Fundamental solutions of Navier's differential operator for elastic Riemann spaces with a finite and with an infinite number of sheets

Abstract

Fundamental solutions of the operator of Navier's differential equation (equilibrium equation) for the elastostatic boundary value problem are established. The solutions are not defined on the ordinary three-dimensional space as the classical Kelvin solution but on Riemann spaces. They can be used as kernels of boundary integral equations. It should be possible to apply integral equations of this type advantageously for the determination of the state of deformation in elastic bodies parts of the surface of which touch or almost touch each other (bodies with slits, certain helical elastic springs, etc.).