Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

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
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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.


References [Enhancements On Off] (What's this?)

  • [1] A. M. Arthurs, Complementary variational principles, Clarendon Press, Oxford, 1970 MR 594935
  • [2] A. M. Arthurs, Dual extremum principles and error bounds for a class of boundary value problems, J. Math. Anal. Appl. 41, 781-795 (1973) MR 0386299
  • [3] S. G. Mikhlin, Variational methods in mathematical physics, Pergamon Press, Oxford, 1964, p. 350 MR 0172493
  • [4] N. Anderson, A. M. Arthurs and P. D. Robinson, Pairs of complementary variational principles, J. Inst. Maths. Applies. 5, 422-431 (1969) MR 0452118
  • [5] R. Frisch-Fay, Flexible bars, Butterworths, London, 1962, p. 35
  • [6] F. V. Rohde, Large deflections of a cantilever beam with uniformly distributed load, Quart. Appl. Math. 11, 337-338 (1953) MR 0056438

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DOI: https://doi.org/10.1090/qam/449135
Article copyright: © Copyright 1975 American Mathematical Society

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