S. Abdelkhalek, P. Montmitonnet, N. Legrand, and P. Buessler, Coupled approach for flatness prediction in cold rolling of thin strip, International Journal of Mechanical Sciences, vol.53, issue.9, pp.661-675, 2011.
DOI : 10.1016/j.ijmecsci.2011.04.001

URL : https://hal.archives-ouvertes.fr/hal-00612471

M. Abramowitz and I. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 1964.

F. Acton, Numerical methods that work, 1990.

O. Alifanov, Inverse heat transfer problems, pp.200-203, 1994.
DOI : 10.1007/978-3-642-76436-3

C. Andersen, B. Ravn, and T. Wanheim, Development of a commercial transducer for measuring pressure and friction on a model die surface, Journal of Materials Processing Technology, vol.115, issue.2, pp.205-211, 2001.
DOI : 10.1016/S0924-0136(01)00807-X

G. Andrews, R. Askey, and R. Roy, Special Functions, of Encyclopedia of Mathematics and its Applications, 1999.

J. Barber, of Solid Mechanics and Its Applications, 2003.

J. Beck, B. Blackwell, and C. St-clair, Inverse heat conduction, ill-posed problems, 1985.

L. Bezerra and S. Saigal, Inverse boundary traction reconstruction with the bem, International Journal of Solids and Structures, vol.32, issue.10, pp.1417-1431, 1995.
DOI : 10.1016/0020-7683(94)00192-Y

J. Blum and W. Marquardt, AN OPTIMAL SOLUTION TO INVERSE HEAT CONDUCTION PROBLEMS BASED ON FREQUENCY-DOMAIN INTERPRETATION AND OBSERVERS, Numerical Heat Transfer, Part B: Fundamentals, vol.23, issue.4, pp.453-478, 1997.
DOI : 10.1080/10407799208944923

S. Bock and K. Gürlebeck, On a spatial generalization of the Kolosov-Muskhelishvili formulae, Mathematical Methods in the Applied Sciences, vol.17, issue.3, pp.223-240, 2009.
DOI : 10.1002/mma.1033

J. Boussinesq, Application des potentiels a l'etude de l'equilibre et du mouvement des solides elastiques, 1885.

H. Bui, Fracture Mechanics, Inverse Problems and Solutions. volume 139 of Solid Mechanics and Its Applications, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00090745

K. Chau, Analytic Solutions for Diametral Point Load Strength Tests, Journal of Engineering Mechanics, vol.124, issue.8, pp.857-883, 1998.
DOI : 10.1061/(ASCE)0733-9399(1998)124:8(875)

K. Chau and X. Wei, Finite solid circular cylinders subjected to arbitrary surface load. Part I ??? Analytic solution, International Journal of Solids and Structures, vol.37, issue.40, pp.5707-5732, 2000.
DOI : 10.1016/S0020-7683(99)00289-9

W. L. Chen and Y. C. Yang, Inverse problem of estimating the heat flux at the roller/workpiece interface during a rolling process, Applied Thermal Engineering, vol.30, issue.10, pp.1247-1254, 2010.
DOI : 10.1016/j.applthermaleng.2010.02.007

R. Corral, R. Colas, and A. Perez, Modeling the thermal and thermoelastic responses of work rolls used for hot rolling steel strip, Journal of Materials Processing Technology, vol.153, issue.154, pp.886-893, 2004.
DOI : 10.1016/j.jmatprotec.2004.04.090

P. Ferdinand, S. Magne, G. Laffont, V. Dewynter, L. Maurin et al., Optical Fiber Sensors from Laboratory to Field Trials: Applications and Trends at CEA LIST, Fiber and Integrated Optics, vol.28, issue.1, pp.81-107, 2009.
DOI : 10.1080/01468030802272559

I. Gradshteyn and I. Ryzhik, Tables of integrals, Series and Products, 1992.

R. Guo, Two-Dimensional Transient Thermal Behavior of Work Rolls in Rolling Process, Journal of Manufacturing Science and Engineering, vol.120, issue.1, pp.28-33, 1998.
DOI : 10.1115/1.2830107

A. Hacquin, Modelisation thermo-mecanique tridimensionnelle du laminage : couplage bande-cylindres [3D thermomechanical modelling of rolling processes : coupling strip and rolls], 1996.

P. Hello and J. Vinet, Analytical models of thermal aberrations in massive mirrors heated by high power laser beams, Journal de Physique, vol.51, issue.12, pp.1267-1282, 1990.
DOI : 10.1051/jphys:0199000510120126700

URL : https://hal.archives-ouvertes.fr/jpa-00212444

P. Hsu, Y. Yang, and C. Chen, A Three-Dimensional Inverse Problem of Estimating the Surface Thermal Behavior of the Working Roll in Rolling Process, Journal of Manufacturing Science and Engineering, vol.122, issue.1, pp.76-82, 2000.
DOI : 10.1115/1.538889

C. Huang, T. Ju, and A. Tseng, The estimation of surface thermal behavior of the working roll in hot rolling process, International Journal of Heat and Mass Transfer, vol.38, issue.6, pp.1019-1031, 1995.
DOI : 10.1016/0017-9310(94)00218-K

A. Iserles, A fast and simple algorithm for the computation of Legendre coefficients, Numerische Mathematik, vol.50, issue.3, pp.529-553, 2011.
DOI : 10.1007/s00211-010-0352-1

J. Jeswiet and W. Rice, The design of a sensor for measuring normal pressure and friction stress in the roll gap during cold rollin, Tenth north american manufacturing research conference proceedings, pp.130-134, 1982.

Z. Jiang and A. Tieu, Modeling of the rolling processes by a 3-D rigid plastic/ visco-plastic finite element method with shifted ICCG method, Comput Struct, vol.40, pp.79-2727, 2001.

K. Keanini, Inverse estimation of surface heat flux distributions during high speed rolling using remote thermal measurements, International Journal of Heat and Mass Transfer, vol.41, issue.2, pp.275-285, 1998.
DOI : 10.1016/S0017-9310(97)00144-0

P. Kotrbacek, M. Raudensky, J. Horsky, and M. Pohanka, Experimental study of heat transfer in hot rolling, Revue de M??tallurgie, vol.103, issue.7-8, pp.333-341, 2005.
DOI : 10.1051/metal:2006134

Y. Kudryavtsev, Unsteady state heat transfer, Iliffe, pp.36-39, 1966.

V. Kutrunov, The quaternion method of regularizing integral equations of the theory of elasticity, Journal of Applied Mathematics and Mechanics, vol.56, issue.5, pp.765-770, 1992.
DOI : 10.1016/0021-8928(92)90062-D

J. Lagergren, M. Arentoft, P. Henningsten, T. Wahneim, N. Jonsson et al., New roll gap measurements of the friction conditions and the normal pressure distribution in cold flat rolling, Ninth international steel rolling conference, 2006.

C. Lanczos, Linear differential operators, 1961.

N. Legrand, N. Labbe, D. Weisz-patrault, A. Ehrlacher, J. Horsky et al., Analysis of Roll Gap Heat Transfers in Hot Steel Strip Rolling through Roll Temperature Sensors and Heat Transfer Models, Key Engineering Materials, vol.504, issue.506, pp.504-506, 2012.
DOI : 10.4028/www.scientific.net/KEM.504-506.1043

URL : https://hal.archives-ouvertes.fr/hal-00668233

N. Legrand, T. Lavalard, and A. Martins, New concept of friction sensor for strip rolling: Theoretical analysis, International Congress on Tribology of Material Processes, 2010.
DOI : 10.1016/j.wear.2011.11.002

N. Legrand, T. Lavalard, and A. Martins, New concept of friction sensor for strip rolling: Theoretical analysis, Tribology in Manufacturing Processes, pp.8-18, 2012.
DOI : 10.1016/j.wear.2011.11.002

C. S. Li, H. L. Yu, G. Y. Deng, X. H. Liu, and G. D. Wang, Numerical Simulation of Temperature Field and Thermal Stress Field of Work Roll During Hot Strip Rolling, Journal of Iron and Steel Research, International, vol.14, issue.5, pp.18-21, 2007.
DOI : 10.1016/S1006-706X(07)60067-3

C. Liu, A. Tieu, B. Ma, and Z. Jiang, Friction measurement in hot rolling of steel, p.44, 2002.

T. Loulou and E. Artioukhine, Numerical solution of 3D unsteady nonlinear inverse problem of estimating surface heat flux for cylindrical geometry Inverse problems in science and engineering 14, pp.39-52, 2006.

A. Love, A Treatise on the Mathematical Theory of Elasticity, 1944.
URL : https://hal.archives-ouvertes.fr/hal-01307751

J. K. Lu, Complexe variable methods in plane elasticity, of Series in pure mathematics. World scientific, 1995.

B. Mandal, N. , and M. , Advances in dual integral equations. Research notes in mathematics, 1999.

D. Meierhofer and K. Stelson, Measurement of the Interfacial Stresses in Rolling Using the Elastic Deformation of the Roll, Journal of Engineering for Industry, vol.109, issue.4, pp.362-369, 1987.
DOI : 10.1115/1.3187140

P. Montmitonnet, Hot and cold strip rolling processes Computer methods in applied mechanics and engineering 195, pp.6604-6625, 2006.

P. Montmitonnet, A. Stephany, S. Cassarini, J. Ponthot, M. Laugier et al., Modeling of metal forming lubrication by o/w emulsions, Int. Conf. Trib. Mat. Proc., Yokohama, pp.85-90, 2007.

N. Muskhelishvili, Singular integral equations : boundary problems of function theory and their application to mathematical physics, 1953.
DOI : 10.1007/978-94-009-9994-7

N. Muskhelishvili, Some basic problems of the mathematical theory of elasticity, 1953.
DOI : 10.1007/978-94-017-3034-1

Y. Ogaki and N. Nakajima, Stress analysis of a circular cylinder of finite length subjected to loads symmetrical to middle plane and to axis of revolution. The science and engineering review of Doshisha University, pp.195-205, 1983.

R. Penrose, The road to reality. A complete guide to the laws of the universe, 2004.

T. Pham, Potentiels élastiques, tenseurs de Green et de Neumann [Elastic potentials, Green and Neumann tensors, 1967.

A. Polyanin and A. Manzhirov, Handbook of integral equations, 2008.

M. Raynaud and J. Bransier, A new finite-difference method for the nonlinear inverse heat conduction problem, Numerical Heat Transfer, vol.9, pp.27-42, 1986.

A. Saboonchi and M. Abbaspour, Changing the geometry of water spray on milling work roll and its effect on work roll temperature, Journal of Materials Processing Technology, vol.148, issue.1, pp.35-49, 2004.
DOI : 10.1016/j.jmatprotec.2004.01.038

A. Saint-venant, Memoire sur la torsion des prismes, Compte rendu de l'Academie des Sciences, pp.233-560, 1855.

H. Saito, The Axially Symmetrical Deformation of a Short Circular Cylinder, Transactions of the Japan Society of Mechanical Engineers, vol.18, issue.68, pp.21-28, 1952.
DOI : 10.1299/kikai1938.18.68_21

F. Scarpa and G. Milano, KALMAN SMOOTHING TECHNIQUE APPLIED TO THE INVERSE HEAT CONDUCTION PROBLEM, Numerical Heat Transfer, Part B: Fundamentals, vol.23, issue.1, pp.79-96, 1995.
DOI : 10.1080/10407788208913448

D. Schnur and N. Zabaras, Finite element solution of two-dimensional inverse elastic problems using spatial smoothing, International Journal for Numerical Methods in Engineering, vol.25, issue.1, pp.57-75, 1990.
DOI : 10.1002/nme.1620300105

I. Sneddon and M. Lowengrub, Crack problems in the classical theory of elasticity. The SIAM series in applied mathematics, 1969.

M. Stein and G. Weiss, Introduction to Fourier analysis on euclidean spaces, 1971.

K. Stelson, A new method to measure normal pressure and frictional stresses in the roll gap during cold rolling, in : Eleventh north american metalworking research conference proceedings, pp.259-264, 1983.

R. Tavares, M. Isac, F. Hamel, and R. Guthrie, Instantaneous interfacial heat fluxes during the 4 to 8 m/min casting of carbon steels in a twin-roll caster, Metallurgical and Materials Transactions B-Process Metallurgy and Materials Processing Science, pp.55-67, 2001.
DOI : 10.1007/s11663-001-0008-8

A. Tsalik, Quaternionic representation of the 3D elastic and thermoelastic boundary problems, Mathematical Methods in the Applied Sciences, vol.154, issue.9, pp.697-708, 1995.
DOI : 10.1002/mma.1670180904

A. Tseng, Finite-Difference Solutions for Heat Transfer in a Roll Rotating at High Speed, Numerical Heat Transfer, Part B: Fundamentals, vol.7, issue.1, pp.113-125, 1984.
DOI : 10.1080/10407798408546960

A. Tseng, J. Chang, M. Raudensky, and J. Horsky, An Inverse Finite-Element Evaluation of Roll Cooling in Hot-Rolling of Steels, Journal of Materials Processing & Manufacturing Science, vol.3, pp.387-408, 1995.

A. Tseng, F. Lin, A. Gunderia, and D. Ni, Roll cooling and its relationship to roll life, Metallurgical Transactions A, vol.62, issue.6, pp.2305-2320, 1989.
DOI : 10.1007/BF02666666

A. Tseng, S. Tong, S. Maslen, and J. Mills, Thermal Behavior of Aluminum Rolling, Journal of Heat Transfer, vol.112, issue.2, pp.301-307, 1990.
DOI : 10.1115/1.2910376

N. Vekua, Systems of singular integral equations, 1964.

M. Wang, H. Yang, Z. Sun, and L. Guo, Analysis of coupled mechanical and thermal behaviors in hot rolling of large rings of titanium alloy using 3D dynamic explicit FEM, Journal of Materials Processing Technology, vol.209, issue.7, pp.3384-3395, 2009.
DOI : 10.1016/j.jmatprotec.2008.07.054

G. Watson, A Treatise on the Theory of Bessel Functions, The Mathematical Gazette, vol.18, issue.231, 1944.
DOI : 10.2307/3605513

D. Weisz-patrault, A. Ehrlacher, and N. Legrand, A new sensor for the evaluation of contact stress by inverse analysis during steel strip rolling, Journal of Materials Processing Technology, vol.211, issue.9, pp.1500-1509, 2011.
DOI : 10.1016/j.jmatprotec.2011.03.025

URL : https://hal.archives-ouvertes.fr/hal-00595237

D. Weisz-patrault, A. Ehrlacher, and N. Legrand, Evaluation of temperature field and heat flux by inverse analysis during steel strip rolling, International Journal of Heat and Mass Transfer, vol.55, issue.4, pp.629-641, 2012.
DOI : 10.1016/j.ijheatmasstransfer.2011.10.048

URL : https://hal.archives-ouvertes.fr/hal-00649450

D. Weisz-patrault, A. Ehrlacher, and N. Legrand, Analytical inverse solution for coupled thermoelastic problem for the evaluation of contact stress during steel strip rolling, Applied Mathematical Modelling, vol.37, issue.4, pp.2212-2229, 2013.
DOI : 10.1016/j.apm.2012.05.013

URL : https://hal.archives-ouvertes.fr/hal-00759710

D. Weisz-patrault, A. Ehrlacher, and N. Legrand, Evaluation of contact stress during rolling process, by three dimensional analytical inverse method, International Journal of Solids and Structures, vol.50, issue.20-21, 2013.
DOI : 10.1016/j.ijsolstr.2013.06.005

URL : https://hal.archives-ouvertes.fr/hal-00946091

D. Weisz-patrault, A. Ehrlacher, and N. Legrand, Fast evaluation of temperature and heat flux during rolling process, by three-dimensional analytical inverse method, International Journal of Thermal Sciences, 2013.

D. Weisz-patrault, A. Ehrlacher, N. Legrand, N. Labbe, J. Horsky et al., Experimental Study of Interfacial Heat Flux and Surface Temperature by Inverse Analysis with Thermocouple (Fully Embedded) during Hot Steel Strip Rolling, Advanced Materials Research, vol.452, issue.453, pp.452-453, 2012.
DOI : 10.4028/www.scientific.net/AMR.452-453.959

URL : https://hal.archives-ouvertes.fr/hal-00656321

G. Wijk, The Point Load Test for the Tensile Strength of Rock, Geotechnical Testing Journal, vol.3, issue.2, pp.49-54, 1980.
DOI : 10.1520/GTJ10902J

A. Yger, Analyse complexe et distributions Mathématiques pour le second cycle, 2001.

G. Zhang, H. Xiao, and C. Wang, Three-Dimensional Model for Strip Hot Rolling, Journal of Iron and Steel Research, International, vol.13, issue.1, pp.23-26, 2006.
DOI : 10.1016/S1006-706X(06)60020-4

H. Zhang, C. Nie, Y. Xiong, D. Xie, and Y. Yu, Approximate analytical models of temperature and thermal stresses for 2D axis-symmetry object with temperature-dependent properties, International Journal of Thermal Sciences, vol.53, pp.100-107, 2012.
DOI : 10.1016/j.ijthermalsci.2011.10.011

X. Zhang, Z. Jiang, A. Tieu, X. Liu, and G. Wang, Numerical modelling of the thermal deformation of CVC roll in hot strip rolling, Journal of Materials Processing Technology, vol.130, issue.131, pp.219-223, 2002.
DOI : 10.1016/S0924-0136(02)00736-7

L. Zone-ching and C. Chang-cheng, Three-dimensional heat-transfer and thermal-expansion analysis of the work roll during rolling, Journal of Materials Processing Technology, vol.49, pp.125-147, 1995.