Complementary variational principles for large deflections of a cantilever beam
Author:
R. I. Reeves
Journal:
Quart. Appl. Math. 33 (1975), 245-254
MSC:
Primary 73.49
DOI:
https://doi.org/10.1090/qam/449135
MathSciNet review:
449135
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: Recent results on complementary variational principles and error bounds are applied to two problems concerning the large deflection of a horizontal cantilever. The results are illustrated by obtaining accurate variational solutions in the form of simple polynomials.
- Arnold Magowan Arthurs, Complementary variational principles, 2nd ed., The Clarendon Press, Oxford University Press, New York, 1980. Oxford Mathematical Monographs. MR 594935
- A. M. Arthurs, Dual extremum principles and error bounds for a class of boundary value problems, J. Math. Anal. Appl. 41 (1973), 781–795. MR 386299, DOI https://doi.org/10.1016/0022-247X%2873%2990249-7
- S. G. Mikhlin, Variational methods in mathematical physics, The Macmillan Co., New York, 1964. Translated by T. Boddington; editorial introduction by L. I. G. Chambers; A Pergamon Press Book. MR 0172493
- N. Anderson, A. M. Arthurs, and P. D. Robinson, Pairs of complementary variational principles, J. Inst. Math. Appl. 5 (1969), no. 4, 422–431. MR 452118
R. Frisch-Fay, Flexible bars, Butterworths, London, 1962, p. 35
- F. Virginia Rohde, Large deflections of a cantilever beam with uniformly distributed load, Quart. Appl. Math. 11 (1953), 337–338. MR 56438, DOI https://doi.org/10.1090/S0033-569X-1953-56438-6
A. M. Arthurs, Complementary variational principles, Clarendon Press, Oxford, 1970
A. M. Arthurs, Dual extremum principles and error bounds for a class of boundary value problems, J. Math. Anal. Appl. 41, 781–795 (1973)
S. G. Mikhlin, Variational methods in mathematical physics, Pergamon Press, Oxford, 1964, p. 350
N. Anderson, A. M. Arthurs and P. D. Robinson, Pairs of complementary variational principles, J. Inst. Maths. Applies. 5, 422–431 (1969)
R. Frisch-Fay, Flexible bars, Butterworths, London, 1962, p. 35
F. V. Rohde, Large deflections of a cantilever beam with uniformly distributed load, Quart. Appl. Math. 11, 337–338 (1953)
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC:
73.49
Retrieve articles in all journals
with MSC:
73.49
Additional Information
Article copyright:
© Copyright 1975
American Mathematical Society