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Consider two concentric circular cylinders of different materials M and N in contact with each other at r = b, as shown below. The interface at r = b is frictionless. The composite cylinder system is subjected to internal pressure P. Let (urM , uθM) and (σrrM , σθθM) denote the radial and tangential displacement and stress components, r espectivel y, in material M. Similarly (urN , uθN) and (σrrN , σθθN) denote the radial and tangential displacement and stress components, respectively, in material N. The boundary condition that need to be satisfied at the frictionless interface between the two cylinders are:
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- urM = urN and σrrM = σrrN and uθM = uθN and σθθM = σθθN
- uθM = uθN and σθθM = σθθN only
- urM = urN and σrrM = σrrN only
- σrrM = σrrN and σθθM = σθθN
Correct Option: C
Due to internal pressure inside the cylinder, st r esses ar e gener at ed bot h in r adi al and circumferential direction. As interface of r = b is frictionless, so stress in radial direction must be equal otherwise relative motion will occur and parallely velocity in radial direction should be equal.
i.e. urM = urN and σrrM = σrrN
In circumferential direction i.e. only ‘’ direction velocity cannot be equal because it depends upon radius i.e. V = rω and ‘r’ is varying.
So , uθM ≠ uθN
Same is for stress in circumferential direction.
i.e. σθθM ≠ σθθN
