Use of the Roben principle in solving three-dimensional problems of the theory of elasticity (Q918292)

The Roben principle is used in solving the integral equations (IE) corresponding to the fundamental spatial problems of the theory of elasticity by the method of successive approximations. It has been established that a possible divergence of the process of successive approximations caused by the lack of accuracy of the computational schemes does not lead to the solution diverging in the stresses. It has been shown that applying the method of successive approximations to the IE of the second interior problem when the boundary conditions are not selfequilibrated, yields a solution which converges in terms of the stresses, corresponding to specific selfequilibrated boundary conditions. A method of solving the boundary value problem is proposed in which the corresponding IE are situated in the spectrum and conditions for the solvability are not satisfied.