An adaptive scheme for random field discretization using KL expansion

Engineering with Computers - Tập 38 Số 4 - Trang 2937-2954 - 2022
Kamaljyoti Nath1, Anjan Dutta1, Budhaditya Hazra1
1Department of Civil Engineering, Indian Institute of Technology Guwahati, Guwahati, Assam 781039, India

Tóm tắt

Từ khóa


Tài liệu tham khảo

Ma X, Zabaras N (2011) A stochastic mixed finite element heterogeneous multiscale method for flow in porous media. J Comput Phys 230(12):4696–4722. ISSN 0021-9991. https://doi.org/10.1016/j.jcp.2011.03.001. http://www.sciencedirect.com/science/article/pii/S0021999111001318

Li J, Tian Y, Cassidy MJ (2015) Failure mechanism and bearing capacity of footings buried at various depths in spatially random soil. J Geotech Geoenviron Eng 141(2):04014099. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001219

Shinozuka M (1972) Probabilistic modeling of concrete structures. ASCE J Eng Mech Div 98:1433–1451

Ditlevsen O (1988) Stochastic model of self-weight load. J Struct Eng 114(1):222–230. https://doi.org/10.1061/(ASCE)0733-9445(1988)114:1(222)

Heng L, Dongxiao Z (2013) Stochastic representation and dimension reduction for non-gaussian random fields: review and reflection. Stoch Environ Res Risk Assess 27(7):1621–1635. https://doi.org/10.1007/s00477-013-0700-7 (ISSN 1436-3259)

Ghanem R, Spanos P (1991) Stochastic finite element: a spectral approach. Spinger-Verlag, New York

Stefanou G (2009) The stochastic finite element method: past, present and future. Comput Methods Appl Mech Eng 198(9):1031–1051. ISSN 0045-7825. https://doi.org/10.1016/j.cma.2008.11.007. http://www.sciencedirect.com/science/article/pii/S0045782508004118

Allaix DL, Carbone VI (2009) Discretization of 2d random fields: a genetic algorithm approach. Eng Struct 31(5):1111–1119. ISSN 0141-0296. https://doi.org/10.1016/j.engstruct.2009.01.008. http://www.sciencedirect.com/science/article/pii/S014102960900011X

Vanmarcke E, Grigoriu M (1983) Stochastic finite element analysis of simple beams. J Eng Mech 109(5):1203–1214. https://doi.org/10.1061/(ASCE)0733-9399(1983)109:5(1203)

Liu WK, Belytschko T, Mani A (1986) Random field finite elements. Int J Numer Methods Eng 23:1831–1845. https://doi.org/10.1002/nme.1620231004

Kiureghian AD, Ke J-B (1988) The stochastic finite element method in structural reliability. Probab Eng Mech 3(2):83–91. ISSN 0266-8920. https://doi.org/10.1016/0266-8920(88)90019-7. http://www.sciencedirect.com/science/article/pii/0266892088900197

Deodatis G (1990) Bounds on response variability of stochastic finite element systems: effect of statistical dependence. Probab Eng Mech 5(2):88–98. ISSN 0266-8920. https://doi.org/10.1016/0266-8920(90)90012-9. http://www.sciencedirect.com/science/article/pii/0266892090900129

Takada T (1990) Weighted integral method in stochastic finite element analysis. Probab Eng Mech 5(3):146–156. ISSN 0266-8920. https://doi.org/10.1016/0266-8920(90)90006-6. http://www.sciencedirect.com/science/article/pii/0266892090900066

Loeve M (1977) Probability theory I. Springer-Verlag, New York

Zhang J, Ellingwood B (1994) Orthogonal series expansions of random fields in reliability analysis. J Eng Mech 120(12):2660–2677. https://doi.org/10.1061/(ASCE)0733-9399(1994)120:12(2660)

Li C, Der Kiureghian A (1993) Optimal discretization of random fields. J Eng Mech 119(6):1136–1154. https://doi.org/10.1061/(ASCE)0733-9399(1993)119:6(1136)

Brenner CE, Bucher C (1995) A contribution to the SFE-based reliability assessment of nonlinear structures under dynamic loading. Probab Eng Mech 10(4):265–273. ISSN 0266-8920. https://doi.org/10.1016/0266-8920(95)00021-6. http://www.sciencedirect.com/science/article/pii/0266892095000216

Wiener N (1938) The homogeneous chaos. Am J Math 60(4):897–936. ISSN 00029327, 10806377. http://www.jstor.org/stable/2371268

Ghanem R, Spanos PD (1990) Polynomial chaos in stochastic finite elements. J Appl Mech 57(1):197–202. https://doi.org/10.1115/1.2888303

Chen Y, Jakeman J, Gittelson C, Xiu D (2015) Local polynomial chaos expansion for linear differential equations with high dimensional random inputs. SIAM J Sci Comput 37(1):A79–A102. https://doi.org/10.1137/140970100

Pranesh S, Ghosh D (2016) Addressing the curse of dimensionality in SSFEM using the dependence of eigenvalues in KL expansion on domain size. Comput Methods Appl Mech Eng 311:457–475. ISSN 0045-7825. https://doi.org/10.1016/j.cma.2016.08.023. http://www.sciencedirect.com/science/article/pii/S0045782516310155

Doostan A, Ghanem RG, Red-Horse J (2007) Stochastic model reduction for chaos representations. Comput Methods Applied Mech Eng 196(37):3951–3966. ISSN 0045-7825. (Special issue honoring the 80th birthday of Professor Ivo Babuška)

Nath K, Dutta A, Hazra B (2019a) An iterative polynomial chaos approach for solution of structural mechanics problem with gaussian material property. J Comput Phys 390:425–451. ISSN 0021-9991. https://doi.org/10.1016/j.jcp.2019.04.014. http://www.sciencedirect.com/science/article/pii/S0021999119302475

Pranesh S, Ghosh D (2018) Cost reduction of stochastic galerkin method by adaptive identification of significant polynomial chaos bases for elliptic equations. Comput Methods Appl Mech Eng 340:54–69. ISSN 0045-7825. https://doi.org/10.1016/j.cma.2018.04.043. http://www.sciencedirect.com/science/article/pii/S0045782518302287

Cheng Kai, Zhenzhou Lu (2018) Adaptive sparse polynomial chaos expansions for global sensitivity analysis based on support vector regression. Comput Struct 194:86–96

Phoon KK, Huang HW, Quek ST (2005) Simulation of strongly non-gaussian processes using Karhunen-Loève expansion. Probab Eng Mech 20(2):188–198. ISSN 0266-8920. https://doi.org/10.1016/j.probengmech.2005.05.007. http://www.sciencedirect.com/science/article/pii/S0266892005000123

Allaix DL, Carbone VI (2010) Numerical discretization of stationary random processes. Probab Eng Mech 25(3):332–347. ISSN 0266-8920. https://doi.org/10.1016/j.probengmech.2010.03.001. http://www.sciencedirect.com/science/article/pii/S0266892010000196

Allaix DL, Carbone VI (2012) Development of a numerical tool for random field discretization. Adv Eng Softw 51:10–19. ISSN 0965-9978. https://doi.org/10.1016/j.advengsoft.2012.04.006. http://www.sciencedirect.com/science/article/pii/S0965997812000695

Huang S, Phoon K-K, Quek ST (2000) Digital simulation of non-gaussian stationary processes using Karhunen - Loéve expansion. In: 8th ASCE specialty conference on probabilistic mechanics and structural reliability, 01

Huang SP, Quek ST, Phoon KK (2001) Convergence study of the truncated Karhunen - Loéve expansion for simulation of stochastic processes. Int J Numer Methods Eng 52(9):1029–1043. https://doi.org/10.1002/nme.255 (ISSN 1097-0207)

Rahman S, Xu H (2005) A meshless method for computational stochastic mechanics. Int J Comput Methods Eng Sci Mech 6(1):41–58. https://doi.org/10.1080/15502280590888649

Betz W, Papaioannou I, Straub D (2014) Numerical methods for the discretization of random fields by means of the Karhunen–Loéve expansion. Comput Methods Appl Mech Eng 271:109–129. ISSN 0045-7825. https://doi.org/10.1016/j.cma.2013.12.010. http://www.sciencedirect.com/science/article/pii/S0045782513003502

Nath K, Dutta A, Hazra B (2019b) An iterative polynomial chaos approach toward stochastic elastostatic structural analysis with non-gaussian randomness. Int J Numer Methods Eng 1–35. https://doi.org/10.1002/nme.6086. https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.6086

Schenk CA, Schuëller GI (2003) Buckling analysis of cylindrical shells with random geometric imperfections. Int J Nonlinear Mech 38(7):1119–1132. ISSN 0020-7462. https://doi.org/10.1016/S0020-7462(02)00057-4. http://www.sciencedirect.com/science/article/pii/S0020746202000574

Charmpis DC, Papadrakakis M (2005) Improving the computational efficiency in finite element analysis of shells with uncertain properties. Comput Methods Appl Mech Eng 194(12):1447–1478. ISSN 0045-7825. https://doi.org/10.1016/j.cma.2003.12.075. http://www.sciencedirect.com/science/article/pii/S0045782504004013. (Special issue on computational methods in stochastic mechanics and reliability analysis)

Blatman G, Sudret B (2008) Sparse polynomial chaos expansions and adaptive stochastic finite elements using a regression approach. C R Mécanique 336(6):518–523 (ISSN 1631-0721)

Nair PB, Keane AJ (2002) Stochastic reduced basis methods. Am Inst Aeronaut Astronaut 40(8):1653–1664

Yamazaki F, Member A, Shinozuka M, Dasgupta G (1988) Neumann expansion for stochastic finite element analysis. J Eng Mech 114(8):1335–1354. https://doi.org/10.1061/(ASCE)0733-9399(1988)114:8(1335)

Zeldin BA, Spanos PD (1998) On random field discretization in stochastic finite elements. J Appl Mech 65(2):320–327. https://doi.org/10.1115/1.2789057 (ISSN 0021-8936)

Pastor M, Binda M, Harčarik T (2012) Modal assurance criterion. Proc Eng 48:543–548. ISSN 1877-7058. https://doi.org/10.1016/j.proeng.2012.09.551. http://www.sciencedirect.com/science/article/pii/S1877705812046140

Shinozuka M, Deodatis G (1988) Response variability of stochastic finite element systems. J Eng Mech 114(3):499–519. https://doi.org/10.1061/(ASCE)0733-9399(1988)114:3(499)

Spanos P, Ghanem R (1989) Stochastic finite element expansion for random media. J Eng Mech 115(5):1035–1053. https://doi.org/10.1061/(ASCE)0733-9399(1989)115:5(1035)