Then,upon substituting, Ex 0 Ey =[T'] 0 (TK 〉+AT[T']H 0 0 One finds again in the first part of the second term a matrix of compliance coefficients,the terms of which are described in details in Equation 11.5.The second part of the second term is written as: ae ca+sar △T -CS △T sa+car -2cs 2cs (c2-s30 2cs(a;-ae) Therefore,the thermomechanical relation for a unidirectional layer written in the axes x.y,different from the e,t coordinates,can be summarized as follows: 「层 詈 cx】 (11.9) Ey 会 G o〉+AT (Yo) 是 气 1 x EEGare given by the relations [11.5] as=ca+s'ar ay sai+ca axy 2cs(a,-a) c=cos;s sin0 2003 by CRC Press LLCThen, upon substituting, One finds again in the first part of the second term a matrix of compliance coefficients, the terms of which are described in details in Equation 11.5. The second part of the second term is written as: Therefore, the thermomechanical relation for a unidirectional layer written in the axes x.y, different from the
,t coordinates, can be summarized as follows: (11.9) ex e y Óg xy ˛ Ô Ô Ô Ô Ì ˝ Ô Ô Ô Ô Ï ¸ [ ] T ¢ 1 E
----- nt
Et –------ 0 n
t E
–------ 1 Et ---- 0 0 0 1 G
t ------- [ ] T sx sy Ótxy ˛ Ô Ô Ô Ô Ì ˝ Ô Ô Ô Ô Ï ¸ = DT T[ ]¢ a
at Ó 0 ˛ Ô Ô Ô Ô Ì ˝ Ô Ô Ô Ô Ï ¸ + DT c 2 s 2 cs s 2 c 2 –cs –2cs 2cs c2 s 2 ( ) – a
at 0 Ó ˛ Ô Ô Ì ˝ Ô Ô Ï ¸ DT c 2 a
s 2 + at s 2 a
c 2 + at 2cs at – a
Ó ( )˛ Ô Ô Ì ˝ Ô Ô Ï ¸ = ex e y Óg xy ˛ Ô Ô Ô Ô Ì ˝ Ô Ô Ô Ô Ï ¸ 1 Ex ----- nyx Ey –------- hxy Gxy -------- n xy Ex –------- 1 Ey ----- mxy Gxy -------- hx Ex ----- my Ey ----- 1 Gxy -------- sx sy Ótxy ˛ Ô Ô Ô Ô Ì ˝ Ô Ô Ô Ô Ï ¸ DT ax ay Óaxy ˛ Ô Ô Ô Ô Ì ˝ Ô Ô Ô Ô Ï ¸ = + Ex, Ey,Gxy,nxy,nyx,hxy,mxy are given by the relations [11.5] ax c 2 a
s 2 = + at ay s 2 a
c 2 = + at axy 2cs at – a
= ( ) c = = cosq ; s sinq TX846_Frame_C11 Page 231 Monday, November 18, 2002 12:26 PM © 2003 by CRC Press LLC