sab, Limit analysis of multi-layered plates. Part I: The homogenized Love???Kirchhoff model, Journal of the Mechanics and Physics of Solids, vol.56, issue.2, 2007.
DOI : 10.1016/j.jmps.2007.05.005

J. Dallot and K. Sab, Limit analysis of multi-layered plates. Part II: Shear effects, Journal of the Mechanics and Physics of Solids, vol.56, issue.2, 2007.
DOI : 10.1016/j.jmps.2007.05.006

E. David, Comportement mécanique des poutres en béton armé renforcées ou réparées par collage de matériaux composites, 1998.

P. De-buhan, Homogénéisation en calcuì a la rupture : le cas du matériau multicouche, C. R. Acd Sci. Paris Série II, issue.296, pp.159-191, 1983.

P. De-buhan, Approche fondamentale du calcuì a la rupture des ouvrages en sol renforcé, 1986.

A. Diaz-diaz, Délaminage des matériaux multicouches ; phénomènes, modèles et critères, 2001.

A. Diaz-diaz and J. Caron, Interface plasticity and delamination onset prediction, Mechanics of Materials, vol.38, issue.7, pp.643-668, 2006.
DOI : 10.1016/j.mechmat.2005.12.001

A. Diaz-diaz, J. Caron, and R. Carreira, Software application for evaluating interfacial stresses in inelastic symmetrical laminates with free edges, Composite Structures, vol.58, issue.2, pp.195-208, 2002.
DOI : 10.1016/S0263-8223(02)00123-X

A. Diaz-diaz, J. Caron, and A. Ehrlacher, Analytical determination of the modes I, II and III energy release rates in a delaminated laminate and validation of a delamination criterion, Composite Structures, vol.78, issue.3, pp.424-432, 2007.
DOI : 10.1016/j.compstruct.2005.11.003

D. Sciuva and M. , A refined transverse shear deformation theory for multilayered anisotropic plates, Atti Accad. Sci. Torino, vol.118, pp.279-295, 1984.

G. Duvaut, Comportement macroscopique d???une plaque perforee periodiquement, Lecture Notes in Mathematics, vol.II, issue.594, 1977.
DOI : 10.1007/BFb0086085

G. Duvaut and A. Metellus, Homogénéisation d'une plaque mince en flexion périodique et symétrique, C.R. Aca. Sci, pp.947-950, 1976.

A. Ehrlacher, T. Naciri, A. Chabot, and J. Caron, Analyse des efforts d'interfacèinterfacè a l'aide d'un modélisation multiphasique des matériaux multicouches (m4), 1994.

I. Ekeland and R. Temam, Convex Analysis and Variational Problems, 1976.
DOI : 10.1137/1.9781611971088

H. Fan and G. Widera, Refined engineering beam theory based on the asymptotic expansion approach, AIAA Journal, vol.29, issue.3, pp.444-449, 1994.
DOI : 10.2514/3.10598

E. Ferrier, ComportementàComportementà l'interface composite-béton des poutres ba renforcées, 1999.

C. Florence and K. Sab, A rigorous homogenization method for the determination of the overall ultimate strength of periodic discrete media and an application to general hexagonal lattices of beams, European Journal of Mechanics - A/Solids, vol.25, issue.1, pp.72-97, 2006.
DOI : 10.1016/j.euromechsol.2005.06.011

H. Garden, R. Quantrill, L. Hollaway, A. Thorne, and G. Parke, An experimental study of the anchorage length of carbon fibre composite plates used to strengthen reinforced concrete beams, Construction and Building Materials, vol.12, issue.4, pp.203-219, 1998.
DOI : 10.1016/S0950-0618(98)00002-6

K. Garett and J. Bailey, Multiple transverse fracture in 90 ? cross-ply laminates of glass fiber-reinforced polyester, Journal of Material Science, vol.12, issue.157, 1977.

G. Geymonat, F. Krasucki, and J. Marigo, Sur la communtativité des passagesàpassagesà la limite en théorie asymptotique des poutres composites, Série II 305, pp.225-228, 1987.

L. Grisard, Modélisation bidimensionnelle de la mise en forme des tôles, 1993.

P. Hamelin and H. Varastehpour, Characterization of concrete-composite plate adhesion. Mechanical Behviour of Adhesive Joints, Testing, pp.167-179, 1997.

P. Hodge, Plastic Analysis of Structures, Journal of Applied Mechanics, vol.27, issue.2, 1959.
DOI : 10.1115/1.3644008

W. Jansze, Strenghtening of rc members in bending by externally bonded steel plate, 1997.

A. Kalamkarov and A. Kolpakov, Analysis, Design and Optimization of Composite Structures, 1997.

J. S. Kao, T. Mura, and S. L. Lee, Limit analysis of orthotropic plates, Journal of the Mechanics and Physics of Solids, vol.11, issue.6, pp.429-436, 1963.
DOI : 10.1016/0022-5096(63)90019-X

G. Kirchhoff, Uber das gleichgewicht and die bewegung einer elastichen scheibe, Journal für reine und angewandte Mathematik, vol.40, pp.51-88, 1850.
DOI : 10.1515/crll.1850.40.51

URL : http://www.digizeitschriften.de/download/PPN243919689_0040/PPN243919689_0040___log7.pdf

R. Kohn and M. Vogelius, A new model for thin plates with rapidly varying thickness, International Journal of Solids and Structures, vol.20, issue.4, pp.333-350, 1984.
DOI : 10.1016/0020-7683(84)90044-1

A. Kolpakov, Calculation of the characteristics of thin elastic rods with a periodic structure, Journal of Applied Mathematics and Mechanics, vol.55, issue.3, pp.358-365, 1991.
DOI : 10.1016/0021-8928(91)90039-W

Y. Lescouarc-'h, Calcul en plasticité des structures, 1983.

T. Lewinski and J. J. Telega, Plates, Laminates and Shells. Asymptotic analysis and homogenization, World Scientific, 1999.
DOI : 10.1142/3539

O. Limam, Dalles en béton armée renforcéesrenforcéesà l'aide de matériaux composites, 2002.

O. Limam, G. Foret, and A. Ehrlacher, RC beams strengthened with composite material: a limit analysis approach and experimental study, Composite Structures, vol.59, issue.4, pp.467-472, 2003.
DOI : 10.1016/S0263-8223(02)00286-6

O. Limam, G. Foret, and A. Ehrlacher, RC two-way slabs strengthened with CFRP strips: experimental study and a limit analysis approach, Composite Structures, vol.60, issue.4, pp.467-471, 2003.
DOI : 10.1016/S0263-8223(03)00011-4

O. Limam, G. Foret, and A. Ehrlacher, Ultimate strength of free-edge composite laminates under tensile loading: A limit analysis approach, Composites Part B: Engineering, vol.37, issue.4-5, pp.286-291, 2006.
DOI : 10.1016/j.compositesb.2006.01.001

O. Limam, V. N-'guyen, and G. Foret, Numerical and experimental analysis of two-way slabs strengthened with CFRP strips, Engineering Structures, vol.27, issue.6, pp.841-845, 2005.
DOI : 10.1016/j.engstruct.2005.01.007

K. H. Lo and R. M. Christensen, A High-Order Theory of Plate Deformation???Part 2: Laminated Plates, Journal of Applied Mechanics, vol.44, issue.4, pp.669-676, 1977.
DOI : 10.1115/1.3424155

R. Miller, The eigenvalue problem for a class of long, thin elastic structures with periodic geometry, Quarterly of Applied Mathematics, vol.52, issue.2, pp.261-282, 1994.
DOI : 10.1090/qam/1276237

O. Millet, A. Cimetiere, and A. Hamdouni, An asymptotic elastic???plastic plate model for moderate displacements and strong strain hardening, European Journal of Mechanics - A/Solids, vol.22, issue.3, pp.369-384, 2003.
DOI : 10.1016/S0997-7538(03)00044-5

URL : https://hal.archives-ouvertes.fr/hal-00312256

R. D. Mindlin, Influence of rotary inertia and shear on flexural motion of isotropic, elastic plates, Journal of Applied Mechanics, vol.18, pp.31-38, 1951.

T. Naciri, A. Ehrlacher, and A. Chabot, Interlaminar stress analysis with a new Multiparticle modelization of Multilayered Materials (M4), Composites Science and Technology, vol.58, issue.3-4, pp.337-343, 1998.
DOI : 10.1016/S0266-3538(97)00085-7

V. Nguyen, Modélisation globale et locale des structures multicouches parélémentsparéléments finis de plaque, 2004.

N. 'guyen, V. Caron, J. Sab, and K. , A model for thick laminates and sandwich plates, Composites Science and Technology, vol.65, pp.475-489, 2005.

D. Oehlers, Premature Failure of Externally Plated Reinforced Concrete Beams, Journal of Structural Engineering, vol.116, issue.4, pp.978-995, 2001.
DOI : 10.1061/(ASCE)0733-9445(1990)116:4(978)

A. E. Omri, A. Fennan, F. Sidoroff, and A. Hihi, Elastic-plastic homogenization for layered composites, European Journal of Mechanics - A/Solids, vol.19, issue.4, pp.585-601, 2000.
DOI : 10.1016/S0997-7538(00)00182-0

D. R. Owen and J. A. Figueiras, Elasto-plastic analysis of anisotropic plates and shells by the semi-loof element, Int. Jour. for Numerical Methods in Engineering, vol.9, pp.521-539, 1983.

J. N. Pagano, Stress fields in composite laminates, International Journal of Solids and Structures, vol.14, issue.5, pp.385-400, 1978.
DOI : 10.1016/0020-7683(78)90020-3

J. N. Pagano and S. R. Soni, Global-local laminate variational model, Int. Jour. of Solids and Structures, vol.19207, 1983.
DOI : 10.1007/978-94-017-2233-9_25

URL : http://www.dtic.mil/get-tr-doc/pdf?AD=ADA121747

H. S. Pham, Dimensionnement d'une poutre mixte bois-beton, 2007.

W. Prager, An Introduction to Plasticity, 1959.

V. Ramana, T. Kant, S. Mortin, P. Dutta, A. Mukherjee et al., Behavior of CFRPC strengthened reinforced concrete beams with varying degrees of strengthening, Composites : Part B : engineering 31, pp.461-470, 2000.
DOI : 10.1016/S1359-8368(00)00022-6

J. Reddy, A generalization of two-dimensional theories of laminated composite plates, Communications in Applied Numerical Methods, vol.44, issue.3, pp.173-180, 1987.
DOI : 10.1002/cnm.1630030303

E. Reissner, Reflections on the Theory of Elastic Plates, Applied Mechanics Reviews, vol.38, issue.11, pp.1453-1464, 1985.
DOI : 10.1115/1.3143699

E. Reissner and Y. Stavsky, Bending and Stretching of Certain Types of Heterogeneous Aeolotropic Elastic Plates, Journal of Applied Mechanics, vol.28, issue.3, pp.402-408, 1961.
DOI : 10.1115/1.3641719

J. G. Ren, A new theory of laminated plate, Composites Science and Technology, vol.26, issue.3, pp.225-239, 1986.
DOI : 10.1016/0266-3538(86)90087-4

T. Roberts, Approximate analysis of shear and normal stress concentrations in the adhesive layers of plated rc beams, The Structural Engineer, vol.67, issue.2, pp.229-233, 1989.

K. Sab, Hills principle and homogenization of random materials. Comptes-Rendus de l, Académie des Sciences, vol.312, issue.1, pp.1-5, 1991.

K. Sab, Homogenization of non-linear random media by a duality method. application to plasticity, Asymptotic Analysis, vol.9, pp.311-336, 1994.

K. Sab, Yield design of thin periodic plates by a homogenization technique and an application to masonry walls, Comptes Rendus M??canique, vol.331, issue.9, pp.641-646, 2003.
DOI : 10.1016/S1631-0721(03)00144-X

K. Sab, J. Dallot, and A. Cecchi, Determination of the Overall Yield Strength Domain of Out-of-Plane Loaded Brick Masonry, International Journal for Multiscale Computational Engineering, vol.5, issue.2, pp.83-92, 2007.
DOI : 10.1615/IntJMultCompEng.v5.i2.20

J. Salençon, Calcuì a la rupture et analyse limite, 1983.

J. Salençon, An introduction to the yield design theory and its application to soil mechanics, Eur. Jour. Mech. A/ Solids, vol.21, pp.715-746, 1990.

J. Sanchez-hubert and E. Sanchez-palencia, Introduction aux méthodes asymptotiques et a l'homogénéisation, 1992.

E. Sanchez-palencia, Non homogeneous media and vibration theory, 1980.

P. Seide, An Improved Approximate Theory for the Bending of Laminated Plates, Mech Today JNC, vol.5, pp.451-466, 1980.
DOI : 10.1016/B978-0-08-024249-1.50039-X

A. Sharif, G. Al-suluimani, I. Basunbul, M. Baluch, and B. Chaleb, Strenghtening of initially loaded reinforced concrete beams using FRP plates, ACI Structure Journal, vol.91, issue.2, pp.160-168, 1994.

V. Sierra-ruiz, J. Destrebec, and M. Grédiac, The transfer length in concrete structures repaired with composites materials : a survey of analytical models and simplified models, Composite Structures, vol.27, pp.3-4, 2002.

S. Smith and J. Teng, FRP-strengthened RC beams. I: review of debonding strength models, Engineering Structures, vol.24, issue.4, pp.385-395, 2002.
DOI : 10.1016/S0141-0296(01)00105-5

S. Srinivas, A refined analysis of composite laminates, Journal of Sound and Vibration, vol.30, issue.4, pp.495-507, 1987.
DOI : 10.1016/S0022-460X(73)80170-1

P. Suquet, Analyse limite et homogénéisation, C.R Acad. Sci. SER. II, vol.296, pp.1355-1358, 1983.

K. Swaminathan and D. Ragounadin, Analytical solutions using a higher-order refined theory for the static analysis of antisymmetric angle-ply composite and sandwich plates, Composite Structures, vol.64, issue.3-4, pp.405-417, 2004.
DOI : 10.1016/j.compstruct.2003.09.042

M. Tahani and A. Nosier, Edge effects of uniformly loaded cross-ply composite laminates, Materials & Design, vol.24, issue.8, pp.647-658, 2003.
DOI : 10.1016/S0261-3069(03)00098-0

B. Taljsten, Defining anchor lengths of steel and CFRP plates bonded to concrete, International Journal of Adhesion and Adhesives, vol.17, issue.4, pp.319-327, 1997.
DOI : 10.1016/S0143-7496(97)00018-3

J. Tarn, An asymptotic theory for nonlinear analysis of multilayered anisotropic plates, Journal of the Mechanics and Physics of Solids, vol.45, issue.7, pp.1105-1120, 1997.
DOI : 10.1016/S0022-5096(96)00130-5

J. J. Telega, Epi-limit on HB and homogenization of heterogeneous plastic plates, Nonlinear Analysis: Theory, Methods & Applications, vol.25, issue.5, pp.499-529, 1995.
DOI : 10.1016/0362-546X(93)E0017-W

T. Triantafilou and E. Plevris, Strengthening of RC beams with epoxy-bonded fibre-composite materials, Materials and Structures, vol.116, issue.2, pp.201-211, 1992.
DOI : 10.1007/BF02473064

H. Varahstepour and P. Hamelin, Analysis and study of failure mechanism of rc beam strenghtened with frp plate. Advanced Composite material in bridge and structures, pp.519-527, 1994.

J. M. Whitney, Shear Correction Factors for Orthotropic Laminates Under Static Load, Journal of Applied Mechanics, vol.40, issue.1, pp.302-304, 1973.
DOI : 10.1115/1.3422950

J. M. Whitney and J. N. Pagano, Shear Deformation in Heterogeneous Anisotropic Plates, Journal of Applied Mechanics, vol.37, issue.4, pp.1031-1036, 1970.
DOI : 10.1115/1.3408654

H. Wright, T. Oduyemi, and H. Evans, The experimental behaviour of double skin composite elements, Journal of Constructional Steel Research, vol.19, issue.2, pp.111-132, 1991.
DOI : 10.1016/0143-974X(91)90036-Z

P. Yang, C. Norris, and Y. Stavsky, Elastic wave propagation in heterogeneous plates, International Journal of Solids and Structures, vol.2, issue.4, pp.665-684, 1966.
DOI : 10.1016/0020-7683(66)90045-X

W. L. Ying, Free-edge effect in anisotropic laminate under extension, bending and twisting, part i : A stress based variational approach, Journal of Applied Mechanics, vol.61, pp.1510-1548, 1994.

S. Zhang, M. Raoof, and L. Wood, PREDICTION OF PEELING FAILURE OF REINFORCED CONCRETE BEAMS WITH EXTERNALLY BONDED STEEL PLATES., Proceedings of the Institution of Civil Engineers : Structures and Buildings, pp.257-269, 1995.
DOI : 10.1680/istbu.1995.27870

Y. Ziraba, M. Baluch, I. Basunbul, A. Sharif, and A. A. Sulaimani, Guidelines towards the design of reinforced concrete beams with external plates, ACI Structural Journal, vol.91, issue.6, pp.639-646, 1994.