×

Reliability computation with local polynomial chaos approximations. (English) Zbl 1156.74049

Summary: We discuss the reliability estimation for structural mechanics problems involving random fields. While in most of the literature on stochastic finite element methods to date only global approximations with Hermite polynomials are considered, the benefits of local approximations are investigated in this paper. Local polynomial approximations in the vicinity of the point of most probable failure are introduced. An adaptive algorithm is proposed, that allows for efficient and accurate computations of failure probabilities.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74E35 Random structure in solid mechanics
74K99 Thin bodies, structures
62N05 Reliability and life testing
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Acharjee, Int. J. Meth. Eng. 66(12) pp 1934– (2006)
[2] Acharjee, Comput. Meth. Appl. Mech. Eng. 195 pp 2289– (2006)
[3] Acharjee, Comput. Struct. 85(5-6) pp 244– (2007)
[4] Babuška, SIAM J. Numer. Anal. 45 pp 1005– (2007)
[5] Babuška, Comput. Meth. Appl. Mech. Eng. 194(1) pp 1251– (2005)
[6] Baroth, Comput. Meth. Appl. Mech. Eng. 195 pp 6479– (2006)
[7] Baroth, Comput. Meth. Appl. Mech. Eng. 196 pp 4419– (2007)
[8] Berveiller, Rev. Eur. Méc. Numér. 15 pp 81– (2006)
[9] Choi, Comput. Struct. 82(13-14) pp 1113– (2004)
[10] Deb, Comput. Meth. Appl. Mech. Eng. 190 pp 6359– (2001)
[11] Desceliers, Int. J. Numer. Meth. Eng. 66 pp 978– (2006)
[12] Doostan, Comput. Meth. Appl. Mech. Eng. 196 pp 3951– (2007)
[13] Field Jr., Probab. Eng. Mech. 19(1-2) pp 65– (2004)
[14] Ghanem, Comput. Meth. Appl. Mech. Eng. 168 pp 19– (1999)
[15] R.G. Ghanem and P.D. Spanos, Stochastic Finite Elements: A Spectral Approach (Springer, New York, 1991). · Zbl 0722.73080
[16] Ghosh, Int. J. Numer. Meth. Eng. 73(2) pp 162– (2008)
[17] Grigoriu, J. Eng. Mech. 132 pp 1277– (2006)
[18] Huang, Probab. Eng. Mech. 22 pp 194– (2007)
[19] Jardak, Comput. Meth. Appl. Mech. Eng. 193 pp 429– (2004)
[20] Le Maitre, J. Comput. Phys. 197(1) pp 28– (2004)
[21] M. Loève, Probability Theory (Springer-Verlag, Berlin, 1977).
[22] Matthies, Comput. Meth. Appl. Mech. Eng. 194(1) pp 1295– (2005)
[23] Proppe, Structural Safety 30(4) pp 277– (2008)
[24] Proppe, Probab. Eng. Mech. 18 pp 1– (2003)
[25] B. Sudret and A. Der Kiureghian, Stochastic finite element methods and reliability - state of the art, Tech. rep., UCB/SEMM-2000/08, Department of Civil & Environmental Engineering, University of California, Berkeley, 2000.
[26] Sudret, Probab. Eng. Mech. 17(4) pp 337– (2002)
[27] R.A. Todor and C. Schwab, Convergence rates for sparse chaos approximations of elliptic problems with stochastic coefficients, Research Report No. 2006-05, Seminar für Angwandte Mathematik, ETH Zürich, Switzerland, 2006. · Zbl 1120.65004
[28] Wan, J. Comput. Phys. 209(2) pp 617– (2005)
[29] Xiu, J. Comput. Phys. 187 pp 137– (2003)
[30] Xu, Comput. Meth. Appl. Mech. Eng. 196 pp 2723– (2007)
[31] Zou, Multiscale Model. Simul. 3(4) pp 940– (2005)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.