SOME TORSION PROBLEMS IN ELASTICITY.
Interim technical rept.,
NORTHWESTERN UNIV EVANSTON IL DEPT OF CIVIL ENGINEERING
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Two mixed boundary value problems of the three-dimensional theory of elasticity are investigated. First, the torsional deformation of an elastic rod perfectly adhering to an elastic half-space is considered. The curved surface of the cylinder and the plane surface of the half-space are assumed stress-free. To satisfy the mixed boundary conditions of this problem, certain dual integral equations are encountered. These integral equations are a special case of a somewhat more general set of integral equations also treated in this work. The second problem considered is the torsion of two finite, coaxial, circular cylinders dissimilar materials in contact. The problem is solved on the assumptions that the base of one cylinder is rigidly fixed while the top of the other cylinder is forced to rotate, and that the curved surface of each cylinder is stress-free. An analytical expression is given relating the angle of twist with the constant shear stress assumed in the slip region, necessary to eliminate a stress singularity. The special case of an external crack, corresponding to zero shear stress in the slip region, is also treated. Griffiths criterion for fracture is used to determine the critical value of applied torque. Author