Investigation of the algebraic system of infinite order occurring in solving the problem for a semi-strip: PMM vol. 37, n≗4, 1973, pp. 715–723

Abstract

The algebraic system of equations of infinite order studied here occurs during the solution of the problem of the theory of elasticity concerning a symmetrically loaded semi-strip clamped at the one end. The system is solved using the iteration method. First, out of the matrix of the system a sub-matrix is selected, characterizing the behavior of the solution at large values of the index of the unknown. It is proved and confirmed by concrete examples, that the solution of the basic system differs little from the solution of a simplified system. An asymptotic expansion is obtained for the solution of the simplified system for the large values of the index of the unknown and an approximate method is given for the determination of its coefficients. An infinite system of algebraic equations for a semi-strip with stress-free longitudinal edges and displacements specified at its end was discussed in [1] where it was proved that the system is completely regular. Earlier [2] the behavior of the solution at large values of the index of the unknown was explained in a different manner, when solving an axisymmetric three-dimensional problem for a rigidly clamped plate. Only the first term of the asymptotics was taken into account when concrete problems were solved.