×

zbMATH — the first resource for mathematics

Stochastic response of structures with small geometric imperfections. (English) Zbl 0654.73033
A probabilistic model of the geometric imperfections of a real structure is proposed, in order to provide a general theory of the stochastic response of structures in the presence of small random deviations from the “perfect” scheme. The main statistical measures of the stochastic response are derived and an application to the study of a particular conservative elastic system is developed.

MSC:
74G60 Bifurcation and buckling
74S30 Other numerical methods in solid mechanics (MSC2010)
60H99 Stochastic analysis
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Koiter W.T., n the stability of elastic equilibrium(inDutch). Thesis, Delft Univ. H.J. Paris, Amsterdam, 1945. English transl. (a) NASA TT-F10, 833, 1967; (b) AFFDL-TR-70-25, 1970.
[2] Hutchinson J.W., Koiter W.T., ostbuckling theoryAppl. Math Rev. 1970,23, 1353.
[3] Koiter W.T., he energy criterion of stability for continuous elastic bodiesProc. Kon. Ned. Akad. Wetench, 1965,568, 178. · Zbl 0146.21103
[4] Koiter W.T., urpose and achievements of research in elastic stabilityProc. Tech Conf. Soc. Eng. Scie. 4th, North Caroline State Univ., Raleigh. N.C., 1966.
[5] Thompson J.M.T., Hunt G.W., general theory of elastic stability Wiley, New York, 1973. · Zbl 0351.73066
[6] Budiansky B., heory of buckling and post-buckling behaviour of elastic structuresAdvances in Appl Mech, 1974,14, 1. · doi:10.1016/S0065-2156(08)70030-9
[7] Arbocz J.,Babcock C.D., xperimental investigation of the effect of general imperfection on the buckling of cylindrical shells NASA Current Report, 1968, CR-1163.
[8] Singer J., Abramovich H., Yaffe R., nitial imperfection measurements of stiffened shells and buckling predictionsIsrael J. of Technology, 1979,17, 324.
[9] Soong T.T., andom differential equations in science and engineering Pergamon, New York, 1973. · Zbl 0348.60081
[10] Elishiakoff I., robabilistic Methods in the Theory of Structures Wiley, New York, 1983.
[11] Augusti G., Baratta A., Casciati F., robabilistic Methods in Structural Engineering Chapman & Hall, New York, 1984. · Zbl 0562.73078
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.