Article

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Title

The application of the general theory of shells to account for the edge effect in a toroidal tank from the internal pressure

Author

R.A. Sabirov

Organization

Reshetnev Siberian State Aerospace University
Krasnoyarsk, 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 effect

References

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[3] Vlasov V. Z. Obshhaja teorija obolochek i ejo prilozhenija v tehnike [General theory of shells and its applications in engineering]. Moscow, Leningrad : Gostehizdat, 1949. Р. 783.

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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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