Reliability‐Based Design of Imperfection‐Sensitive Structures
Publication: Journal of Engineering Mechanics
Volume 117, Issue 6
Abstract
It is well known that certain structural systems that exhibit bifurcation buckling may be sensitive to the small structural imperfections. A general method for the reliability‐based design of such imperfection‐sensitive structures is developed. The method is based on a regular perturbation analysis in terms of the imperfection magnitude around the prebuckling equilibrium state of the corresponding perfect structure. The structural imperfections are represented as a weakly stationary random process with a prespecified autocorrelation function. The new approach results in simple analytical formulae for the design value of the imperfection magnitude at any desired reliability level. All the imperfection modes are taken into account, and no restrictions, besides the usual smoothness requirements, need be imposed on the imperfection patterns. The analysis holds equally well for both simple and compound buckling of conservative elastic systems, and allows the consideration of more than one different forms of structural imperfections at the same time. As an example, the reliability‐based design of a column on a linear elastic foundation is investigated. Numerical results on the effect of imperfections, which invalidate certain intuitively anticipated design improvements, are obtained.
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References
1.
Arbocz, J., Potier‐Ferry, M., Singer, J., and Tvergaard, V. (1987). Buckling and post buckling. Springer, New York, N.Y.
2.
Brush, D. O., and Almroth, B. O. (1975). Buckling of bars, plates, and shells. McGraw‐Hill, New York, N.Y.
3.
Bucher, C. G., and Shinozuka, M. (1986). “Structural response variability II.” J. Engrg. Mech., ASCE, 114(12), 2035–2054.
4.
Elishakoff, I. (1979). “Buckling of a stochastically imperfect finite column on a nonlinear elastic foundation.” J. Appl. Mech. Trans. ASME, 46(2), 411–416.
5.
Gourlay, A. R., and Watson, G. A. (1973). Computational methods for matrix eigenproblems. Wiley and Sons, New York, N.Y.
6.
Harr, M. E. (1987). Reliability based design in civil engineering. McGraw‐Hill, New York, N.Y.
7.
Hunt, G. W. (1986). “Hidden asymmetries of elastic and plastic bifurcation.” Appl. Mech. Review, 38(8), 1165–1186.
8.
Hutchinson, J. W., and Koiter, W. T. (1970). “Postbuckling theory.” Appl. Mech. Review, 23, 1353–1366.
9.
Kardara, A., Bucher, C. G., and Shinozuka, M. (1989). “Structural response variability III.” J. Engrg. Mech., ASCE, 115(8), 1726–1747.
10.
Koiter, W. T. (1963). “Elastic stability and post‐buckling behavior.” Non‐linear problems. R. E. Langer, ed., University of Wisconsin Press, Madison, Wis.
11.
Palassopoulos, G. V. (1973). “On the buckling of axially compressed thin cylindrical shells.” J. Struct. Mech., 2(3), 177–193.
12.
Palassopoulos, G. V. (1980). “A probabilistic approach to the buckling of thin cylindrical shells with general random imperfections: Solution of the corresponding deterministic problem.” Theory of shells, W. T. Koiter and G. K. Mikhailov, eds., North‐Holland, Amsterdam, the Netherlands, 417–443.
13.
Palassopoulos, G. V. (1989). “Optimization of imperfection sensitive structures.” J. Engrg. Mech., ASCE, 115(8), 1663–1682.
14.
Palassopoulos, G. V., and Shinozuka, M. (1973). “On the elastic stability of thinshells.” J. Struct. Mech., 1(4), 439–449.
15.
Reddy, J. N. (1986). Applied functional analysis and variational methods in engineering. McGraw‐Hill, New York, N.Y.
16.
Shinozuka, M. (1986). “Structural response variability.” J. Engrg. Mech., ASCE, 113(6), 825–842.
17.
Thompson, J. M. T. (1982). Instabilities and catastrophes in science and engineering. Wiley and Sons, New York, N.Y.
18.
Thompson, J. M. T., and Hunt, G. W. (1973). A general theory of elastic stability. Wiley and Sons, New York, N.Y.
19.
Timoshenko, S. P., and Gere, J. M. (1961). Theory of elastic stability. McGraw‐Hill, New York, N.Y.
20.
Yaglom, A. M. (1962). Stationary random functions. Dover, New York, N.Y.
21.
Yamaki, N. (1984). Elastic stability of circular cylindrical shells. North‐Holland, New York, N.Y.
Information & Authors
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Published In
Journal of Engineering Mechanics
Volume 117 • Issue 6 • June 1991
Pages: 1220 - 1240
Copyright
Copyright © 1991 ASCE.
History
Published online: Jun 1, 1991
Published in print: Jun 1991
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