O. Ditlevsen and H. Madsen, Structural Reliability Methods, 1996.

M. Lemaire, Fiabilité des structures, Hermes, 2005.

A. Hasofer and N. Lind, An exact and invariant first order reliability format, Journal of Engineering Mechanics ASCE, vol.100, issue.EM1, pp.111-121, 1974.

R. Rackwitz and B. Fiessler, Structural reliability under combined random load sequences, Computers & Structures, vol.9, issue.5, pp.484-494, 1979.
DOI : 10.1016/0045-7949(78)90046-9

D. Kiureghian, A. De-stefano, and M. , Efficient Algorithm for Second???Order Reliability Analysis, Journal of Engineering Mechanics, vol.117, issue.12, pp.37-49, 1991.
DOI : 10.1061/(ASCE)0733-9399(1991)117:12(2904)

Y. Zhang, D. Kiureghian, and A. , Two Improved Algorithms for Reliability Analysis, Proceedings of the 6th IFIP WG7
DOI : 10.1007/978-0-387-34866-7_32

T. Haukaas, D. Kiureghian, and A. , Strategies for finding the design point in non-linear finite element reliability analysis, Probabilistic Engineering Mechanics, vol.21, issue.2, pp.133-147, 2006.
DOI : 10.1016/j.probengmech.2005.07.005

L. Gallimard, Error bounds for the reliability index in finite element reliability analysis, International Journal for Numerical Methods in Engineering, vol.12, issue.3, pp.781-994, 2011.
DOI : 10.1002/nme.2496

P. Colombi and L. Faravelli, Stochastic Finite Elements Via Response Surface: Fatigue Crack Growth Problems, Probabilistic Methods for Structural Design, pp.313-338, 1997.
DOI : 10.1007/978-94-011-5614-1_14

M. Pendola, M. A. Lemaire, M. Hornet, and P. , Combination of finite element and reliability methods in nonlinear fracture mechanics, Reliability Engineering & System Safety, vol.70, issue.1, pp.15-27, 2000.
DOI : 10.1016/S0951-8320(00)00043-0

A. Ammar, B. Mokdada, F. Chinesta, and R. Keunings, A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids, Journal of Non-Newtonian Fluid Mechanics, vol.139, issue.3, pp.153-176, 2011.
DOI : 10.1016/j.jnnfm.2006.07.007

URL : https://hal.archives-ouvertes.fr/hal-01004909

P. Ladevèze, Nonlinear Computational Structural Mechanics -New Approaches and Non-incremental Methods of Calculation, 1999.

O. Allix and P. Vidal, A new multi-solution approach suitable for structural identification problems, Computer Methods in Applied Mechanics and Engineering, vol.191, issue.25-26, pp.25-262727, 2002.
DOI : 10.1016/S0045-7825(02)00211-6

URL : https://hal.archives-ouvertes.fr/hal-01366984

A. Nouy, A priori model reduction through Proper Generalized Decomposition for solving time-dependent partial differential equations, Computer Methods in Applied Mechanics and Engineering, vol.199, issue.23-24, pp.23-241603, 2010.
DOI : 10.1016/j.cma.2010.01.009

URL : https://hal.archives-ouvertes.fr/hal-00455635

F. Chinesta, A. Ammar, A. Leygue, and R. Keunings, An overview of the proper generalized decomposition with applications in computational rheology, Journal of Non-Newtonian Fluid Mechanics, vol.166, issue.11, pp.578-592, 2011.
DOI : 10.1016/j.jnnfm.2010.12.012

URL : https://hal.archives-ouvertes.fr/hal-01061441

P. Vidal, L. Gallimard, and O. Polit, Assessment of a composite beam finite element based on the proper generalized decomposition, Composite Structures, vol.94, issue.5, pp.1900-1910, 2012.
DOI : 10.1016/j.compstruct.2011.12.016

URL : https://hal.archives-ouvertes.fr/hal-01366922

A. Mohamed, M. Lemaire, J. Mitteau, and E. Meister, Finite element and reliability: a method for compound variables???application on a cracked heating system, Nuclear Engineering and Design, vol.185, issue.2-3, pp.185-202, 1998.
DOI : 10.1016/S0029-5493(98)00184-8

D. Kiureghian, A. Liu, and P. , Structural Reliability under Incomplete Probability Information, Journal of Engineering Mechanics, vol.112, issue.1, pp.85-104, 1986.
DOI : 10.1061/(ASCE)0733-9399(1986)112:1(85)

D. Kiureghian, A. Dakessian, and T. , Multiple design points in first and second-order reliability, Structural Safety, vol.20, issue.1, pp.37-49, 1998.
DOI : 10.1016/S0167-4730(97)00026-X

Z. Shi and J. Shen, Convergence of the Polak Ribière Polyak conjugate gradient method. Nonlinear Analysis: Theory, Methods and Applications, vol.66, issue.6, pp.1428-1441, 2007.