 Solution

ID: past-exam-of-the-solid-mechanics-course-of-the-university-of-oxford/2023/3/b/ii/solution

The pressure adjustment from part (i) can be written

T = T_{0} (t) + q (x, t) 1, q = - ρ ξ + C (t) .

Indeed, since

div (q 1) = \nabla q

\nabla q = ρ \ddot{x}_{0} = - ρ \nabla ξ .

Thus

q + ρ ξ

C (t)

is fixed by any prescribed pressure or surface traction datum. In terms of the usual compressive pressure multiplier,

p = p_{0} - q = p_{0} + ρ ξ - C (t)

. The plus sign in

q 1

therefore does not identify

q

with the compressive multiplier

p

itself.

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