PSI - Issue 17
B. Boukert et al. / Procedia Structural Integrity 17 (2019) 37–43
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B.Boukert et al/ Structural Integrity Procedia 00 (2019) 000 – 000
2
1. Introduction
Research in aeronautics has a great focus in composite materials, especially for structure members and engine. The composite materials present many advantages like rigidity and lightness. During their operation, aeronautical structures are subjected to variable conditions in terms of temperature and humidity. T . Particular attention is given to the behavior of the thick plates in hygrothermal environment. Several theories of high order which satisfy the boundary conditions can be found in the literature. Ambarsumian [1] proposed a transverse shearing function to explain the deformation of laminates. A similar method was used by Soldatos and Timarci [2] for the dynamic analysis of laminates. Other new functions are presented by Reddy [3] [4] [5], Touratier [6], Karama [7], Soldatos [8], Krishna Murthy [9], Levinson [10], and the various high order theories were compared by Aydogdu [11]. A.M.Zenkour [12] treated the static thermo-elastic response of symmetric and anti-symmetric cross-ply laminated plates. O.Sayman [13] studied the stress behavior for a composite, with a metal matrix under linear thermal loading. Later O.Sayman [14][15] studied the stress behavior for a composite with a metal matrix under parabolic thermal loading. Reddy [16] studied the problem of thick plate under sinusoidal mechanical loading with linear thermal loading. Pipes & al [17] studied the stress state in a composite laminate by taking into consideration the temperature and absorbed moisture. B.Boukert [18] [19] [20] analysed different cases of hygrothermal loading on a thick composite plate and calculate the stress state with different environmental conditions. Z.Sereir [21] developed a simple method to calculate residual stress in hygrothermal environment. Basi & al [22] considered the hygrothermal effects in a developed theory to calculate the stresses state in a thick composite plate. The present paper deals with higher order shear deformation theory developed by Reddy and consider a rectangular composite plate with length a, width b and thickness h, made of T300/5208.The plate is subjected to a sinusoidal transverse mechanical load q(x, y) and temperat ure/moisture field ∆T(x, y, z) / ∆ C(x, y, z), The moisture field ∆ C(x, y, z) is calculated by using Fick equation. The plate is referred to a coordinate system (x, y, z) with the coordinates x and y along the in-plane directions and z along the thickness direction. The plate is composed of orthotropic cross ply layers. The purpose of this paper is to examine the influence of environment (temperature and concentration) on the behavior of a thick composite plate. Several numerical simulations have been done in different environmental cases to examine the effect of temperature and humidity.
2. Model description
A third order plate theory developed by Reddy[4][16] is used in this paper through a cubic function of the thickness coordinate, where ( u o , v o , w o ) are the displacement components along the ( x, y, z ) directions, respectively, of a point on the midplane (i.e., z=0 ). ø x and ø y denote rotations about the y and x axes [24-25][16].
w
4
3
0
( , , ) u x y z u z x y = + ( , )
z
(
)
−
+
x
x
0
2
x
4 h
3
(1)
w
3
0
( , , ) v x y z v z x y = + ( , )
z
(
)
−
+
y
y
0
2
y
h
3
( , , ) w x y z w x y = ( , )
0
The stress resultants are related to the strains by:
0 1 3
0 2
N M B D F P E F H = A B E
Q R D F = A D
(2)
,
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