Abstract
Some analyses of the static and dynamic buckling of imperfection-sensitive structures with small random imperfections are reviewed and extended. Statistical properties such as the mean of buckling load and the probability of failure at specified loads are presented for structures whose response and buckling loads can be characterized by one imperfection parameter. For structures for which ergodicity assumptions are reasonable an analysis is presented for determing the dynamic buckling loads for impulsive loading. These buckling loads are compared with results for static and step loading.
This work was supported in part by the National Science Foundation under Grant GP-33679X.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bolotin, V. V.: Statistical Methods in the Nonlinear Theory of Elastic Shells. NASA TT F-85, 1962.
Bolotin, V. V.: Statistical Methods in Structural Mechanics, Chapter 4. Holden-Day, 1965.
Thompson, J. M. T.: Toward a General Statistical Theory of Imperfection- Sensitivity in Elastic Post-Buckling. J. Mech. Phys. Solids 15 413–417 (1967).
Roorda, J.: Some Statistical Aspects of the Buckling of Imperfection-Sensitive Structures. J. Mech. Phys. Solids 17 111–123 (1969).
Budiansky, B.: Dynamic Buckling of Elastic Structures: Criteria and Estimates, in Dynamic Stability of Structures, edited by G. Herrmann. New York: Pergamon 1966, pp. 83–106.
Fräser, W. B.: Buckling of Structures with Random Imperfections. Ph. D. thesis. Harvard University, 1965.
Amazigo, J. C.: Buckling under Axial Compression of Long Cylindrical Shells with Random Axisymmetric Imperfections. Quart. Appl. Math. 26, 4, 537–566 (1969).
Eraser, W. B.; Budiansky, B.: The Buckling of a Column with Random Initial Deflections. J. Appl. Math. 36 233–240 (1969).
Amazigo, J. C.; Budiansky, B.; Carrier, G. F.: Asymptotic Analyses of the Buckling of Imperfect Columns’on Nonlinear Elastic Foundations. Int. J. Solids Struct. 6, 883–900 (1971).
Amazigo, J. C.: Buckling of Stochastically Imperfect Columns on Nonlinear Elastic Foundations. Quart. Appl. Math. 29, 403–409 (1971).
Amazigo, J. C.; Budiansky, B.: Asymptotic Formulas for the Buckling Stresses of Axially Compressed Cylinders with Localized or Random Axisymmetric Imperfections. J. Appl. Mech. 39, 179–184 (1972).
Amazigo, J. C.: Asymptotic Analysis of the Buckling of Externally Pressurized Cylinders with Random Imperfections. Quart. Appl. Math. 31, 429–442 (1974).
Amazigo, J. C.: Dynamic Buckling of Structures with Random Imperfections. Stochastic Problems in Mechanics. Ed. H. Leipholz, Univ. of Waterloo Press 1974, pp. 243–254.
Budiansky, B.; Hutchinson, J. W.: Dynamic Buckling of Imperfection-Sensitive Structures. Proc. XI Internat. Cong. Appl. Mech., Munich, 1964.
Koiter, W. T.: On the Stability of Elastic Equilibrium (in Dutch). Thesis, Delft, Amsterdam, 1945; English translation: NASA TT F-10, 1967, pp. 883.
Amazigo, J. C.; Frank, D.: Dynamic Buckling of an Imperfect Column on Nonlinear Foundation. Quart. Appl. Math. 31 1–9 (1973).
Lockhart, D.; Amazigo, J. C.: Dynamic Buckling of Externally Pressurized Imperfect Cylindrical Shells, J. Appl. Mech. 42, 316–320 (1975).
Batdorf, S. B.: A Simplified Method of Elastic-Stability Analysis for Thin Cylindrical Shells. NACA Report 874, 1947.
Budiansky, B.; Amazigo, J. C.: Initial Post-Buckling Behavior of Cylindrical Shells under External Pressure. J. Math, and Physics 47, 3, 233–235 (1968).
Dow, D. A.: Buckling and Post-Buckling Tests of Ring-Stiffened Cylinders Loaded by Uniform “External Pressure”. NASA Langley Research Center TN D-3111, 1965.
Erdelyi, A.: Asymptotic Expansions. Dover 1956, p. 51.
Arbocz, J.: The Effect of Initial Imperfections on Shell Stability in Thin-Shell Structure. Ed. Y. C. Fung and E. E. Sethler, Prenctice Hall 1974.
Videc, B. P.; Sanders, J. L.: Application of Khas’minskii’s Limit Theorem to the Buckling Problem of a Column with Random Initial Deflection to appear in Quart. Appl. Math.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1976 Springer-Verlag, Berlin/Heidelberg
About this paper
Cite this paper
Amazigo, J.C. (1976). Buckling of Stochastically Imperfect Structures. In: Budiansky, B. (eds) Buckling of Structures. International Union of Theoretical and Applied Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-50992-6_16
Download citation
DOI: https://doi.org/10.1007/978-3-642-50992-6_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-50994-0
Online ISBN: 978-3-642-50992-6
eBook Packages: Springer Book Archive