Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-28T13:27:30.020Z Has data issue: false hasContentIssue false
  • English
  • Français

Second order effects in the flexure of isotropic incompressible elastic cylinders

Published online by Cambridge University Press:  24 October 2008

W. S. Blackburn
Get access Rights & Permissions [Opens in a new window]

Extract

General methods of successive approximations for problems in the theory of large elastic deformations have been proposed by Signorini (9), Misicu (5), Rivlin (6), Green and Spratt (4) and Rivlin and Topakoglu (7). Rivlin has applied his method to the problem of torsion of cylinders as far as terms of the second order. A solution of the problem of second order effects in the torsion of incompressible cylinders of arbitrary cross-section has been given by Green and Shield (3) in terms of complex potential functions, and the complete details of the stress distribution can be obtained once certain integral equations are solved. Blackburn and Green (l) have considered the second order effects in the deformation of compressible cylinders by forces on the ends. For the problems of torsion and bending by couples they obtained details of the displacements and stress distributions in terms of two complex potential functions which satisfy a certain boundary condition. The second order torsion problem has also been discussed by Sheng(8).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 53 , Issue 4 , October 1957 , pp. 907 - 921
Copyright
Copyright © Cambridge Philosophical Society 1957

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Blackburn, W. S. and Green, A. E.Proc. Roy. Soc. A, 240 (1957), 408.Google Scholar
(2)Capildeo, R.Proc. Camb. Phil. Soc: 49 (1953), 308.CrossRefGoogle Scholar
(3)Green, A. E. and Shield, R. T.Phil. Trans. A, 244 (1951), 47.Google Scholar
(4)Green, A. E. and Spratt, E. B.Proc. Roy. Soc. A, 224 (1954), 347.Google Scholar
(5)Misicu, M.Studii Cere. Mec. Met. 4 (1953), 31.Google Scholar
(6)Rivlin, R. S.J. Rat. Mech. Anal. 2 (1953), 53.Google Scholar
(7)Rivlin, R. S. and Topakoglu, C.J. Rat. Mech. Anal. 3 (1954), 581.Google Scholar
(8)Sheng, P. L.Secondary elasticity (Taipei, 1955).Google Scholar
(9)Signorini, A.atti 24 Riunion Soc. Ital. Prozi. Sci. 3 (1936), 6.Google Scholar
(10)Sokolnikoff, I. S.Mathematical theory of elasticity, 2nd ed. (New York, 1956).Google Scholar