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IssuesArchive of Issues2005-3pp.46-50

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R. L. Salganik, "Thermoelastic and poroelastic deformation of a multi-layer structure formed by layers resistant to bending (continuum approximation)," Mech. Solids. 40 (3), 46-50 (2005)
Year 2005 Volume 40 Number 3 Pages 46-50
Title Thermoelastic and poroelastic deformation of a multi-layer structure formed by layers resistant to bending (continuum approximation)
Author(s) R. L. Salganik (Moscow)
Abstract In the continuum approximation, the equations for linearly inelastic deformation of a multi-layer structure with the layers that can slip with respect to each other and are resistant to bending are derived. The inelastic nature of the deformation is due to either temperature changes (thermoelasticity) or pore pressure changes (for a fluid-saturated porous material; poroelasticity). Thus, a particular case of inelasticity is considered where the strain behavior of the material is the same during its loading and unloading. The layers are assumed to be plane, their material is uniform and isotropic. The temperature and pore pressure gradients are assumed to be relatively small, which allows the temperature and pore pressure differences through the layer thickness to be neglected. Deformation of each layer in the structure is modeled in terms of the classical theory of weak bending of thin plates with allowance for contact between adjacent layers. The characteristic scales of variation of all fields as functions of coordinates are assumed fairly large in comparison with the layer thickness, which justifies the continuum description of deformation of the structures under consideration. The layers are subjected to a normal uniformly distributed pressure which, hence, does not affect the layer deflection and prevents the delamination. It is also assumed that the effects of the longitudinal loading of the layers on their deflections can be neglected. An approach is considered which enables these problems to be reduced to those treated on the basis of the homogeneous deformation equations for the structure. An illustrative example is given, and possible applications of the results obtained are discussed.
References
1.  V. V. Bolotin and Yu. N. Novichkov, Mechanics of Multilayer Structures [in Russian], Mashinostroenie, Moscow, 1980.
2.  A. M. Freudental and H. Geiringer, The Mathematical Theories of the Inelastic Continuum [Russian translation], Fizmatgiz, Moscow, 1962.
3.  G. Sonntag,"Die is Schichten gleigher Dicke reibungsfrei geschichtete Halbebene mit periodisch vertreilter Randbelastung," Forsch. Geb. Ingenieurwesen, Bd. 23, H. 1/2, S. 3-8, 1957.
4.  R. L. Salganik, "Continuum approximation in the description of layered material deformation," Izv. AN. MTT [Mechanics of Solids]old, No. 3, pp. 48-56, 1987.
5.  R. L. Salganik, "Mixed static boundary-value problems for laminated elastic structures formed by bending resistant layers (a continuum approximation)", Izv. AN. MTT [Mechanics of Solids], No. 1, pp. 88-97, 2004.
6.  R. Christensen, Introduction to Mechanics of Composites [Russian translation], Moscow, Mir, 1982.
7.  S. P. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells [Russian translation], Nauka, Moscow, 1966.
10.  R. L. Salganik, and K. B. Ustinov, "Crack-like formation of failure-decided angle points on middle planes of the layers resistant to bending in multi-layer structure - a continuum model", Intern. J. Fract., Vol. 128, pp. 41-48, 2004.
11.  R. Goodman, Mechanics of Rocks [Russian translation], Stroiizdat, Moscow, 1987.
Received 21 August 2003
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