Torsion of a finite elastic cylindrical rod partially bonded to an elastic half space
Authors:
L. M. Keer and N. J. Freeman
Journal:
Quart. Appl. Math. 26 (1969), 567-573
DOI:
https://doi.org/10.1090/qam/99837
MathSciNet review:
QAM99837
Full-text PDF Free Access
Abstract |
References |
Additional Information
Abstract: A solution is given for the problem of axially symmetric torsion of a finite elastic cylindrical rod partially bonded to an elastic half space. The problem is formulated in a manner that involves coupling between dual Dini series and dual integral equations. Auxiliary functions are introduced and the problem is reduced to the solution of a Fredholm integral equation of the second kind. Approximate closed-form results are obtained when the radius of the bonded region is less than one-half the radius of the cylinder. Fractional order singularities in the stress are noted and calculated for the case when the crack vanishes.
I. N. Sneddon, R. P. Srivastav, and S. C. Mathur, The Reissner-Sagoci problem for a long cylinder of finite radius, Quart. J. Mech. Appl. Math. 19, 123 (1966)
N. J. Freeman and L. M. Keer, Torsion of a cylindrical rod welded to an elastic half space, J. Appl. Mech. 34, 687 (1967)
R. A. Westmann, Discussion of [2], J. Appl. Mech. 35, 197 (1968)
M. L. Williams, Stress singularities resulting from various boundary conditions in angular corners of plates in extension, J. Appl. Mech. 19, 526 (1952)
- E. T. Copson, On certain dual integral equations, Proc. Glasgow Math. Assoc. 5 (1961), 21–24 (1961). MR 199660
- R. P. Srivastav, Dual series relations. III. Dual relations involving trigonometric series, Proc. Roy. Soc. Edinburgh Sect. A 66 (1962/63), 173–184 (1964). MR 166544
N. J. Freeman and L. M. Keer, Torsion of elastic cylinders in contact, Int. J. Solids Structures 3, 799 (1967)
I. N. Sneddon, R. P. Srivastav, and S. C. Mathur, The Reissner-Sagoci problem for a long cylinder of finite radius, Quart. J. Mech. Appl. Math. 19, 123 (1966)
N. J. Freeman and L. M. Keer, Torsion of a cylindrical rod welded to an elastic half space, J. Appl. Mech. 34, 687 (1967)
R. A. Westmann, Discussion of [2], J. Appl. Mech. 35, 197 (1968)
M. L. Williams, Stress singularities resulting from various boundary conditions in angular corners of plates in extension, J. Appl. Mech. 19, 526 (1952)
E. T. Copson, On certain dual-integral equations, Proc. Glasgow Math. Assoc. 5, 21 (1961)
R. P. Srivastav, Dual-series relations—II. Dual relations involving Dini series, Proc. Roy. Soc. Edin., A, 66, 173 (1964)
N. J. Freeman and L. M. Keer, Torsion of elastic cylinders in contact, Int. J. Solids Structures 3, 799 (1967)
Additional Information
Article copyright:
© Copyright 1969
American Mathematical Society
