Vestnik St. Petersburg University, Mathematics

, Volume 52, Issue 2, pp 207–213

Numerical Algorithm for Investigating the Stress-Strain State of Cylindrical Shells of Railway Tanks

Mechanics

Abstract

On the basis of the synthesis of the grid and Godunov orthogonal sweep methods, an algorithm is proposed for solving a boundary value problem in partial derivatives describing the stress-strain state of a shell of revolution of a copper of a railway tank. A cylindrical shell arbitrarily loaded by inertial forces and pressure is considered under the combined fastening conditions at its ends. The grid method according to the explicit scheme has made it possible to transform the equation system of the shell theory to eight differential equations of the first order with respect to the meridional coordinate and the fourth order with respect to the circumferential coordinate to the system of algebraic equations with a five-diagonal matrix, whose non-zero elements are eight-order matrices. To solve the system of algebraic equations with a rare matrix of non-zero elements, the sweep method is applied in which the Gram-Schmidt orthogonalization of “sweep” vectors is used to eliminate the accumulation of computational errors, which allows us to exclude the formation of a singular matrix from the “sweep” vectors when calculating the coefficients of the solution to the boundary value problem. An example is considered in which the stress-strain state of the shell of the boiler of a railway tank undergoes the internal forces variable along the meridional and circumferential coordinates and has a rigid fastening at each end of one part of the circle and a free state at another part.

Keywords

grid method orthogonal sweep boundary value problem stress-strain state of the shell of revolution sweep method Gram-Schmidt orthogonalization of vectors

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