Once the calculations are performed,one obtains the following expressions for the stiffness coefficients Ey,where c=cose and s=sine. E12 E Exa E 正 with: E1(0)=cE+s4E,+2c22(yE+2G) E2(0)s'E+cEr+2c's(vuEc+2G) Es(0)=c2s(Ee+E-2vnE)+(c2-s)Gur (11.8) E2(0)=c2s2(Ee+B-4G)+(c*+s)y,E E3(0)=-cs{c2E-s2E-(c2-s)(yeE+2G)》 E23(0)=-cs{s2Ee-c2E,+(c2-s3)(eE+2G)} expressions in which: Et=E/(1-vervn):EE/(1-vervne) The rate of variation of stiffness coefficients Ey as functions of the angle 0 is repre sented in Figure 11.2 for a ply characterized by moduli E and E,with very different values,for example the case of unidirectional layers of fiber/resin. 11.3 CASE OF THERMOMECHANICAL LOADING 11.3.1 Compliance Coefficients When considering the temperature variations,one must substitute the stress-strain Equation 11.1 with Equation 10.9: 言 01oe de E 0 ,}+△Ta, Ye) 0 0 1 0 See characteristics of the fiber/resin unidirectionals in Paragraph 3.3.3. See Section 10.5. 2003 by CRC Press LLCOnce the calculations are performed, one obtains the following expressions for the stiffness coefficients , where c = cosq and s = sinq. (11.8) The rate of variation of stiffness coefficients as functions of the angle q is repre sented in Figure 11.2 for a ply characterized by moduli E
and Et with very different values, for example the case of unidirectional layers of fiber/resin.8 11.3 CASE OF THERMOMECHANICAL LOADING 11.3.1 Compliance Coefficients When considering the temperature variations,9 one must substitute the stress–strain Equation 11.1 with Equation 10.9: 8 See characteristics of the fiber/resin unidirectionals in Paragraph 3.3.3. 9 See Section 10.5. Eij sx sy Ótxy ˛ Ô Ô Ì ˝ Ô Ô Ï ¸ E11 E12 E13 E21 E22 E23 E31 E32 E33 ex e y Óg xy ˛ Ô Ô Ì ˝ Ô Ô Ï ¸ = with: E11( ) q c 4 E
s 4 Et 2c 2 s 2 nt
E
+ 2G
t = + + ( ) E22( ) q s 4 E
c 4 Et 2c 2 s 2 nt
E
+ 2G
t = + + ( ) E33( ) q c 2 s 2 ( ) E
+ Et – 2nt
E
c 2 s 2 ( ) – 2 = + G
t E12( ) q c 2 s 2 E
+ Et – 4G
t ( ) c 4 s 4 = + ( ) + nt
E
E13( ) q –cs c 2 E
s 2 – Et c 2 s 2 ( ) – nt
E
+ 2G
t = { } – ( ) E23( ) q –cs s 2 E
c 2 – Et c 2 s 2 ( ) – nt
E
+ 2G
t = { } + ( ) expressions in which: E
E
/ 1 – n
tnt
= ( ) : Et Et/ 1 – n
tnt
= ( ) Eij e
et Óg
t˛ Ô Ô Ô Ô Ì ˝ Ô Ô Ô Ô Ï ¸ 1 E
----- nt
Et –------ 0 n
t E
–------ 1 Et ---- 0 0 0 1 G
t ------- s
st Ót
t˛ Ô Ô Ô Ô Ì ˝ Ô Ô Ô Ô Ï ¸ = DT a
at Ó 0 ˛ Ô Ô Ô Ô Ì ˝ Ô Ô Ô Ô Ï ¸ + TX846_Frame_C11 Page 229 Monday, November 18, 2002 12:26 PM © 2003 by CRC Press LLC