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

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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.

**[1]**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)**[2]**N. J. Freeman and L. M. Keer,*Torsion of a cylindrical rod welded to an elastic half space*, J. Appl. Mech.**34**, 687 (1967)**[3]**R. A. Westmann, Discussion of [2], J. Appl. Mech.**35**, 197 (1968)**[4]**M. L. Williams,*Stress singularities resulting from various boundary conditions in angular corners of plates in extension*, J. Appl. Mech.**19**, 526 (1952)**[5]**E. T. Copson,*On certain dual integral equations*, Proc. Glasgow Math. Assoc.**5**(1961), 21–24 (1961). MR**0199660****[6]**R. P. Srivastav,*Dual series relations. III. Dual relations involving trigonometric series*, Proc. Roy. Soc. Edinburgh Sect. A**66**(1962/1963), 173–184 (1964). MR**0166544****[7]**N. J. Freeman and L. M. Keer,*Torsion of elastic cylinders in contact*, Int. J. Solids Structures**3**, 799 (1967)

Additional Information

DOI:
https://doi.org/10.1090/qam/99837

Article copyright:
© Copyright 1969
American Mathematical Society