Dynamic buckling of an imperfect column on nonlinear foundation
Authors:
John C. Amazigo and Deborah Frank
Journal:
Quart. Appl. Math. 31 (1973), 1-9
DOI:
https://doi.org/10.1090/qam/99711
MathSciNet review:
QAM99711
Full-text PDF Free Access
References |
Additional Information
- Julian D. Cole, Perturbation methods in applied mathematics, Blaisdell Publishing Co. Ginn and Co., Waltham, Mass.-Toronto, Ont.-London, 1968. MR 0246537
G. F. Carrier and C. E. Pearson, Ordinary differential equations, p. 210, Blaisdell, 1968
W. B. Fraser and B. Budiansky, The buckling of a column with random initial deflections, J. Appl. Mech. 36, 233–240 (1969)
J. C. Amazigo, B. Budiansky and G. F. Carrier, Asymptotic analyses of the buckling of imperfect columns on nonlinear elastic foundations, Int. J. Solids Structures 6, 1341–1356 (1970)
J. C. Amazigo, Buckling of stochastically imperfect columns on nonlinear elastic foundations, Quart. Appl. Math. 29, 403–409 (1971)
B. Budiansky and J. W. Hutchinson, Dynamic buckling of imperfection-sensitive structures, in Proceedings of the Eleventh International Congress of Applied Mechanics, Springer-Verlag, Berlin, 1966
J. W. Hutchinson and B. Budiansky, Dynamic buckling estimates, AIAA Journal 4, 525–530 (1966)
B. Budiansky, Dynamic buckling of elastic structures: criteria and estimates, in Dynamic stability of structures, edited by G. Herrmann, Pergamon, New York, 1966
W. T. Koiter, On the stability of elastic equilibrium (in Dutch), thesis, Delft, Amsterdam 1945; English translation issued as NASA TT F-10, p. 833, 1967
D. A. Danielson, Dynamic buckling loads of imperfection-sensitive structures from perturbation procedures, AIAA Journal 7, 1506–1510 (1969)
- Edward L. Reiss and Bernard J. Matkowsky, Nonlinear dynamic buckling of a compressed elastic column, Quart. Appl. Math. 29 (1971), 245–260. MR 286344, DOI https://doi.org/10.1090/S0033-569X-1971-0286344-8
- J. J. Stoker, Nonlinear Vibrations in Mechanical and Electrical Systems, Interscience Publishers, Inc., New York, N.Y., 1950. MR 0034932
- Paul F. Byrd and Morris D. Friedman, Handbook of elliptic integrals for engineers and physicists, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete. Bd LXVII, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1954. MR 0060642
C. S. Hsu, On dynamic stability of elastic bodies with prescribed initial conditions, Int. J. Engng. Sci. 4, 1–21 (1966)
J. D. Cole, Perturbation methods in applied mathematics, Ch. 3, Blaisdell, 1968
G. F. Carrier and C. E. Pearson, Ordinary differential equations, p. 210, Blaisdell, 1968
W. B. Fraser and B. Budiansky, The buckling of a column with random initial deflections, J. Appl. Mech. 36, 233–240 (1969)
J. C. Amazigo, B. Budiansky and G. F. Carrier, Asymptotic analyses of the buckling of imperfect columns on nonlinear elastic foundations, Int. J. Solids Structures 6, 1341–1356 (1970)
J. C. Amazigo, Buckling of stochastically imperfect columns on nonlinear elastic foundations, Quart. Appl. Math. 29, 403–409 (1971)
B. Budiansky and J. W. Hutchinson, Dynamic buckling of imperfection-sensitive structures, in Proceedings of the Eleventh International Congress of Applied Mechanics, Springer-Verlag, Berlin, 1966
J. W. Hutchinson and B. Budiansky, Dynamic buckling estimates, AIAA Journal 4, 525–530 (1966)
B. Budiansky, Dynamic buckling of elastic structures: criteria and estimates, in Dynamic stability of structures, edited by G. Herrmann, Pergamon, New York, 1966
W. T. Koiter, On the stability of elastic equilibrium (in Dutch), thesis, Delft, Amsterdam 1945; English translation issued as NASA TT F-10, p. 833, 1967
D. A. Danielson, Dynamic buckling loads of imperfection-sensitive structures from perturbation procedures, AIAA Journal 7, 1506–1510 (1969)
E. L. Reiss and B. J. Matkowsky, Nonlinear dynamic buckling of a compressed elastic column, Quart. Appl. Math. 29, 245–260 (1971)
J. J. Stoker, Nonlinear vibrations in mechanical and electrical systems, Interscience, New York, 1950, p. 202
P. F. Byrd and M. D. Friedman, Handbook of elliptic integrals for engineers and physicists, Springer-Verlag, Berlin, 1954
C. S. Hsu, On dynamic stability of elastic bodies with prescribed initial conditions, Int. J. Engng. Sci. 4, 1–21 (1966)
Additional Information
Article copyright:
© Copyright 1973
American Mathematical Society
