14 / 15
Ю.И. Димитриенко, Ю.В. Юрин
14
Инженерный журнал: наука и инновации
# 10·2017
Comparative stress analysis in nonsymmetrical multilayer
composite plates in the asymptotic theory
and three-dimensional finite element calculation
© Yu.I. Dimitrienko, Yu.V. Yurin
Bauman Moscow State Technical University, Moscow, 105005, Russia
The article analyzes the accuracy of previously developed multilayer thin plates’ asymp-
totic theory. We compare the solution results of the bending problem for a multilayer
asymmetric plate under pressure obtained in the asymptotic theory and in the exact
three-dimensional elasticity theory. The problem solution in the asymptotic theory for the
asymmetric plate case was obtained for the first time. The paper shows that the plate
layers’ arrangement asymmetry leads to the longitudinal plate displacements at trans-
verse pressure. We used a software finite-element ANSYS package with a specially con-
structed finite element mesh to solve the elasticity theory three-dimensional problem. This
grid allows for a finite element nodes thickening along the plate thickness while main-
taining a relatively small grid lateral elements total number. The paper compares all
stresses distributed along the plate thickness, obtained by means of the asymptotic theory
and finite elements method. We show that the developed asymptotic theory provides high
solution accuracy for all stress components, including transverse and shear stresses.
Keywords:
asymptotic theory of plates, multilayer thin plates, asymmetric plates, finite
element method, lateral stresses, numerical simulation
REFERENCES
[1]
Grigolyuk E.I., Kulikov G.M.
Mekhanika kompozitsionnykh materialov —
Mechanics of Composite Materials
, 1988, vol. 24, no. 4, pp. 698–704.
[2]
Ghugal Y.M., Shmipi R.P.
Journal of Reinforced Plastics and Composites
,
2001, vol. 20, no. 3, pp. 255–272.
[3]
Tornabene F.
Computer Methods in Applied Mechanics and Engineering
, 2011,
no. 200, pp. 931–952.
[4]
Alfutov N.A., Zinoviev P.A., Popov B.G.
Raschet mnogosloynykh plastin i
obolochek iz kompozitsionnykh materialov
[Calculation of multilayer plates and
shells made of composite materials]. Moscow, Mashinostroenie Publ., 1980, 324 p.
[5]
Sheshenin S.V.
Izvestiya RAN. Mekhanika tverdogo tela
—
Mechanics of Solids.
A Journal of the Russian Academy of Sciences
, 2006, no. 6, pp. 71–79.
[6]
Zveryaev E.M., Makarov G.I.
Prikladnaya matematika i mekhanika — Journal
of Applied Mathematics and Mechanics
,
RAS
, 2008, vol. 72, no. 2, pp. 308–321.
[7]
Nazarov S.A., Svirs G.H., Slutsky A.S.
Matematicheskii Sbornik — Sbornik:
Mathematics
,
2011, vol. 202, no. 8, pp. 41–80.
[8]
Kohn R.V., Vogelius M.
International Journal of Solids and Structures
, 1984,
vol. 20, no. 4, pp. 333–350.
[9]
Panasenko G.P., Reztsov M.V.
Dokl. AN SSSR
—
Reports of Acad. Sci. USSR
,
1987, vol. 294, no. 5, pp. 1061–1065.
[10]
Levinski T., Telega J.J.
Plates, laminates and shells
.
Asymptotic analysis and
homogenization
. Singapore, London, World Sci. Publ., 2000, 739 p.
[11]
Kolpakov A.G.
Homogenized models for thin-walled nonhomogeneousstructures
with initial stresses
. Berlin, Heidelberg, SpringerVerlag, 2004, 228 p.