Two-dimensional equations of thin elastic plate made of anisotropic inhomogeneous material are delivered by using asymptotic expansion in powers of the relative plate thickness. In the general case anisotropy is described by 21 elastic moduli. Partial cases of elastic moduli are also discussed. The proposed model is compared with the classic models of Kirchhof–Love and of Timoshenko–Reissner.
REFERENCES
1.
V.A.
Rodionova
, B.F.
Titaev
, K.F.
Chernykh
, Applied theory of anisotropic plates and shells
. St.Petersburg Univ. Press
(1996
)2.
L.A.
Agalovjan
, Asymptotic theory of anisotropic plates and shells
. Nauka
, Moscow
(1997
)3.
J.N.
Reddy
, Mechanics of laminated composite plates and shells
. CRC Press
, 2004
. 831
p.4.
P.E.
Tovstik
, On the asymptotic character of approximate models of beams, plates and shells. Vestnik St.Petersburg Univ. Mathematics
. Allerton Press
. 2007. N 3
. Pp. 49
–54
(2007
)5.
P.E.
Tovstik
, T.P.
Tovstik
, On the 2D models of plates and shells including the transversal shear
. ZAMM
, 2007
, 87
, No 2
, 160
–171
.6.
P.E.
Tovstik
, T.P.
Tovstik
, One-dimensional models of a beam made of an anisotropic material with oblique anisotropy
. Mechanics of Solids
. Volume 46
, Issue 6
, pp 888
–897
(2011
)7.
P.E.
Tovstik
, Two-dimensional models of plates made of an anisotropic material
. Doklady Physics
. Vol. 54
. No 4
, pp. 205
–209
(2009
)8.
P.E.
Tovstik
, T.P.
Tovstik
, Two-dimensional models of shells made of an anisotropic material
Acta mechanica.
2014
. V. 225
, no 3
. 647
–661
.9.
P.E.
Tovstik
, T.P.
Tovstik
, Two-dimensional linear model of anisotropic shells. SSTA
. 2013
. Gdansk
. V.3
, 153
–156
.10.
Y.
Vetukov
, A.
Kuzin
, M.
Krommer
, Asymptotic splitting of the three-dimensional problem of elasticity for non-homogeneous piezoelectric plates
Int. J. of Solids and Structures
, 2011
, v. 40
, 12
–23
.11.
P.
Schnieder
, R.
Kienzler
, An algorithm for the automatisation of pseudo reductions of PDE systems arising from the uniform-approximation technique. (2011
) In: Shell-like structures. Non-classical theories and applications
. Berlin
. Springer
. 377
–390
.
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