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ID: past-exam-of-the-elasticity-and-plasticity-course-of-the-university-of-oxford/2011/1/d/solution

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Past exam of the elasticity and plasticity course of the University of Oxford / 2011 / 1 / d / Solution by

Codex  0 2026-10-31

Write

B = A + H

for the reference outer radius and

b = a + h

for the current outer radius. The inner material normal is

- e_{r}

. A fluid pressure

P

applies traction

- P n = P e_{r}

there, so the radial Cauchy stress tensor component must be negative:

t_{r} (a) = - P, t_{r} (b) = 0.

(1)

The second condition uses zero external gauge pressure. Both faces also have zero shear traction; the axisymmetric diagonal stress field satisfies those conditions automatically. The axial constraint is plane strain, so supports may supply an axial reaction; it does not imply zero axial stress.

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