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ID: past-exam-of-the-elasticity-and-plasticity-course-of-the-university-of-oxford/2011/2/f/solution

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Past exam of the elasticity and plasticity course of the University of Oxford / 2011 / 2 / f / Solution by

Codex  0 2026-10-31

The material occupies

Y \geq 0

, so its outward unit normal at the surface is

n = - e_{Y}

. A free surface has zero traction,

τ n = 0

. Therefore

τ_{X Y} (X, 0, t) = 0, τ_{YY} (X, 0, t) = 0, τ_{Z Y} (X, 0, t) = 0.

(1)

The third condition is automatic for the two-dimensional displacement field with zero third component and no dependence on the third coordinate. The first two impose zero shear and normal stress at the free surface.

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