Interval Monte Carlo methods for structural reliability

Structural Safety - Tập 32 Số 3 - Trang 183-190 - 2010
Hao Zhang1, Robert L. Mullen2, Rafi L. Muhanna3
1School of Civil Engineering, University of Sydney, NSW 2006, Australia
2Department of Civil Engineering, Case Western Reserve University, Cleveland, OH 44106, USA
3School of Civil and Environmental Engineering, Georgia Institute of Technology, Savannah, GA 31407, USA

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Tài liệu tham khảo

Melchers, 1999

Kiureghian, 2009, Aleatory or epistemic? Does it matter?, Struct Saf, 31, 105, 10.1016/j.strusafe.2008.06.020

Ang, 1975, Probability concepts in engineering planning and design, vol. 1

Dempster, 1967, Upper and lower probabilities induced by a multi-valued mapping, Ann Mater Stat, 38, 325, 10.1214/aoms/1177698950

Kendall, 1974, Foundations of a theory of random sets, 322

Ferson S, Kreinovich V, Ginzburg L, Myers DS, Sentz K, Constructing probability boxes and Dempster-Shafer structures, Tech. Rep. SAND2002-4015, Sandia National Laboratories, 2003.

Williamson R. Probabilistic arithmetic. PhD thesis, University of Queensland, Austrialia, 1989.

Penmetsa, 2002, Efficient estimation of structural reliability for problems with uncertain intervals, Comput Struct, 80, 1103, 10.1016/S0045-7949(02)00069-X

Tucker WT, Ferson S. Probability bounds analysis in environmental risk assessment. In: Applied biomathematics, Setauket, 2003.

Tonon, 2006, Using random set theory to calculate reliability bounds for a wing structure, Struct Infrastruct Eng, 2, 191, 10.1080/15732470600590689

Oberguggenberger, 2008, Reliability bounds through random sets: non-parametric methods and geotechnical applications, Comput Struct, 86, 1093, 10.1016/j.compstruc.2007.05.040

Qiu, 2008, Probabilistic interval reliability of structural systems, Int J Solids Struct, 45, 2850, 10.1016/j.ijsolstr.2008.01.005

Der Kiureghian, 2008, Analysis of structural reliability under parameter uncertainties, Probab Eng Mech, 23, 351, 10.1016/j.probengmech.2007.10.011

Ellingwood, 2009, Quantifying and communicating uncertainty in seismic risk assessment, Struct Saf, 31, 179, 10.1016/j.strusafe.2008.06.001

Reid, 2009, Confidence and risk, Struct Saf, 31, 98, 10.1016/j.strusafe.2008.06.006

Tonon, 2004, Using random set theory to propagate epistemic uncertainty through a mechanical system, Reliab Eng Syst Saf, 85, 169, 10.1016/j.ress.2004.03.010

Dubois, 1991, Random sets and fuzzy interval analysis, Fuzzy Sets Syst, 42, 87, 10.1016/0165-0114(91)90091-4

Hall, 2004, Random sets of probability measures in slope hydrology and stability analysis, J Appl Math Mech, 84, 710

Rao, 1997, Analysis of uncertain structural systems using interval analysis, AIAA J, 35, 727, 10.2514/2.164

Ganzerli, 1999, Load and resistance convex models for optimum design, Struct Optim, 17, 259, 10.1007/BF01207002

Qiu, 1998, Antioptimization of structures with large uncertain-but-non-rand parameters via interval analysis, Compt Meth Appl Mech Eng, 152, 361, 10.1016/S0045-7825(96)01211-X

McWilliam, 2000, Anti-optimisation of uncertain structures using interval analysis, Comput Struct, 79, 421, 10.1016/S0045-7949(00)00143-7

Pownuk A. Efficient method of solution of large scale engineering problems with interval parameters. In: Muhanna RL, Mullen RL (Eds.), Proceedings of NSF workshop on reliable engineering computing, Savannah, GA, 2004.

Koyluoglu, 1995, Interval algebra to deal with pattern loading and structural uncertainty, J Eng Mech, ASCE, 121, 1149, 10.1061/(ASCE)0733-9399(1995)121:11(1149)

Möller, 2004

Mullen, 1999, Bounds of structural response for all possible loadings, J Struct Eng, ASCE, 125, 98, 10.1061/(ASCE)0733-9445(1999)125:1(98)

Muhanna, 2001, Uncertainty in mechanics problems-interval-based approach, J Eng Mech, ASCE, 127, 557, 10.1061/(ASCE)0733-9399(2001)127:6(557)

Dessombz, 2001, Analysis of mechanical systems using interval computations applied to finite elements methods, J Sound Vib, 238, 949, 10.1006/jsvi.2000.3191

Muhanna, 2005, Penalty-based solution for the interval finite element methods, J Struct Eng, ASCE, 131, 1102, 10.1061/(ASCE)0733-9399(2005)131:10(1102)

Zhang H. Nondeterministic linear static finite element analysis: an interval approach. PhD thesis, Georgia Institute of Technology, USA, 2005.

Muhanna, 2007, Combined axial and bending stiffness in interval finite-element methods, J Struct Eng, ASCE, 133, 1700, 10.1061/(ASCE)0733-9445(2007)133:12(1700)

Moore, 1966

Neumaier, 1990

Sun microsystems. Interval arithmetic in high performance technical computing. Sun microsystems (a white paper), September 2002.

Knüppel, 1994, Profil/bias-a fast interval library, Computing, 53, 277, 10.1007/BF02307379

Rump, 1990, Rigorous sensitivity analysis for systems of linear and nonlinear equations, Math Comput, 54, 721, 10.1090/S0025-5718-1990-1011445-5

Rohn, 1998, Enclosing solutions of linear equations, SIAM J Numer Anal, 35, 524, 10.1137/S0036142996299423

Ziemian RD. Advanced methods of inelastic analysis in the limit states design of steel structures. PhD thesis, Cornell University, Ithaca, NY, 1990.