We use complex variable methods to establish two sets of specific conditions which
ensure the existence of uniform and hydrostatic internal membrane stress
resultants and bending moments inside two through-thickness nonelliptical elastic
inhomogeneities embedded in an infinite isotropic laminated Kirchhoff plate
subjected to uniform remote membrane stress resultants and bending moments.
These conditions can be interpreted as restrictions on the remote membrane
stress resultants and bending moments for the given material and geometric
parameters. We show that when these conditions are met, explicit expressions are
available for the uniform stress resultants inside the two inhomogeneities
and the constant hoop stress resultants on the matrix side along the two
interfaces.