Buckling of columns and rearrangements of functions
Author:
David C. Barnes
Journal:
Quart. Appl. Math. 41 (1983), 169-180
MSC:
Primary 73H05; Secondary 73K40
DOI:
https://doi.org/10.1090/qam/719503
MathSciNet review:
719503
Full-text PDF Free Access
References |
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Additional Information
- David C. Barnes, Rearrangements of functions and lower bounds for eigenvalues of differential equations, Applicable Anal. 13 (1982), no. 4, 237–248. MR 670658, DOI https://doi.org/10.1080/00036818208839395
- Earl R. Barnes, The shape of the strongest column and some related extremal eigenvalue problems, Quart. Appl. Math. 34 (1976/77), no. 4, 393–409. MR 493674, DOI https://doi.org/10.1090/S0033-569X-1977-0493674-3
T. Clausen, Uber die Form Architektonisher Saulen, Bull. Phys.-Math. Astronum., Tome 1, 1849–1853
- R. Courant and D. Hilbert, Methods of mathematical physics. Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953. MR 0065391
- G. F. D. Duff, Differences, derivatives, and decreasing rearrangements, Canadian J. Math. 19 (1967), 1153–1178. MR 224758, DOI https://doi.org/10.4153/CJM-1967-105-0
- H. J. Ettlinger, Existence theorems for the general real self-adjoint linear system of the second order, Trans. Amer. Math. Soc. 19 (1918), no. 1, 79–96. MR 1501089, DOI https://doi.org/10.1090/S0002-9947-1918-1501089-3
Hardy Littlewood and Pólya, Inequalities, Cambridge University Press, Cambridge, 1964
- E. L. Ince, Ordinary Differential Equations, Dover Publications, New York, 1944. MR 0010757
- Joseph B. Keller, The shape of the strongest column, Arch. Rational Mech. Anal. 5 (1960), 275–285 (1960). MR 128160, DOI https://doi.org/10.1007/BF00252909
J. L. Lagrange, Sur la figure des colonnes, Miscellanea Tourinesia (Royal Society of Turin), Tomus V 123 (1770–1773); Also Oevures Vol. 2, 125–170
Pólya and SzegÖ, Isoperimetric inequalities in mathematical physics, Princeton, 1951
- Binyamin Schwarz, On the extrema of the frequencies of nonhomogeneous strings with equimeasurable density, J. Math. Mech. 10 (1961), 401–422. MR 0125271
G. J. Simitses, An introduction to the elastic stability of structures, Prentice-Hall, Englewood Cliffs, N.J., 1976
G. J. Simitses, M. P. Kamat and C. Y. Smith, Strongest column by the finite element displacement method, AIAA J. 11, 1231 (1961)
- I. Tadjbakhsh and J. B. Keller, Strongest columns and isoperimetric inequalities for eigenvalues, Trans. ASME Ser. E. J. Appl. Mech. 29 (1962), 159–164. MR 137381
- Stephen P. Timoshenko, Theory of elastic stability, Engineering Societies Monographs, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1961. 2nd ed; In collaboration with James M. Gere. MR 0134026
D. C. Barnes, Rearrangements of functions and lower bounds for eigenvalues of differential equations, J. Appl. Anal.(to appear)
E. R. Barnes, The shape of the strongest column and some related extremal eigenvalue problems, Quart. Appl. Math. 34, 393–409 (1977)
T. Clausen, Uber die Form Architektonisher Saulen, Bull. Phys.-Math. Astronum., Tome 1, 1849–1853
R. Courant and D. Hilbert, Methods of mathematical physics, Interscience, New York, 1953
G. F. D. Duff, Differences, derivatives and decreasing rearrangements, Canad. J. Math. 19, 1153–1178 (1967)
H. J. Ettlinger, Existence theorems for the general real self-adjoint linear system of second order, Trans. Amer. Math. Soc. 19, 79 (1918)
Hardy Littlewood and Pólya, Inequalities, Cambridge University Press, Cambridge, 1964
E. L. Ince, Ordinary differential equations, Dover, New York, 1956
J. B. Keller, The shape of the strongest column, Arlch. Rational Mech. Anal. 5, 275–285 (1960)
J. L. Lagrange, Sur la figure des colonnes, Miscellanea Tourinesia (Royal Society of Turin), Tomus V 123 (1770–1773); Also Oevures Vol. 2, 125–170
Pólya and SzegÖ, Isoperimetric inequalities in mathematical physics, Princeton, 1951
B. Schwarz, On the extrema of the frequencies of nonhomogeneous strings with equimeasurable density, J. Math. Mech. 10, 401 (1961)
G. J. Simitses, An introduction to the elastic stability of structures, Prentice-Hall, Englewood Cliffs, N.J., 1976
G. J. Simitses, M. P. Kamat and C. Y. Smith, Strongest column by the finite element displacement method, AIAA J. 11, 1231 (1961)
I. Tadjbakhsh and J. B. Keller, Strongest columns and isoperimetric inequalities for eigenvalues, J. Appl. Mech. 29, 159 (1962)
S. P. Timeshenko and J. M. Gere, Theorey of elastic stability, McGraw-Hill, New York, 1961
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Article copyright:
© Copyright 1983
American Mathematical Society
