On theory of elasticity boundary value problems properties of exact solutions in a half-strip and their application to theory of residual stresses in rocks

A solution of the first basic odd-symmetric boundary value problem in the theory of elasticity in a half-strip with free longitudinal sides is constructed. It is represented as series in Papkovich–Fadle eigenfunctions whose coefficients are found in an explicit form by using the biorthogonal to the Papkovich–Fadle eigenfunctions. The solution describes the residual stresses in an infinite strip with zero boundary conditions on its sides and the displacements arising when residual stresses are released, as a result of the formation of a rock rupture.