N Zo FIGURE 2.7 Definition of ply coordinates,Zk. N ∑，医- (2.35c) The ply coordinates zk,(k =1,2...N),where N is the number of plies in the laminate,are defined in Figure 2.7 and may be calculated from the following recursion formula: z=-h/2 。k=0 (2.36a) Zk =Zk-1+hk k=1,2,.,N (2.36b) in which hk is the ply thickness of the kth ply. For the steady-state condition considered,the temperature change is uniform throughout the laminate,and the thermal force resultants are determined from N n Q12 Q16 Ny Qi2 Qz Q26 (亿k-Zk-1)△T (2.37 k=】 Niy Qzo The moisture-induced force resultants [NM,NM,NM]are obtained in the same manner as the thermal force resultants,but by replacing [o yl with [B,B,Bol,and AT with AM in Equation (2.37). The thermal moment resultants [M,My,My]are determined from M Qu 12 Q16 C.x M (2.38) M Q66 ©2003 by CRC Press LLC(2.35c) The ply coordinates zk, (k = 1, 2…N), where N is the number of plies in the laminate, are defined in Figure 2.7 and may be calculated from the following recursion formula: (2.36a) (2.36b) in which hk is the ply thickness of the kth ply. For the steady-state condition considered, the temperature change is uniform throughout the laminate, and the thermal force resultants are determined from (2.37) The moisture-induced force resultants are obtained in the same manner as the thermal force resultants, but by replacing [αx, αy, αxy] with [βx, βy, βxy], and ∆T with ∆M in Equation (2.37). The thermal moment resultants are determined from (2.38) FIGURE 2.7 Definition of ply coordinates, zk. ij ij k k k k N D = 1 3 ( ) Q zz ( ) − − = ∑ 3 1 3 1 zh k 0 =− = 2 0 zz h k N kk k = + =… −1 1 2,, , N N N = QQQ QQQ QQQ (z z ) T x T y T xy T k 11 12 16 12 22 26 16 26 66 k x y xy k k k N                                     − − = ∑ α α α 1 1 ∆ [N , N , N ] x M y M xy M [M ,M ,M ] x T y T xy T M M M = 2 QQQ QQQ QQQ (z z ) T x T y T xy T k 11 12 16 12 22 26 16 26 66 k x y xy k k k N                                     − − = ∑ 1 2 1 2 1 α α α ∆ TX001_ch02_Frame Page 22 Saturday, September 21, 2002 4:48 AM © 2003 by CRC Press LLC