T. Abdo and R. Rackwitz, A new b-point Algorithm for Large Time-Invariant and Time-Variant Reliability Problems. Reliability and Optimisation of Structures, pp.1-11, 1990.

S. Adhikari, . Aiaa-/-asme-/-asce-/-ahs-/, and . Structures, A Non-Parametric Approach for Uncertainty Quantification in Elastodynamics, 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference<BR> 14th AIAA/ASME/AHS Adaptive Structures Conference<BR> 7th, p.47, 2006.
DOI : 10.2514/6.2006-1630

G. B. Baecher and T. S. Et-ingra, Stochastic FEM in settlement predictions, Journal of the Geotechnical Engineering Division, vol.107, issue.4, pp.449-463, 1981.

H. Baldeweck, Méthodes aux éléments finis stochastiques, Application a la géotechnique, Thèse de doctorat, 1999.

J. Baroth, L. Bode, B. Ph, and M. Fogli, Numerical convergence of a stochastic finite element method in a lognormal context, Appl. of Sta. and Prob. in Civil Engineering, issue.1, p.217224, 2003.

J. Baroth, L. Bodé, B. Ph, and M. Fogli, SFE method using Hermite polynomials: An approach for solving nonlinear mechanical problems with uncertain parameters, Computer Methods in Applied Mechanics and Engineering, vol.195, issue.44-47, pp.6479-6501, 2006.
DOI : 10.1016/j.cma.2006.02.001

M. Berveiller and B. Sudret, Thèse sur les éléments finis stochastiques Rapport d'avancement 1Elements finis stochastique: approches intrusives et non intrusives pour des analyses de fiabilite, These de doctorat-IFMA & UBP. [BOS93], 2003.

L. F. Boswell and C. Mello, Dynamics of Structural Systems, 1993.

K. Breitung, W. Brzakala, and I. Elishakoff, Asymptotic approximations for multinormal integrals Lessons pertaining to the finite element method for stochastic problems, learned from simplest example Non-linear Finite Element Analysis of Solids and Structures Weighted integral method -I. Stochastic stiffness matrix, Journal of Engineering Mechanics Chaos, solution and fractals Journal of Engineering Mechanics, vol.110, issue.18, pp.357-3661217, 1984.

G. Deodatis and L. Graham, The Weighted Integral Method and the Variability Response Function as Part of a SFEM Formulation. Uncertainty Modeling in Finite Element, Fatigue & Stability of Structures, pp.71-116, 1997.

D. Kiureghian, A. Liu, and P. L. , 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)

O. Ditlevsen and H. O. Madsen, Structural reliability methods, 1996.

G. Dreyfus, J. Martinez, M. Samuelides, M. B. Gordon, F. Badran et al., Improved finite element method for stochastic problems, Chaos, Solitons and Fractals, vol.5, issue.5, pp.833-846, 1995.

I. Elishakoff, Y. Ren, and M. Shinozuka, Some exact solutions for the bending of beams with spatially stochastic stiffness, International Journal of Solids and Structures, vol.32, issue.16, pp.2315-2327, 1995.
DOI : 10.1016/0020-7683(94)00257-W

I. Elishakoff, N. Impollonia, and Y. J. Ren, New exact solutions for randomly loaded beams with stochastic flexibility, International Journal of Solids and Structures, vol.36, issue.16, pp.2325-2340, 1999.
DOI : 10.1016/S0020-7683(98)00113-9

R. G. Ghanem, P. D. Spanos, and R. Ghanem, Stochastic Finite Elements with Multiple Random Non-Gaussian Properties, Journal of Engineering Mechanics, vol.125, issue.1, pp.26-40, 1991.
DOI : 10.1061/(ASCE)0733-9399(1999)125:1(26)

T. Gmür, Dynamique des structures. Presses Polytechniques et Universitaires Romandes, 1997.

L. L. Graham and G. Deodatis, Variability response functions for stochastic plate bending problems, Structural Safety, vol.20, issue.2, pp.167-188, 1998.
DOI : 10.1016/S0167-4730(98)00006-X

A. Gupta, D. Nagar-chapman, &. Hall, /. Crc, . London et al., An Exact and Invariant First Order Reliability Format, Matrix Variate Distributions, Monographs & surveys in Pure & Applied Mathematics J. Eng. Mech. ASCE, vol.100, pp.1-111, 1974.

R. V. Hogg and A. T. Craig, Introduction to mathematical statistics, 1989.

K. Hornik, M. Stinchcombe, and H. Et-white, Multilayer feedforward networks are universal approximators, Multilayer feedforward networks are universal approximators, pp.359-366, 1989.
DOI : 10.1016/0893-6080(89)90020-8

J. F. Imbert, Analyse des structures par éléments finis, 1991.

S. Isukapalli, Uncertainty Analysis of Transport- Transformation Models, 1999.

S. S. Isukapalli, S. Kadry, and R. Younes, Uncertainty Analysis of Transport- Transformation Models The State University of New Jersey Etude Probabiliste d'un Système Mécanique à Paramètres Incertains par une Technique Basée sur la Méthode de Transformation, Proceeding of CanCam. Canada. [KAD05b] Kadry S., 2005b. A Proposed Method to Solve A Non-Linear Mechanical System with Uncertain Parameters. Proceeding of 10th Jubilee National Congress on Theoretical and Applied Mechanics, pp.13-16, 1999.

S. Kadry, A Probabilistic Analysis of Uncertain Mechanical Structure, Proceeding of 10th Jubilee National Congress on Theoretical and Applied Mechanics, pp.13-16, 2005.

S. Kadry, K. El-tawil, and A. Chateauneuf, One-Dimensional Transformation Method in Reliability Analysis, Proceedings of the 8th international conference on Computational and Structure Technology. CST, 2006.

S. Kadry, K. El-tawil, and A. Chateauneuf, Multi-Dimensional Transformation Method in Reliability Analysis, Proceedings of the 13th IFIP conference on Reliability and Optimization of Structural Systems. Japan, 2006.

S. Kadry, K. El-tawil, and A. Chateauneuf, Random eigenvalue problem in stochastic system, Proceedings of the 8th international conference on Computational and Structure Technology. CST, 2006.

S. Kadry, A. Chateauneuf, and K. El-tawil, Statistical analysis of linear random differential equation, WSEAS transaction on Mathematics. Accepted, 2007.

S. Kadry, Analysis of a non-linear system by a new technique based on the Continuation method, Applied Mathematics and Computation, vol.187, issue.2, 2007.
DOI : 10.1016/j.amc.2006.09.039

S. Kadry, K. El-tawil, and A. Chateauneuf, An Efficient Method (TRBDO) for Reliability-Based Design Optimization based on Transformation with Finite Element Analysis, AHS/ASC Structures, Structural Dynamics, and Materials Conference. Hawaii, 2007.

S. Kadry, K. El-tawil, and A. Chateauneuf, Probabilistic Analysis of Eigenvalue of Stochastic Systems, Journal of Applied Sciences, vol.ISSN, pp.1812-5654, 2007.

M. Lemaire and A. Mohamed, Finite Element and Reliability: A happy marriage?, Reliability and optimization of structural systems, pp.3-14, 2000.

M. Lemaire, Evaluation des indices de fiabilité associés a des modèles de mécanique des structures, 1992.

M. Lemaire, Reliability and mechanical design, Reliability Engineering & System Safety, vol.55, issue.2, pp.163-170, 1997.
DOI : 10.1016/S0951-8320(96)00083-X

M. Lemaire, A. Mohamed, and O. Flores-macias, The use of finite element codes for the reliability of structural systems, Reliability and Optimization of Structural Systems' 96, pp.7-7, 1997.

E. Lund, Finite Element based design sensitivity analysis and optimization, 1994.

H. O. Madsen, S. Krenk, and N. C. Lind, Methods of Structural Safety, 1986.

S. Mahadevan, S. Huang, and R. Rebba, A stochastic response surface method for random field problems, Proc. 9th Int. Conf on Applications of Statistics and Probability Civil Engineering (ICASP9), pp.177-184, 2003.

P. Malliavin, Stochastic Analysis Linearized mechanical model to evaluate reliability of offshore structures, Structural Safety, vol.17, pp.167-193, 1995.

G. Muscolino, G. Ricciardi, and N. Et-impollonia, Improved dynamic analysis of structures with mechanical uncertainties under deterministic input, Probabilistic Engineering Mechanics, vol.15, issue.2, pp.199-212, 2000.
DOI : 10.1016/S0266-8920(99)00021-1

A. Nataf, Détermination des distributions dont les marges sont données. Comptes Rendus de l, Académie des Sciences, vol.225, pp.42-43, 1962.

B. Puig, F. Poirion, and C. Soize, Non-Gaussian simulation using Hermite polynomial expansion: convergences and algorithms, Probabilistic Engineering Mechanics, vol.17, issue.3, pp.253-264, 2002.
DOI : 10.1016/S0266-8920(02)00010-3
URL : https://hal.archives-ouvertes.fr/hal-00686282

R. Rackwitz and B. Fiessler, Structural reliability under combined random load sequences, Computers & Structures, vol.9, issue.5, pp.489-94, 1978.
DOI : 10.1016/0045-7949(78)90046-9

G. I. Schuëller, L. A. Bergman, C. G. Bucher, G. Dasgupta, G. Deodatis et al., Remarks on Multivariate Transformation, Ann. Math. Stat, vol.23, 1952.

A. Johnson, H. J. Naess, M. Pradlwarter, K. Shinozuka, P. D. Sobczyk et al., A stateof-the-art report on computational stochastic mechanics Stochatic Structural Dynamics: Progress in Theory and Applications, chapitre Stochastic Finite Element Analysis: an Introduction Stochastic finite element analysis: an introduction, Stochastic structural dynamics: progress in theory and application, pp.197-321, 1988.

C. Soize, Random matrix theory for modeling uncertainties in computational mechanics, Computer Methods in Applied Mechanics and Engineering, vol.194, issue.12-16, pp.12-16, 2005.
DOI : 10.1016/j.cma.2004.06.038
URL : https://hal.archives-ouvertes.fr/hal-00686187

B. Sudret and A. Der-kiureghian, Stochastic finite elements and reliability", a state of-the-art report, 2000.

B. Sudret and A. Der-kiureghian, Comparison of finite element methods, Prob. Eng. Mech, vol.17, p.337348, 2002.

T. Takada, Weighted integral method in stochastic finite element analysis, Probabilistic Engineering Mechanics, vol.5, issue.3, pp.146-156, 1990.
DOI : 10.1016/0266-8920(90)90006-6

T. Takada, Weighted integral method in multi-dimensional stochastic finite element analysis, Probabilistic Engineering Mechanics, vol.5, issue.4, pp.158-166, 1990.
DOI : 10.1016/0266-8920(90)90016-D

T. Takada, G. Reliability, . Denver, . Connecticut, K. El-tawil et al., P. ? Reliability Method to Solve Mechanical Problems With Implicit Limit States Méthodes Fiabilistes Adaptées Aux Structures A Comportement Mécaniques Complexes et Applications a l'Evaluation de Règlements de Construction Métallique. Thèse de doctorat de l'école doctorale sciences pour l'ingénieur de Clermont-Ferrand Stochastic Finite Elements for Elastodynamics: Random Field and Shape Uncertainty Modelling Using Direct and Modal Perturbation-Based Approaches, Proceedings of the 6th Specialty Conference on Probabilistic Mechanics and StructuralVAN03a] Van den Nieuwenhof B Thèse de doctorat, 1991.

. Van03b, B. Van-den-nieuwenhof, and J. Coyette, Modal approaches for the stochastic finite element analysis of structures with material and geometric uncertainties, Computer Methods in Applied Mechanics and Engineering, vol.192, pp.3705-3729, 2003.

E. H. Vanmarcke and M. Grigoriu, Stochastic Finite Element Analysis of Simple Beams, Journal of Engineering Mechanics, vol.109, issue.5, pp.1203-1214, 1983.
DOI : 10.1061/(ASCE)0733-9399(1983)109:5(1203)

E. P. Wigner, On the Distribution of the Roots of Certain Symmetric Matrices, The Annals of Mathematics, vol.67, issue.2, pp.325-327, 1958.
DOI : 10.2307/1970008

J. Wishart, The generalized product moment distribution in samples from a normal multivariate population, Biometrika, vol.20, issue.A, pp.32-52, 1928.

D. Xiu and G. E. Karniadakis, The Wiener-Askey polynomial chaos for stochastic differentiel equations, J. Sci. Comput, vol.24, issue.2, pp.617-644, 2002.

J. Zhang and B. Ellingwood, SFEM in nonlinear reliability analysis, Proc. of ICOSSAR'97, p.867874, 1998.