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Volumn 46, Issue 24, 2003, Pages 4681-4693

A new stochastic approach to transient heat conduction modeling with uncertainty

Author keywords

Polynomial chaos; Random medium; Stochastic modeling; Transient heat conduction; Uncertainty

Indexed keywords

GALERKIN METHODS; POLYNOMIALS; RANDOM PROCESSES; THERMAL CONDUCTIVITY;

EID: 0141792397     PISSN: 00179310     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0017-9310(03)00299-0     Document Type: Article
Times cited : (225)

References (39)
  • 2
    • 0003234757 scopus 로고
    • On randomized solutions of Laplace's equation
    • Babuska I. On randomized solutions of Laplace's equation Casopis Pest. Mater. 36 1961 269-276
    • (1961) Casopis Pest. Mater. , vol.36 , pp. 269-276
    • Babuska, I.1
  • 3
    • 0016973380 scopus 로고
    • The random steady-state diffusion problem. I. Random generalized solutions to Laplace's equation
    • Bécus G.A. Cozzarelli F.A. The random steady-state diffusion problem. I. Random generalized solutions to Laplace's equation SIAM J. Appl. Math. 31 1976 134-147
    • (1976) SIAM J. Appl. Math. , vol.31 , pp. 134-147
    • Bécus, G.A.1    Cozzarelli, F.A.2
  • 4
    • 0016971836 scopus 로고
    • The random steady-state diffusion problem. II: Random solutions to nonlinear inhomogeneous, steady-state diffusion problems
    • Bécus G.A. Cozzarelli F.A. The random steady-state diffusion problem. II: random solutions to nonlinear inhomogeneous, steady-state diffusion problems SIAM J. Appl. Math. 31 1976 148-158
    • (1976) SIAM J. Appl. Math. , vol.31 , pp. 148-158
    • Bécus, G.A.1    Cozzarelli, F.A.2
  • 5
    • 0016973667 scopus 로고
    • The random steady-state diffusion problem. III: Solutions to random diffusion problems by the method of random successive approximations
    • Bécus G.A. Cozzarelli F.A. The random steady-state diffusion problem. III: solutions to random diffusion problems by the method of random successive approximations SIAM J. Appl. Math. 31 1976 159-178
    • (1976) SIAM J. Appl. Math. , vol.31 , pp. 159-178
    • Bécus, G.A.1    Cozzarelli, F.A.2
  • 6
    • 0000148817 scopus 로고
    • The orthogonal development of nonlinear functionals in series of Fourier-Hermite functionals
    • Cameron R.H. Martin W.T. The orthogonal development of nonlinear functionals in series of Fourier-Hermite functionals Ann. Math. 48 1947 385-392
    • (1947) Ann. Math. , vol.48 , pp. 385-392
    • Cameron, R.H.1    Martin, W.T.2
  • 7
    • 0031080202 scopus 로고    scopus 로고
    • Sensitivity analysis of one-dimensional heat transfer in tissue with temperature-dependent perfusion
    • Davis C.R. Saidel G.M. Harasaki H. Sensitivity analysis of one-dimensional heat transfer in tissue with temperature-dependent perfusion J. Biomech. Eng. 119 1997 77-80
    • (1997) J. Biomech. Eng. , vol.119 , pp. 77-80
    • Davis, C.R.1    Saidel, G.M.2    Harasaki, H.3
  • 8
    • 0035964634 scopus 로고    scopus 로고
    • Solution of stochastic partial differential equations using Galerkin finite element techniques
    • Deb M.K. Babuska I. Oden J.T. Solution of stochastic partial differential equations using Galerkin finite element techniques Comput. Methods Appl. Mech. Eng. 190 2001 6359-6372
    • (2001) Comput. Methods Appl. Mech. Eng. , vol.190 , pp. 6359-6372
    • Deb, M.K.1    Babuska, I.2    Oden, J.T.3
  • 9
    • 0026204804 scopus 로고
    • Weighted integral method. I: Stochastic stiffness matrix
    • Deodatis G. Weighted integral method. I: stochastic stiffness matrix J. Eng. Mech. 117 8 1991 1851-1864
    • (1991) J. Eng. Mech. , vol.117 , Issue.8 , pp. 1851-1864
    • Deodatis, G.1
  • 10
    • 0026204584 scopus 로고
    • Weighted integral method. II: Response variability and reliability
    • Deodatis G. Shinozuka M. Weighted integral method. II: response variability and reliability J. Eng. Mech. 117 8 1991 1865-1877
    • (1991) J. Eng. Mech. , vol.117 , Issue.8 , pp. 1865-1877
    • Deodatis, G.1    Shinozuka, M.2
  • 11
    • 0028152249 scopus 로고
    • Transient effects of uncertainties on the sensitivities of temperatures and heat fluxes using stochastic finite elements
    • Fadale T.D. Emery A.F. Transient effects of uncertainties on the sensitivities of temperatures and heat fluxes using stochastic finite elements J. Heat Trans. 116 1994 808-814
    • (1994) J. Heat Trans. , vol.116 , pp. 808-814
    • Fadale, T.D.1    Emery, A.F.2
  • 12
    • 0033528038 scopus 로고    scopus 로고
    • Ingredients for a general purpose stochastic finite element formulation
    • Ghanem R.G. Ingredients for a general purpose stochastic finite element formulation Comput. Methods Appl. Mech. Eng. 168 1999 19-34
    • (1999) Comput. Methods Appl. Mech. Eng. , vol.168 , pp. 19-34
    • Ghanem, R.G.1
  • 13
    • 0033008165 scopus 로고    scopus 로고
    • Stochastic finite elements for heterogeneous media with multiple random non-Gaussian properties
    • Ghanem R.G. Stochastic finite elements for heterogeneous media with multiple random non-Gaussian properties ASCE J. Eng. Mech. 125 1 1999 26-40
    • (1999) ASCE J. Eng. Mech. , vol.125 , Issue.1 , pp. 26-40
    • Ghanem, R.G.1
  • 14
    • 0029776146 scopus 로고    scopus 로고
    • Numerical solution of spectral stochastic finite element systems
    • Ghanem R.G. Kruger R.M. Numerical solution of spectral stochastic finite element systems Comput. Methods Appl. Mech. Eng. 129 1996 289-303
    • (1996) Comput. Methods Appl. Mech. Eng. , vol.129 , pp. 289-303
    • Ghanem, R.G.1    Kruger, R.M.2
  • 15
    • 0033329066 scopus 로고    scopus 로고
    • Propagation of uncertainty in complex physical systems using a stochastic finite elements approach
    • Ghanem R.G. Red-Horse J. Propagation of uncertainty in complex physical systems using a stochastic finite elements approach Physica D 133 1999 137-144
    • (1999) Physica D , vol.133 , pp. 137-144
    • Ghanem, R.G.1    Red-Horse, J.2
  • 17
    • 0026955551 scopus 로고
    • Direct numerical solution of diffusion problems with intrinsic randomness
    • He X. Georgiadis J.G. Direct numerical solution of diffusion problems with intrinsic randomness Int. J. Heat Mass Transfer 35 1992 3141-3151
    • (1992) Int. J. Heat Mass Transfer , vol.35 , pp. 3141-3151
    • He, X.1    Georgiadis, J.G.2
  • 18
    • 0031148476 scopus 로고    scopus 로고
    • Stochastic finite element modelling in linear transient heat transfer
    • Hien T.D. Kleiber M. Stochastic finite element modelling in linear transient heat transfer Comput. Methods Appl. Mech. Eng. 144 1997 111-124
    • (1997) Comput. Methods Appl. Mech. Eng. , vol.144 , pp. 111-124
    • Hien, T.D.1    Kleiber, M.2
  • 19
    • 0031647529 scopus 로고    scopus 로고
    • On solving nonlinear transient heat transfer problems with random parameters
    • Hien T.D. Kleiber M. On solving nonlinear transient heat transfer problems with random parameters Comput. Methods Appl. Mech. Eng. 151 1998 287-299
    • (1998) Comput. Methods Appl. Mech. Eng. , vol.151 , pp. 287-299
    • Hien, T.D.1    Kleiber, M.2
  • 20
    • 0033175901 scopus 로고    scopus 로고
    • Stochastic finite element modeling of transient heat transfer in layered composites
    • Kaminski M. Hien T.D. Stochastic finite element modeling of transient heat transfer in layered composites Int. Commun. Heat Mass Transfer 26 6 1999 801-810
    • (1999) Int. Commun. Heat Mass Transfer , vol.26 , Issue.6 , pp. 801-810
    • Kaminski, M.1    Hien, T.D.2
  • 24
    • 0035149888 scopus 로고    scopus 로고
    • Uncertainty analysis of temperature prediction of biological bodies subject to randomly spatial heating
    • Liu J. Uncertainty analysis of temperature prediction of biological bodies subject to randomly spatial heating J. Biomech. 34 2001 1637-1642
    • (2001) J. Biomech. , vol.34 , pp. 1637-1642
    • Liu, J.1
  • 27
    • 0023288358 scopus 로고
    • Applications of probabilistic finite element methods in elastic/plastic dynamics
    • Liu W.K. Belytschko T. Mani A. Applications of probabilistic finite element methods in elastic/plastic dynamics J. Eng. Ind., ASME 109 1987 2-8
    • (1987) J. Eng. Ind., ASME , vol.109 , pp. 2-8
    • Liu, W.K.1    Belytschko, T.2    Mani, A.3
  • 28
    • 0003981320 scopus 로고
    • fourth ed. New York: Springer-Verlag
    • Loève M. Probability Theory fourth ed. 1977 Springer-Verlag New York
    • (1977) Probability Theory
    • Loève, M.1
  • 31
    • 0020842793 scopus 로고
    • Stochastic finite element analysis of simple beams
    • Vanmarcke E.H. Grigoriu M. Stochastic finite element analysis of simple beams J. Eng. Mech. 109 1983 1203-1214
    • (1983) J. Eng. Mech. , vol.109 , pp. 1203-1214
    • Vanmarcke, E.H.1    Grigoriu, M.2
  • 32
    • 0001760833 scopus 로고
    • On stationary processes in the plane
    • Whittle P. On stationary processes in the plane Biometrika 41 1954 434-449
    • (1954) Biometrika , vol.41 , pp. 434-449
    • Whittle, P.1
  • 33
    • 0000786435 scopus 로고
    • The homogeneous chaos
    • Wiener N. The homogeneous chaos Am. J. Math. 60 1938 897-936
    • (1938) Am. J. Math. , vol.60 , pp. 897-936
    • Wiener, N.1
  • 35
    • 0037184252 scopus 로고    scopus 로고
    • Modeling uncertainty in steady-state diffusion problems via generalized polynomial chaos
    • Xiu D. Karniadakis G.E. Modeling uncertainty in steady-state diffusion problems via generalized polynomial chaos Comput. Methods Appl. Math. Eng. 191 2002 4927-4948
    • (2002) Comput. Methods Appl. Math. Eng. , vol.191 , pp. 4927-4948
    • Xiu, D.1    Karniadakis, G.E.2
  • 36
    • 0037249229 scopus 로고    scopus 로고
    • The Wiener-Askey polynomial chaos for stochastic differential equations
    • Xiu D. Karniadakis G.E. The Wiener-Askey polynomial chaos for stochastic differential equations SIAM J. Sci. Comput. 24 2 2002 619-644
    • (2002) SIAM J. Sci. Comput. , vol.24 , Issue.2 , pp. 619-644
    • Xiu, D.1    Karniadakis, G.E.2
  • 37
    • 0037408312 scopus 로고    scopus 로고
    • Modeling uncertainty in flow simulations via generalized polynomial chaos
    • Xiu D. Karniadakis G.E. Modeling uncertainty in flow simulations via generalized polynomial chaos J. Comput. Phys. 187 2003 137-167
    • (2003) J. Comput. Phys. , vol.187 , pp. 137-167
    • Xiu, D.1    Karniadakis, G.E.2
  • 38
    • 0011074291 scopus 로고    scopus 로고
    • Stochastic modeling of flow-structure interactions using generalized polynomial chaos
    • Xiu D. Lucor D. Su C.-H. Karniadakis G.E. Stochastic modeling of flow-structure interactions using generalized polynomial chaos J. Fluids Eng. 124 2002 51-59
    • (2002) J. Fluids Eng. , vol.124 , pp. 51-59
    • Xiu, D.1    Lucor, D.2    Su, C.-H.3    Karniadakis, G.E.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.