Selection of Random Field Mesh in Finite Element Reliability Analysis
Publication: Journal of Engineering Mechanics
Volume 119, Issue 4
Abstract
Random fields are often used in reliability analysis to model the uncertainties that possess spatial variabilities. Within the framework of finite element reliability methods, the domain of each field is discretized into a mesh of random field elements and the value for each element is represented by a single random variable. The selection of random field mesh is important since it influences the accuracy of the reliability analysis. In this study, how to select and refine the random field mesh in finite element reliability analysis is investigated. An expression is derived to compare the improvements made by various refinements of a coarse mesh. Further exploration of the expression shows that the gradient of the limit‐state function plays a key role in the selection of a random field mesh. A criterion for selecting random field meshes is devised as follows: Adopt a coarse mesh in the area where the gradient of the limit‐state function with respect to the discretized variables is small, and a fine mesh in the area where the gradient is large. The selection rule developed in this study is verified by a beam and a plate examples.
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References
1.
Der Kiureghian, A. (1987). “Multivariate distribution models for structural reliability.” Trans. 9th Int. Conf. on Struct. Mech. in Reactor Tech., 373–379.
2.
Der Kiureghian, A., and Ke, B.‐J. (1988). “The stochastic finite element method in structural reliability.” Probabilistic Engrg. Mech., 3(2), 83–91.
3.
Der Kiureghian, A., and Liu, P.‐L. (1986). “Structural reliability under incomplete probability information.” J. Engrg. Mech., ASCE, 112(1), 85–104.
4.
Grigoriu, M. (1984). “Crossings of non‐Gaussian translation processes.” J. Engrg. Mech., 110(4), 610–620.
5.
Hisada, T. and Nakagiri, S. (1985). “Role of the stochastic finite element method in structural safety and reliability.” Proc., 4th Int. Conf. on Struct. Safety and Reliability, 385–394.
6.
Lawrence, M. (1987). “Basis random variables in finite element analysis.” Int. J. Numer. Methods Eng., 24, 1849–1863.
7.
Liu, P.‐L. (1990). “Size effect of random field elements on finite‐element reliability methods.” Proc., 3rd IFIP WG 7.5 Working Conf. on Reliability and Optimization of Struct. Systems, 223–239.
8.
Liu, W. K., Belytschko, T., and Mani, A. (1986). “Random field finite elements.” Int. J. Numer. Methods in Engrg., 23, 1831–1845.
9.
Liu, W. K., Belytschko, T., and Mani, A. (1987). “Applications of probabilistic finite element methods in elastic/plastic dynamics.” Engineering for Industry, ASME, 109, 2–8.
10.
Spanos, P. D., and Ghanem, R. (1988). “Stochastic finite element expansion for random media.” J. Eng. Mech., ASCE, 115(5), 1035–1053.
11.
Vanmarcke, E. H., and Grigoriu, M. (1983). “Stochastic finite element analysis of simple beams.” J. Eng. Mech., ASCE, 109(5), 1203–1214.
12.
Yamazaki, F., Shinozuka, M., and Dasgupta, G. (1988). “Neumann expansion for stochastic finite element analysis.” J. Eng. Mech., ASCE, 114(8), 1335–1354.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 119 • Issue 4 • April 1993
Pages: 667 - 680
Copyright
Copyright © 1993 American Society of Civil Engineers.
History
Received: May 18, 1992
Published online: Apr 1, 1993
Published in print: Apr 1993
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