SOLUTION OF THE RING FOR ELASTIC MATERIALS EXHIBITING COUPLE-STRESSES.
Rept. for 1 Nov 64-30 Sep 65,
RENSSELAER POLYTECHNIC INST TROY N Y DEPT OF MECHANICS
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Interest in the couple-stress theory of elasticity which was introduced by E. and F. Cosserat has been revived by Mindlin and others. This investigation is based on the equations presented in a paper by Mindlin and Tiersten and another paper by Mindlin. A general solution to the ring problem in the form of infinite series is obtained by applying the Helmholtz decomposition to the displacement vector and then using the finite Fourier transform. Several examples are solved using the general solution. For a disk loaded with a constant couple-stress on its boundary and a point moment at its center and for a ring loaded with constant couple-stresses on both boundaries, the solutions consist of a finite number of terms. For a disk loaded with a normal stress over a portion of its circumference and a point force at its center, the solution is an infinite series. An infinite series solution is also found for a layered media problem where a ring bonded to a disk of different material is loaded by a constant normal stress over a portion of its outer circumference while a point force is applied at the center of the disk. The first time problems are solved explicitly, but the last is solved numerically on a computer. An interesting part of the final results of the layered media problem is a boundary layer phenomenon exhibited at the interface by the shear stress in the radial direction. Author