Thermoelastoplastic deformation of noncircular cylindrical shells |
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Authors: | V A Merzlyakov |
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Institution: | (1) S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kyiv, Ukraine |
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Abstract: | A method to determine the nonstationary temperature fields and the thermoelastoplastic stress-strain state of noncircular
cylindrical shells is developed. It is assumed that the physical and mechanical properties are dependent on temperature. The
heat-conduction problem is solved using an explicit difference scheme. The temperature variation throughout the thickness
is described by a power polynomial. For the other two coordinates, finite differences are used. The thermoplastic problem
is solved using the geometrically nonlinear theory of shells based on the Kirchhoff-Love hypotheses. The theory of simple
processes with deformation history taken into account is used. Its equations are linearized by a modified method of elastic
solutions. The governing system of partial differential equations is derived. Variables are separated in the case where the
curvilinear edges are hinged. The partial case where the stress-strain state does not change along the generatrix is examined.
The systems of ordinary differential equations obtained in all these cases are solved using Godunov's discrete orthogonalization.
The temperature field in a shell with elliptical cross-section is studied. The stress-strain state found by numerical integration
along the generatrix is compared with that obtained using trigonometric Fourier series. The effect of a Winkler foundation
on the stress-strain state is analyzed
Translated from Prikladnaya Mekhanika, Vol. 44, No. 8, pp. 79–90, August 2008. |
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Keywords: | thermoelastoplasticity noncircular cylindrical shell Kirchhoff-Love hypotheses linearization method explicit difference scheme Godunov's discrete orthogonalization cylindrical shell of elliptical cross-section |
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