Author:
Chupin V.V., ,Chernogubov D.E.
Abstract
An algorithm for studying the stress-strain state of elastic thin-walled shell systems consisting of shells of revolution has been developed. To solve the nonlinear problem of strong bending of a thin isotropic shell of revolution, in which no restrictions are imposed on the angles of rotation of the normal to the original coordinate surface and the relative linear deformation is small compared to unity, we used the Newton-Kantorovich, which reduces the nonlinear boundary value problem to an iterative sequence of linear boundary value problems. A method was applied to reduce the linear boundary problems to several Cauchy problems, which were integrated numerically using the Runge- Kutta method. To ensure the stability of the solution of stiff Cauchy problems, S.K. Godunov’s method of discrete orthogonalization was applied. Based on this algorithm, a computer program was written to determine the parameters of the stress-strain state of shells with a wide range of changes in geometric, physical, and force parameters and boundary conditions. The stress-strain state of sloping spherical panels of constant thickness with pinching on the outer contour under uniform external pressure has been studied. The process of the formation of loops on the deformation curve depending on the height of the shell has been investigated. Changes in the height of the shell with a constant support contour radius simulates the initial irregularity in its manufacture.
Publisher
FSAEIHE South Ural State University (National Research University)
Reference8 articles.
1. 1. Novozhilov V.V. Osnovy nelineynoy teorii uprugosti (Fundamentals of Nonlinear Elasticity). Moscow, Gostehizdat Publ, 1948, 211 p. (in Russ.).
2. 2. Gavryushin S.S. Razrabotka metodov rascheta i proektirovaniya uprugikh obolochechnykh konstruktsiy pribornykh ustroystv: diss. ... d-ra tekhn. nauk (Development of Methods for Calculating and Designing Elastic Shell Structures of Instrument Devices: Dissertation. dr. eng. sci.). Moscow, 1994, 316 p. (in Russ.).
3. 3. Gavryushin S.S. Chislennoe modelirovanie protsessov nelineynogo deformirovaniya tonkikh uprugikh obolochek (Numerical Modeling of the Processes of Nonlinear Deformation of Thin Elastic Shells). Matematicheskoe modelirovanie i chislennye metody. 2014, Iss. 1, pp. 115-130. (in Russ.).
4. 4. Grigolyuk E.I., Lopanitsyn E.A. Vliyanie osesimmetrichnykh nachal'nykh nepravil'nostey sfericheskoy obolochki na ee kriticheskuyu nagruzku (Influence of Axisymmetric Initial Irregularities of a Spherical Shell on its Critical Load). Izvestiya MGTU MAMI, 2008, no. 1(5), pp. 233-246. (in Russ.).
5. 5. Grigolyuk É.I., Lopanitsyn E.A. Asymmetric Behavior of a Sloping Spherical Shell under Finite Deflections. Doklady Physics, 2003, Vol. 48, no. 2, pp. 80-83.