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An elastic, isotropic, homogeneous, circular cylinder of height L and radius R is
perfectly fit into a rigid tube with perfectly lubricated walls as sketched. A uniform pressure p is
applied to the open end of the cylinder. The cylinder has Young’s modulus E and Poisson’s ratio
nu.
(a) Write down the set of field equations and boundary conditions for this problem.
(b) Solve for displacement (u) vector, strain (epsilon ) and stress (σ) matrices.
[Hint: Guess the displacement field as u = 0, v=0, w=kz]
(c) Assume that the material fails when the maximum shear stress exceeds τf. At what value of p
does this occur?