GATE 2019 Mechanical Engineering Q30

Question

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 ($u_r^M$, $u_	heta^M$) and ($\sigma_{rr}^M$, $\sigma_{	heta	heta}^M$) denote the radial and tangential displacement and stress components, respectively, in material M. Similarly, ($u_r^N$, $u_	heta^N$) and ($\sigma_{rr}^N$, $\sigma_{	heta	heta}^N$) denote the radial and tangential displacement and stress components, respectively, in material N. The boundary conditions that need to be satisfied at the frictionless interface between the two cylinders are:

Accepted Answer

$u_r^M = u_r^N$ and $\sigma_{rr}^M = \sigma_{rr}^N$ only

Answer

$u_r^M = u_r^N$ and $\sigma_{rr}^M = \sigma_{rr}^N$ and $u_	heta^M = u_	heta^N$ and $\sigma_{	heta	heta}^M = \sigma_{	heta	heta}^N$

Answer

$u_	heta^M = u_	heta^N$ and $\sigma_{	heta	heta}^M = \sigma_{	heta	heta}^N$ only

Answer

$\sigma_{rr}^M = \sigma_{rr}^N$ and $\sigma_{	heta	heta}^M = \sigma_{	heta	heta}^N$ only