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_rr^M, σ_θθ^M) denote the radia

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_rr^M, σ_θθ^M) denote the radial and tangential displacement and stress components, respectively, in material M. Similarly, (u_r^N, u_θ^N) and (σ_rr^N, σ_θθ^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 σ_rr^M = σ_rr^N only. At the frictionless interface between the two materials, the radial displacements must be equal to ensure continuity, and the radial stresses must also be equal to maintain equilibrium. The tangential components do not need to match because there is no friction to enforce that condition.

Solution

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