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_{θ}^{M}) and (σ_{π}^{µ}, σ_{θ θ}^{M}) denote the radial and tangential displacement and stress components, respectively, in material M Similarly, (u_{r}^{N}, u_{θ}^{N}) and (σ_{π}^{N}, σ_{ω i}^{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 :

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_{θ}^{M}) and (σ_{π}^{µ}, σ_{θ θ}^{M}) denote the radial and tangential displacement and stress components, respectively, in material M Similarly, (u_{r}^{N}, u_{θ}^{N}) and (σ_{π}^{N}, σ_{ω i}^{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 :

Examsnet · Accepted Answer

Correct Answer is :  urM=urN and σrM=σrN only

GATE Mechanical Engineering (ME) 2019 Shift 2 Solved Paper