With the aid of a gauge condition analogous to the Coulomb gauge of electromagnetic theory, the integral form of the solutions of the three fundamental boundary value problems of elasto-dynamics are obtained. These solutions are given in terms of surface distributions of the displacement potentials and their derivatives, together with volume distributions of the body forces, and surface distributions of the applied stresses and/or prescribed displacements.

The integral representations are used to formulate sets of simultaneous integral equations whose solutions are the desired surface distributions of the displacement potentials. In addition to considering problems involving more than one media, this paper presents an extension of previous work which considered the corresponding two-dimensional problems.

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