Abstract
The present paper is devoted to the explicit solutions of the equilibrium boundary value problems (BVPs) for an elastic circle and for full plane with circular hole with a double-voids structure. The regular solution of the system of equations for an isotropic material with a double-voids structure is constructed by means of the elementary (harmonic, bi-harmonic and meta-harmonic) functions. The Dirichlet-type BVPs for a circle and for a plane with a circular hole are solved explicitly. The obtained solutions are presented as absolutely and uniformly convergent series.
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