Analytical solutions are given for the stress fields,
in both compression and far-field shear, in a twodimensional
elastic body containg two interacting
non-circular pores. The two complex potentials
governing the solutions are found by using a
conformal mapping from a preimage annulus with
those potentials expressed in terms of the SchottkyKlein
prime function for the annulus. Solutions
for a three-parameter family of elastic bodies with
two equal symmetric pores are presented and the
compressibility of a special family of pore pairs is
studied in detail. The methodology extends to two
unequal pores.
The importance for boundary value problems of
plane elasticity of a special class of planar domains
known as quadrature domains is also elucidated. This
observation provides the route to generalization of
the mathematical approach here to finding analytical
solutions for the stress fields in bodies containing any
finite number of pores.