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IssuesArchive of Issues2008-1pp.112-116

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K. I. Romanov, "Plate and shell buckling by the Karman scheme under creep conditions," Mech. Solids. 43 (1), 112-116 (2008)
Year 2008 Volume 43 Number 1 Pages 112-116
DOI 10.3103/S002565440801010X
Title Plate and shell buckling by the Karman scheme under creep conditions
Author(s) K. I. Romanov (Bauman Moscow State Technical University, 2-ya Baumanskaya 5, Moscow, 107005, Russia)
Abstract The problem of stability and buckling of plates under creep conditions has been studied in the fundamental papers [1-4]. In the papers [5, 6], the theory of buckling of rods and plates is developed in the framework of the dominating bending model [7], where the forces in the midplane of the plate were determined independently of the solution of the bending problem.

In what follows, we use the Karman scheme [8] to derive two basic differential equations of the coupled theory of the plane stress state and bending. We solve the problem of buckling of a rectilinear plate for linearly viscous (Newtonian) medium and show that the Karman scheme gives an essential correction to the solution of the bending problem for initial deflections comparable with the plate thickness.
References
1.  Yu. N. Rabotnov and S. A. Shesterikov, "Stability of Columns and Plates in Creep," Prikl. Mat. Mekh. 21(3), 406-412 (1957) [J. Appl. Math. Mech. (Engl. Transl.)].
2.  I. G. Teregulov, Bending and Stability of Thin Plates and Shells under Creeping (Nauka, Moscow, 1969) [in Russian].
3.  L. M. Kurshin, "On Statements of Stability Problems under Creeping Conditions (a Survey)," in Problems of Plasticity and Creeping Theory (Mir, Moscow, 1979) [in Russian].
4.  N. J. Hoff, Longitudinal Bending and Stability (Izd-vo Inostr. Liter., Moscow, 1979) [in Russian].
5.  K. I. Romanov, "Energy Method in the Theory of Buckling of Rheonomic Rods," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 3, 125-134 (2004) [Mech. Solids (Engl. Transl.) 39 (3), 101-108 (2004)].
6.  K. I. Romanov, "Critical Time in the Theory of Buckling of Plates Subject to Creep," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 5, 114-120 (2004) [Mech. Solids (Engl. Transl.) 39 (5), 91-96 (2004)].
7.  A. A. Ilyushin, Plasticity and Elastic-Plastic Strains (Gostekhizdat, Moscow-Leningrad, 1948) [in Russian].
8.  S. P. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells (McGraw-Hill, New York, 1959; Nauka, Moscow, 1966).
9.  N. N. Malinin, Computations of Creeping of Engineering Construction Elements (Mashinostrornie, Moscow, 1981) [in Russian].
10.  K. I. Romanov, "Analysis of Plate Buckling under Creeping Conditions," Vestnik MGTU, Ser. Mashinostr., No. 4, 91-97 (1995).
11.  K. I. Romanov, "Analysis of a Rectangular Plate Buckling under Creeping Conditions," Vestnik MGTU, Ser. Mashinostr., No. 3, 109-116 (1999).
12.  A. S. Volmir, Stability of Deformable Systems (Nauka, Moscow, 1967) [in Russian].
13.  Fyn Yuan-Chen and E. E. Sekler, "Instability of Thin Elastic Plates," in: Elastic Shells (Izd-vo Inostr. Liter., Moscow, 1962) [in Russian].
Received 07 February 2005
Link to Fulltext http://www.springerlink.com/content/863v528246x0t1n8
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