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IssuesArchive of Issues2010-6pp.769-777

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N.F. Morozov and P.E. Tovstik, "Surface Layer Stability under Force and Temperature Loading," Mech. Solids. 45 (6), 769-777 (2010)
Year 2010 Volume 45 Number 6 Pages 769-777
DOI 10.3103/S0025654410060026
Title Surface Layer Stability under Force and Temperature Loading
Author(s) N.F. Morozov (Saint-Petersburg State University, Universitetskaya nab. 7-9, St.†Petersburg, 199034 Russia, morozov@nm1016.spb.edu)
P.E. Tovstik (Saint-Petersburg State University, Universitetskaya nab. 7-9, St.†Petersburg, 199034 Russia, peter.tovstik@mail.ru)
Abstract We study stability of an elastic homogeneous or multilayer plate with a free surface under the action of force and temperature deformations. We show that possible buckling modes can be of two types. For each of these two types, we study the dependence of the critical strain on the wavelength. It was found that, for a homogeneous layer, a decrease in the wavelength leads to a decrease in the critical strain and, for a multilayer material with alternating hard and soft layers, a strain wave of finite length arises in buckling.
Keywords surface stability, homogeneous or multilayer elastic material, force and temperature loading, buckling modes
References
1.  N. F. Morozov, M. V. Paukshto, and P. E. Tovstik, "Stability of a Surface Layer under a Thermal Loading," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 1, 130-139 (1998) [Mech. Solids (Engl. Transl.) 33 (1), 106-113 (1998)].
2.  N. F. Morozov, M. V. Paukshto, and P. E. Tovstik, "Influence of the Volume Diffusion on the Instability of a Surface Layer under Thermal Loading," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 4, 96-101 (1999) [Mech. Solids (Engl. Transl.) 34 (4), 81-85 (1999)].
3.  N. F. Morozov, B. N. Semenov, and P. E. Tovstik, "Continual and Discrete Models in the Problem of Stability of a Three-Layer Nano-Plate," Teor. Prikl. Mekh., No. 19, 37-41 (2005).
4.  L. E. Panin and V. E. Panin, "Chessboard" Effect and Mass Transfer in Interfacial Media of Organic and Inorganic Nature," Fizich. Mezomekh. 10 (6), 5-20 (2007) [Phys. Mesomech. (Engl. Transl.) 11 (1-2), 5-18 (2008)].
5.  P. E. Tovstik, "Stability of a Multilayer Plate on an Elastic Foundation," in Proc. 3rd All-Russia Conf. on Elasticity (Rostov-on-Don, 2003), pp. 365-368.
6.  N. F. Morozov and P. E. Tovstik, "On Modes of Surface Stability," in Problems of Nonlinear Mechanics of Solids (Kazan, 2009), pp. 270-273.
7.  N. F. Morozov and P. E. Tovstik, "On Modes of Buckling for a Plate on an Elastic Foundation," Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela, No. 4, 30-42 (2010) [Mech. Solids (Engl. Transl.) 45 (4), 519-528 (2010)].
8.  N. F. Morozov and P. E. Tovstik, "Bulk and Surface Stability Loss of Materials," in Multiscaling of Synthetic and Natural Systems with Self-Adaptive Capacity (Taiwan, 2010), pp. 27-30.
9.  N. F. Morozov and P. E. Tovstik, "Volume and Surface Stability of Transversely Isotropic Material," in Advanced Problems in Mechanics. 38th Summer School (St. Petersburg, 2010).
10.  M. A. Il'gamov, V. A. Ivanov, and B. V. Gulin, Strength, Stability, and Dynamics of Shells with an Elastic Filler (Nauka, Moscow, 1977).
1.  P. Ciarlet, Mathematical Elasticity (North-Holland, Amsterdam, 1988).
12.  T. M. Cherry, "Uniform Asymptotic Formulae for Functions with Transition Points," Trans. Amer. Math. Soc. 68, 224-257 (1950).
13.  F. W. J. Olver, Asymptotics and Special Functions (Academic Press, New York, 1974; Nauka, Moscow, 1990).
14.  M. Abramowitz and I. A. Stegun (Editors), Handbook of Mathematical Functions, with Formulas, Graphs, and Mathematical Tables (Dover, New York, 1972; Nauka, Moscow, 1979).
Received 09 September 2010
Link to Fulltext http://www.springerlink.com/content/k672036968253m56/
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