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IssuesArchive of Issues2006-5pp.52-56

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N. V. Minaeva, "On a nearly homogeneous stress-strain state of a plate," Mech. Solids. 41 (5), 52-56 (2006)
Year 2006 Volume 41 Number 5 Pages 52-56
Title On a nearly homogeneous stress-strain state of a plate
Author(s) N. V. Minaeva (Voronezh)
Abstract An analytic method for approximately solving problems describing the stress-strain state of solids was developed in [1-4]. It is well known that if in the space of parameters characterizing the external action one wishes to find the boundaries of the domain where the solution of the corresponding problem continuously depends on the characteristics of geometric imperfections of the body, then one should construct an auxiliary linearized problem, where the boundary conditions must be posed on the boundary of the body in the deformed state. In the present paper, for the case of plane strain, we linearize the boundary conditions given in integral form on the boundary of the body in the deformed state. By way of example, we consider the problem on compression of an elastically supported strip.
References
1.  A. Yu. Ishlinskii, "Study of equilibrium stability problems for elastic bodies from the viewpoint of mathematical theory of elasticity," Ukrain. Mat. Zh., Vol. 6, No. 2, pp. 140-146, 1954.
2.  A. Yu. Ishlinskii and D. D. Ivlev, Mathematical Theory of Plasticity [in Russian], Fizmatlit, Moscow, 2001.
3.  A. N. Guz' and Yu. N. Nemish, "Boundary shape perturbation method in continuum mechanics (a survey)," Prikl. Mekhanika, Vol. 23, No. 9, pp. 3-29, 1978.
4.  A. N. Guz' and Yu. N. Nemish, Boundary Shape Perturbation Method in Continuum Mechanics [in Russian], Vyshcha Shkola, Kiev, 1989.
5.  A. N. Kolmogorov and S. V. Fomin, Elements of Theory of Functions and Functional Analysis [in Russian], Nauka, Moscow, 1976.
6.  N. V. Minaeva, Perturbation Methods in Mechanics of Solids [in Russian], Nauch. Kniga, Moscow, 2002.
7.  D. D. Ivlev, Mechanics of Plastic Media. Volume 2 [in Russian], Fizmatlit, Moscow, 2002.
Received 22 December 2004
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