Abstract
The vector potentials of the displacements of the general solutions of static Boussinesq and Papkovich problems are presented in a form which leads to the splitting of the vector equations of the potentials in cylindrical and spherical coordinates into two scalar potentials. The solutions of the equations of the scalar potentials for finite bodies of canonical form contain orthogonal systems of functions on the coordinate surfaces in the region occupied by the body considered, including its boundary surfaces. One thereby creates the prerequisites for converting the boundary conditions into infinite systems of linear algebraic equations after expanding the stresses or displacements, specified on the boundary surfaces, in orthogonal functions of the equations of the potentials.
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