PSI - Issue 13

B. Boukert et al. / Procedia Structural Integrity 13 (2018) 174–180 B.Boukert et al/ Structural Integrity Procedia 00 (2018) 000–000

175

2

Similar method was used by Soldatos and Timarci [2] for the analysis of laminate dynamics, and other new functions have appears, Reddy [3] [4] [5] [6] [7] [8], Touratier [9], Karama [10], Soldatos [11], Krishna Murthy [12] [13] [14], Levinson [15], while the various high order theories were compared by Aydogdu [16]. Zenkour[17] treated the static thermo-elastic response of symmetric and anti-symmetric cross-ply laminated plates. Sayman [18] studied the stresses behavior for a composite, with a metal matrix under linear thermal loading, and later he [19][20] studied the stresses behavior for a composite with a metal matrix under parabolic thermal loading. Reddy [21] has treated the problem of thick plate under sinusoidal mechanical loading with linear thermal loading. Pipes & al [22] studied stresses state by taking into consideration the temperature and absorbed moisture in laminated composite plate, Boukert [23] treated different cases of hygrothermal loading on thick composite plate and calculated stress state with different environmental conditions. Basi & al [24] considered the hygrothermal effects to calculate the stresses state in a thick composite plate. Patel & al [25] analysed the problem of static and dynamic behavior of a thick laminated plate, subjected to hygrothermal loading using a higher order theory. Lo & al [26] studied the behavior of a laminated plate in hygrothermal environment using a global local higher order theory. 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 temperature/moisture field ∆T(x,y,z)/∆C(x,y,z). 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 thick composite plate, Several 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[27][17] 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 [27-31][21].

w



4

3

0

( , , ) u x y z u z x y    ( , )

(

)

z







0

x

x

2

x



3

4 h

w



3

0

( , , ) v x y z v z x y    ( , )

(

)

z







(1)

0

y

y

2

y



3

h

( , , ) w x y z w x y  ( , )

0

The equation of motion of the third order theory are derived using the principle virtual displacement:

xx N N x y Nxy N x y Q Q        y



xy

0

 



yy

0

 

2

2

2

xy P P 





P

4 (



yy

x

xx

2

)

0

q  

 





(2)

2

2

2

x  

y

x y

 

3

h x 

y



2 M M Q x y M M Q x y Where M M P Q Q R h h                   2 0 0 4 4 : , 3 xx xy x xy yy y ij ij ij ij ij

ij