N. Khomasuridze

Representation of Solutions of Some Boundary Value Problems of Elasticity by a Sum of the Solutions of Other Boundary Value Problems

Basic static boundary value problems of elasticity are considered for a semi-infinite curvilinear prism $\Omega=\{\rho_0<\rho<\rho_1,$ $\alpha_0<\alpha<\alpha_1,$ $0<z<\infty\}$ in generalized
cylindrical coordinates $\rho,$ $\alpha$, $z$ with Lam\'{e} coefficients $h_\rho=h_\alpha=h(\rho,\alpha),$ $h_z=1$. It is proved that the solution of some boundary value problems of elasticity can be reduced to the sum of solutions of other boundary value problems of elasticity. Besides its cognitive significance, this fact also enables one to solve some non-classical elasticity problems.