GATE Mechanical Engineering (ME) 2019 Shift 2 Solved Paper

Consider two concentric circular cylinders of different materials $\mathit{M}$ and $\mathit{N}$ in contact with each other at $\mathit{r}=\mathit{b}$, as shown below. The interface at $\mathit{r}=\mathit{b}$ is frictionless. The composite cylinder system is subjected to internal pressure $\mathit{P}$. Let $\left({\mathit{u}}_{\mathit{r}}^{\mathit{M}},{\mathit{u}}_{\mathit{\theta }}^{\mathit{M}}\right)$ and $\left({\mathit{\sigma }}_{\mathit{\pi }}^{\mathit{\mu }},{\mathit{\sigma }}_{\mathit{\theta }\mathit{\theta }}^{\mathit{M}}\right)$ denote the radial and tangential displacement and stress components, respectively, in material M Similarly, $\left({\mathit{u}}_{\mathit{r}}^{\mathit{N}},{\mathit{u}}_{\mathit{\theta }}^{\mathit{N}}\right)$ and $\left({\mathit{\sigma }}_{\mathit{\pi }}^{\mathit{N}},{\mathit{\sigma }}_{\mathit{\omega }\mathit{i}}^{\mathit{N}}\right)$ 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 :