Numerical algorithm of investigation of stress-strain state of cylindrical shells of railway tank

Abstract

On the basis of synthesis of methods of grids and orthogonal sweeps of grids system of algebraic equations of big dimension the algorithm of the decision of a boundary value problem in partial derivatives describing the stress-strain state of a shell of rotation of a copper of the railway tank is offered. The shell is cylindrical, loaded arbitrarily by inertial forces and pressure, has combined fastening conditions at the ends. The method of grids according to the explicit scheme allowed the system of equations of the theory of shells reduced to eight differential equations of the first order with respect to the meridional coordinate and the fourth order with respect to the circumferential, to lead to a system of algebraic equations having a five-diagonal matrix, non-zero elements of which are eighth order matrices. To solve a system of algebraic equations with a rare matrix of non-zero elements, the method of run is applied, in which to eliminate the accumulation of computational errors, the orthogonalization of “run” vectors by Gram - Schmidt is applied, which allows to exclude the formation of a singular matrix from the “run” vectors when calculating the coefficients of solving the boundary value problem. An example is considered in which the stress-strain state of the shell of the boiler of a railway tank tests the inertial forces variable along the meridional and circumferential coordinates and has a rigid fastening at each end on the part of the circle and a free state on the remaining part.