Abstract
Representations of Galerkin type are obtained for the displacement vector, polarization vector and the potential fields in the static plane theory of elastic dielectrics using the method of associated matrices. Fundamental matrix solutions of an infinite elastic dielectric plane subjected to a concentrated body force, electric force and charge density are derived from the singular solutions of harmonic, biharmonic and Helmholtz equations. Using boundary operatorsY, Z, M, the fundamental matrix solutions, and Betti's formulae, a matrix Λ(x, y) is constructed and an integral representation for (u1,u2,P1,P2, ϕ) is obtained. Discontinuity theorems are stated for the double layer potential andQ operator of the single layer potential. By means of these theorems, the solutions of interior and exterior boundary value problems are reduced to the solution of a system of five singular integral equations. The index of one of the systems is shown to be zero and it is concluded that Fredholm theorems and its alternatives hold.
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