Semi-inverse solutions in nonlinear theory of elastic shells

• Autorzy: Zubov L. M.
• Konferencja: 33rd Solid Mechanics Conference, 05-09.09.2000, Zakopane, Polska
• Języki publikacji: EN

Abstrakty

EN

The semi-inverse method is applied to the solution of static problems in the nonlinear theory of elastic shells. This method consists in construction of particular solutions in such a way that the initial system of equations is reduced to a system of a smaller number of independent variables. Two nonlinear models, one of the Love type and another of the Cosserat type, are considered. For these models, several two-parameter families of finite deformations are found; then the system of partial differential equations of equilibrium reduces to a system of nonlinear ordinary differential equations. The semi-inverse solutions found are valid for prismatic and toroidal shells, as well as for shells of revolution. These solutions are of practical significance. They describe torsion of a prismatic shell under large angles of twist, strong flexure of a thin-walled cylinder of arbitrary cross-section, spatial bending of a shell having the shape of a sector of a surface of revolution, straightening of a toroidal shell to a cylindrical surface, and some other types of large deformations.

Słowa kluczowe

EN

semi-inverse method; deformation of shells; elastic shells

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2001
• Tom: Vol. 53, nr 4-5
• Strony: 599--610
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Zubov L. M.

• Department of Mechanics and Mathematics, Rostov State University, Zorge Street, 5, 344090, Rostov-on-Don, Russia

Bibliografia

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• 3. W. PIETRASZKIEWICZ, Geometrically nonlinear theories of thin elastic shells, Advances in Mechanics, 12, 1, 51-130, 1989.
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• 5. L. M. ZUBOV, The methods of nonlinear elasticity in the shell theory, (in Russian), Rostov Univ. Press, Rostov, 1982.
• 6. L. M. ZUBOV, S. U. OVSEENKO, The torsion of momentless shells of revolution under large deformations, (in Russian), Proc. of the 14-th All-Union Conference on the Theory of Shells and Plates, 1, Tbilisi Univ. Press, Tbilisi, 597-602, 1987.
• 7. P. A. ZHILIN, Main equations of the nonclassical theory of elastic shells, (in Russian), Trudy Lenigrad Politech. Inst., 386, 29-46, 1982.
• 8. L. M. ZUBOV, Nonlinear theory of dislocation and disclination in elastic bodies, Springer-Verlag, 1997.
• 9. S.S. ANTMAN, Nonlinear problems of elasticity, Springer-Verlag, 1995.
• 10. A. LIBAI, J. G. SIMMONOS, The nonlinear theory of elastic shells, 2nd Ed., Cambridge Univ. Press, 1998.