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IssuesArchive of Issues2008-1pp.86-99

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O. R. Kuznetsov, "Analysis of right closed thin-walled prismatic shells supported by stringers with geometric and physical nonlinearity taken into account," Mech. Solids. 43 (1), 86-99 (2008)
Year 2008 Volume 43 Number 1 Pages 86-99
DOI 10.3103/S0025654408010081
Title Analysis of right closed thin-walled prismatic shells supported by stringers with geometric and physical nonlinearity taken into account
Author(s) O. R. Kuznetsov (Saratov State Technical University, Politekhnicheskaya 77, Saratov, 410054, Russia, orkuzn@ya.ru)
Abstract We consider thin-walled right-angle closed prismatic shells with rigid contour of the transverse cross-section. Such shells underlie the schemes used in the analysis of various thin-walled spatial structures. The use of nonlinear physical and geometric relations in the computations permits numerically obtaining the strength margin of the corresponding structures.

In the present paper, we propose methods for obtaining a boundary value problem and analyzing such shells with nonlinear factors taken into account; the problem is presented as a system of linear differential equations with variable coefficients. We show that, within the approach proposed, this boundary value problem has a fixed structure independent of the special form of nonlinearity. The entire variety of problems of static analysis of right-angle prismatic shells with nonlinear factors taken into account can be reduced to solving this boundary value problem. Methods for taking a specific nonlinearity into account are treated as various methods for obtaining expressions for the variable coefficients in the matrices of the boundary value problem.

We present methods for solving this boundary value problem numerically; these methods are independent of the specific form of the nonlinearity.
References
1.  V. Z. Vlasov, Selected Works, Vols. I-III (Nauka, Moscow, 1962, 1062, 1964) [in Russian].
2.  I. F. Obraztsov and G. G. Onanov, Structural Mechanics of Slanted Thin-Walled Systems (Mashinostroenie, Moscow, 1973) [in Russian].
3.  V. A. Ignatíev, O. L. Sokolov, J. Altenbach, and W. Kissing V. A. Ignatíev, O. L. Sokolov, I. Altenbakh, and V. Kissing, Calculation of Thin-Walled Spatial Designs of Plate and Plate-Rod Structures (Stroiizdat, Moscow, 1996) [in Russian].
4.  S. P. Ivanov, "Computation of Nonlinear Plate-Like Systems by V. Z. Vlasovís Variational Method," Izv. Vyssh. Uchebn. Zaved. Stroitelstvo, No. 6, 23-29 (2002).
5.  P. I. Tatarinov, "Nonlinear Problems of Pure Bending of a Caisson Structure," Izv. Vyssh. Uchebn. Zaved. Aviats. Tekh., No. 4, 57-65 (1970).
6.  V. V. Petrov, The Successive Load Method in the Nonlinear Theory of Plates and Shells (Izd-vo Saratov Univ., Saratov, 1975) [in Russian].
7.  O. R. Kuznetsov, "Resolving Equations for Calculating Right-Angle Closed Prismatic Shells with Physical Nonlinearity Taken into Account," in Problems of Strength and Plasticity (Izd-vo Nizhegorodskogo Univ., Nizhnii Novgorod, 2004), No. 66, pp. 157-167 [in Russian].
8.  A. N. Danilin, N. N. Zuev, A. B. Kostrichenko, and V. I. Shalashilin, "Various Versions of Geometrically Nonlinear Relations for Large Deformations," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 3, 53-63 (2004) [Mech. Solids (Engl. Transl.) 39 (3), 40-48 (2004)].
9.  S. K. Godunov, "Numerical Solution of Boundary Value Problems for Systems of Linear Ordinary Differential Equations," Uspekhi Mat. Nauk 16(3), 171-174 (1961) [Russian Math. Surveys (Engl. Transl.)]
10.  V. V. Petrov, "Two-Step Method of Successive Perturbation of Parameters Used to Solve Nonlinear Problems of Mechanics of Deformable Solid," in Problems of Structure Member Strength under the Action of Loads and Working Media (Izd-vo Saratov Gos. Tekh. Univ., Saratov, 2001), pp. 6-12 [in Russian].
Received 03 June 2005
Link to Fulltext http://www.springerlink.com/content/09245v279v73622g
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