Effects of Uncertain Material Properties on Structural Stability
Publication: Journal of Structural Engineering
Volume 121, Issue 4
Abstract
The effects of uncertain material properties on the elastic stability of structural members and frames are analyzed using a stochastic finite-element method. The uncertain material properties are modeled as continuous random fields by a series expansion involving orthogonal functions. The expanded random fields are incorporated into the finite-element formulation leading to an eigenvalue problem involving random parameters. A mean-centered second-order perturbation technique is used to find the probabilistic characteristics of the buckling load. Illustrations involving a simply supported beam, a simply supported beam on an elastic foundation, and a frame are presented. These illustrations demonstrate the impact on instability of characteristics of the random fields, including correlation length and coefficients of variation of random flexural rigidity and/or random elastic foundation modulus, finite-element mesh selection, and the interrelation between statistical and finite-element modeling. A comparison of the perturbation solutions with the results from Monte Carlo simulation serves to validate the solutions and identify some of their limitations.
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References
1.
Boyce, W. E.(1961). “Buckling of a column with random initial displacements.”J. Aerosp. Sci., 28, 308–312.
2.
Chang, C. C., and Yang, T. Y.(1991). “Random vibration of flexible, uncertain beam element.”J. Engrg. Mech., ASCE, 117(10), 2329–2349.
3.
Chen, W. F., and Lui, E. M. (1987). Structural stability: Theory and implementation . Elsevier Sci. Publishing Co., New York, N.Y.
4.
Deodatis, G.(1989). “Stochastic FEM sensitivity analysis of nonlinear dynamic problems.”Probabilistic Engrg. Mech., 4(3), 135–141.
5.
Der Kiureghian, A., and Ke, J-B. (1987). “The stochastic finite element method in structural reliability.”Stochastic structural mechanics (Lecture Notes in Engrg. No. 31), Y. K. Lin and G. I. Schuëller, eds., Springer-Verlag, Berlin, West Germany, 84–109.
6.
Elishakoff, I.(1979a). “Buckling of a stochastically imperfect finite column on a nonlinear elastic foundation.”J. Appl. Mech., 46(2), 411–416.
7.
Elishakoff, I.(1979b). “Simulation of space random fields for solution of stochastic boundary value problems.”J. Acoustical Soc. of Am., 65(2), 399–403.
8.
Frazer, W. B., and Budiansky, B.(1969). “The buckling of a column with random initial deflection.”J. Appl. Mech., 36(2), 233–240.
9.
Ghanem, R. G., and Spanos, P. D.(1991). “Spectral stochastic finite element formulation for reliability analysis.”J. Engrg. Mech., ASCE, 117(10), 2351–2373.
10.
Grigoriu, M., Khater, M., and O'Rourke, T. (1985). Stochastic beams on elastic foundation . ASCE, New York, N.Y., 96–106.
11.
Hisada, T., and Nakagiri, S. (1985). “Role of the stochastic finite element method in structural safety and reliability.”Structural safety and reliability (Proc. 4th Int. Conf. on Struct. Safety and Reliability), Shinko Printing Ltd., Kyoto, Japan, 385–394.
12.
Jeong, G. D. (1992). “Critical buckling load statistics of uncertain column.”Probabilistic Mech. and Struct. and Geotech. Reliability, Proc. 6th Specialty Conf., 563–566.
13.
Lawrence, M.(1987). “Basis random variables in finite element analysis.”Int. J. Numer. Meth. in Engrg., 24(10), 1849–1863.
14.
Li, C. C., and Der Kiureghian, A.(1993). “Optimal discretization of random fields.”J. Engrg. Mech., ASCE, 119(6), 1136–1154.
15.
Lin, S. C., and Kam, T. Y.(1992). “Buckling analysis of imperfect frames using a stochastic finite element method.”Comput. & Struct., 42(6), 895–901.
16.
Liu, P. L., and Der Kiureghian, A.(1991). “Finite element reliability of geometrically nonlinear uncertain structures.”J. Engrg. Mech., ASCE, 117(8), 1806–1825.
17.
Liu, W. K., Belytschko, T., and Mani, A.(1986). “Random field finite elements.”Int. J. Numer. Meth. in Engrg., 23, 1831–1845.
18.
Shinozuka, M., and Astill, C. J.(1972). “Random eigenvalue problems in structural analysis.”AIAA J., 10(4), 456–462.
19.
Spanos, P. D., and Ghanem, R. G.(1989). “Stochastic finite element expansion for random media.”J. Engrg. Mech., ASCE, 115(5), 1035–1053.
20.
Timoshenko, S. P., and Gere, J. M. (1961). Theory of elastic stability. McGraw-Hill, New York, N.Y.
21.
Varmarcke, E., and Grigoriu, M.(1983). “Stochastic finite element analysis of simple beam.”J. Engrg. Mech., ASCE, 109(5), 1203–1214.
22.
Zhang, J., and Ellingwood, B.(1994). “Orthogonal series expansion of random fields in first-order reliability analysis.”J. Engrg. Mech., ASCE, 121(12), 2660–2677.
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Copyright © 1995 American Society of Civil Engineers.
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Published online: Apr 1, 1995
Published in print: Apr 1995
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