, Structural reliability methods, 1996.
, Structural reliability. ISTE, 2010.
An exact and invariant first order reliability format, J. Eng. Mech. -ASCE, vol.1, issue.100, pp.111-121, 1974. ,
Structural reliability under random load sequences, Computer and Structures, vol.5, issue.9, pp.484-494, 1979. ,
Efficient algorithm for second-order reliability analysis, J. Eng. Mech, vol.12, issue.117, pp.37-49, 1991. ,
Strategies for finding the design point in non-linear finite element reliability analysis, Probabilistic Engineering Mechanics, issue.21, pp.133-147, 2006. ,
Error bounds for the reliability index in finite element reliability analysis, International Journal for Numerical Methods in Engineering, vol.87, issue.8, pp.781-794, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-01689922
Coupling finite element and reliability analysis through proper generalized decomposition model reduction, International Journal for Numerical Methods in Engineering, vol.95, issue.13, pp.1079-1093, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-01366918
Stochastic finite elements via response surface: fatigue crack growth problems, Probabilistic Methods for Structural Design, pp.313-338, 1997. ,
Combination of finite element and reliability methods in nonlinear fracture mechanics, Reliability Engineering and System Safety, vol.70, issue.1, pp.15-27, 2000. ,
Comparison of finite element reliability methods, Prob. Eng. Mech, vol.17, pp.337-348, 2002. ,
Stochastic finite elements: a non intrusive approach by regression, Eur. J. Comput. Mech, vol.15, issue.1-3, pp.81-92, 2006. ,
An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis, Prob. Eng. Mech, vol.25, issue.2, pp.183-197, 2010. ,
Multi-element stochastic reduced basis methods, Comput. Methods Appl. Mech. Eng, vol.197, pp.1495-1506, 2008. ,
Reduced basis approach for variational problems with stochastic parameters: application to heat conduction with variable robin coefficient, Comp. Meth. in Applied Mech. and Engrg, vol.198, pp.3187-3206, 2009. ,
URL : https://hal.archives-ouvertes.fr/inria-00311463
Reduced basis techniques for stochastic problems, Arch. Comput. Methods Engrg, vol.17, pp.435-454, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-00470522
Reduced order models for random functions application to stochastic problems, Appl. Math. Model, vol.33, pp.161-175, 2009. ,
Adaptive reduced basis strategy based on goal oriented error assessment for stochastic problems, Comp. Meth. in Applied Mech. and Engrg, pp.116-127, 2012. ,
Reduced basis methods for parametrized partial differential equations with stochastic influences using the Karhunen Loeve expansion, SIAM/ASA J. Unc. Quant, vol.1, pp.79-105, 2013. ,
Accurate and efficient evaluation of failure probability for partial different equations with random input data, Comput. Methods Appl. Mech. Eng, vol.267, pp.233-260, 2013. ,
Towards error bounds of the failure probability of elastic structures using reduced basis models, International Journal for Numerical Methods in Engineering, vol.112, issue.9, pp.1216-1234, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01633909
a survey of rare event simulation methods for static input-output models, Simulation Modelling Partice and Theory, vol.49, pp.287-304, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-01081888
A study on the cross-entropy method for rare-event probability estimation, INFORMS Journal on Computing, vol.19, issue.3, pp.381-394, 2007. ,
An efficient surrogate-based method for computing rare failure probability, Journal of Computational Physics, vol.230, issue.24, pp.8683-8697, 2011. ,
Kriging-based adaptive importance sampling algorithms for rare event estimation, Structural Safety, vol.44, pp.1-10, 2013. ,
Multifidelity preconditioning of the cross-entropy method for rare event simulation and failure probability estimation, SIAM/ASA Journal on Uncertainty Quantification, vol.6, issue.2, pp.737-761, 2018. ,
Certification of projection-based reduced order modelling in computational homogenisation by the constitutive relation error, Int. J. Numer. Meth. in Engng, vol.97, issue.6, pp.395-422, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-00780840
Certified real-time solution of parametrized partial differential equations, Handbook of Materials Modeling, pp.1523-1558, 2005. ,
Stochastic Finite Elements: A spectral Approach, Revised Edition, 2003. ,
Robust goal-oriented error estimation based on the constitutive relation error for stochastic problems, Computers and Structures, pp.189-195, 2012. ,
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. ,
Importance sampling in structural systems, Structural Safety, issue.6, pp.3-10, 1989. ,
A benchmark study on importance sampling techniques in strucural reliability, Struct. Safe, vol.12, issue.4, pp.255-276, 1993. ,
A class of optimum importance sampling strategies, Inf. Sci, vol.84, issue.1-2, pp.139-160, 1995. ,
The cross-entropy method for combinatorial and continuous optimization, Methodology Comput. Appl. Probab, vol.2, pp.127-190, 1999. ,
A tutorial on the cross-entropy method, Annals of Operation Research, vol.134, pp.19-67, 2005. ,
Reduced basis approximation and a posteriori error estimation for stress intensity factors, International Journal for Numerical Methods in Engineering, vol.72, issue.10, pp.1219-1259, 2007. ,
Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations, Arch Comput Methods Eng, vol.15, pp.229-275, 2008. ,
URL : https://hal.archives-ouvertes.fr/hal-01722593
Reduced basis approximation and a-posteriori error estimation for the coupled stokes-darcy system, Advances in Computational Mathematics, vol.41, pp.1131-1157, 2015. ,
A posteriori pointwise upper bound error estimates in the finite element method, International journal for numerical methods in engineering, vol.36, issue.8, pp.1279-1298, 1993. ,
On goal-oriented error estimation for elliptic problems : application to the control of pointwise errors, Comp. Meth. in Applied Mech. and Engrg, vol.176, pp.313-331, 1999. ,
Local error estimates of fem for displacements and stresses in linear elasticity by solving local neumann problems, Int. J. Numer. Meth. in Engng, vol.52, pp.727-746, 2001. ,
Practical methods for a posteriori error estimation in engineering applications, Int. J. Numer. Meth. in Engng, vol.56, pp.1193-1224, 2003. ,
New bounding techniques for goal-oriented error estimation applied to linear problems, International Journal for Numerical Methods in Engineering, vol.93, issue.13, pp.1345-1380, 2012. ,
Output bounds for reduced-order approximations of elliptic partial differential equations, Comp. Meth. in Applied Mech. and Engrg, vol.190, pp.3413-3426, 2001. ,
Estimation of the validity domain of hyper-reduction approximations in generalized standard elastoviscoplasticity. Advanced Modeling and Simulation in Engineering Sciences, vol.2, pp.1-19, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01237733
A fast, certified and tuning free two-field reduced basis method for the metamodelling of affinely-parametrised elasticity problems, Computer Methods in Applied Mechanics and Engineering, vol.298, pp.121-158, 2016. ,
A posteriori global error estimator based on the error in the constitutive relation for reduced basis approximation of parametrized linear elastic problems, Applied Mathematical Modelling, vol.40, pp.4271-4284, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01305736
A constitutive relation error estimator based on traction-free recovery of the equilibrated stress, Int. J. for Num. Meth. in Engrg, vol.78, issue.4, pp.460-482, 2009. ,
URL : https://hal.archives-ouvertes.fr/hal-01689801
Evaluation of the local quality of the von mises's stress and l2-norm of the stress, Engineering Computations, vol.68, issue.7/8, pp.876-897, 2006. ,
Bounds for linear-functional outputs of coercive partial differential equations: local indicators and adaptive refinement, Advances in Adaptive Computational Methods, vol.47, pp.199-216, 1998. ,