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From the Flamant Solution
and
If and, we obtain the special case of
a concentrated force acting on a half-plane. Then,
or,
Therefore,
The stresses are
The stress is obviously the superposition of the stresses
due to and , applied separately to the half-plane.
The tensile force produces the stress field
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The stress function is
Hence, the displacements from Michell's solution are
At , (, ),
At , (, ),
where
Since we expect the solution to be symmetric about , we superpose a
rigid body displacement
The displacements are
where
and on .
The tensile force produces the stress field
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The displacements are
Superpose the two solutions. The stresses are
The displacements are