Article
Cover
![№3-4 2016](../journal/archive/18/cover.jpg)
Title
The application of the general theory of shells to account for the edge effect in a toroidal tank from the internal pressureAuthor
R.A. SabirovOrganization
Reshetnev Siberian State Aerospace UniversityKrasnoyarsk, Russian Federation
Abstract
The aim of this work consists in the application of the equations of General shell theory to study local bending moment factors, the so-called boundary effect when calculating stress-strain state of the Toroidal tank from internal pressure. In the work repeated the derivation of the General theory of shells of V. Z. Vlasov in the system of curvilinear coordinates. The obtained expression of the internal membrane forces, bending moments, and torques. Composed of a General differential equation of equilibrium the calculation of isotropic shells of variable thickness and curvature. To calculate the toroidal tank introduced a toroidal coordinate system; allowing the equation transformed into an equation for the solution of axisymmetric problems. To reduce the order of derivatives, the resulting equation of equilibrium is transformed into a variational equation. Differential operators replaced by finite-difference counterparts, the integration is replaced by summation step. The continuum problem is reduced to the problem of discrete, variational-difference, finite number of variables. The calculation of the torus the inner pressure; tor supported on the outer and inner edges powerful ribs. The calculations showed the occurrence of bending moments in the ribs, which are sharply damped at a distance from ribs, is a manifestation of the edge effect. Away from the edges, detected by the almost membrane state. The calculated values of longitudinal membrane forces in a region remote from the edges coincide with the values obtained by using the Laplace equations of the membrane theory.Keywords
theory of shells, Thor, edge effectReferences
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For citing this article
Sabirov R.A. The application of the general theory of shells to account for the edge effect in a toroidal tank from the internal pressure // The Research of the Science City, 2016, no. 3-4, pp. 25-31.
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