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1 Gu Gx(θ)= E E G(0= 1 4c2++2) (c2-s) Gu 器=2-言 ∫c2s2 =-2c s2 c2 G -心-管} =-2cs(v-va G对 E ； (13.8) 13.3 CASE OF A PLY One can observe from Equation 13.7 that the stress-strain relations in the plane x,y appear decoupled in the case when o=0.We suppose that this applies for the plies making a thin laminate.Each ply will be characterized in its plane by the following relations which are extracted from relations 13.5 and 13.7: In the orthotropic axes e,t: El -V4 0 e -Vu (13.9) 1E 0 0 0 ti In the xy axes,making an angle 0 with the orthotropic axes: The orthotropic axes of Equation 13.5 are denoted as for a ply (see Section 3.3.1). 2003 by CRC Press LLC(13.8) 13.3 CASE OF A PLY One can observe from Equation 13.7 that the stress–strain relations in the plane x,y appear decoupled in the case when szz = 0. We suppose that this applies for the plies making a thin laminate. Each ply will be characterized in its plane by the following relations which are extracted from relations 13.510 and 13.7: In the orthotropic axes ,t: (13.9) In the x,y axes, making an angle q with the orthotropic axes: ➡ ➡ ; ; 10 The orthotropic axes of Equation 13.5 are denoted as l,t,z for a ply (see Section 3.3.1). 1 Gxz -------- s 2 2 1( ) + n Et -------------------- c 2 Gt = + ------- Gxz( ) q 1 s 2 2 1( ) + n Et -------------------- c 2 Gt + ------- = -------------------------- 1 Gxy -------- 4c 2 s 2 1 E ---- 1 Et ---- 2 nt Et + + ------ Ë ¯ Ê ˆ c 2 s 2 ( ) – 2 Gt = + --------------------- Gxy( ) q 1 4c 2 s 2 1 E ----- 1 Et ---- 2nt Et + + ------ Ë ¯ Ê ˆ c 2 s 2 ( ) – 2 Gt + --------------------- = ----------------------------------------------------------------------- hxy Gxy -------- 2cs c 2 E ---- s 2 Et – ----º Ó Ì Ï = – º c 2 s 2 ( ) – nt Et ------ 1 2Gt – ---------- Ë ¯ Ê ˆ ˛ ˝ ¸ + mxy Gxy -------- 2cs s 2 E ---- c 2 Et – ----º Ó Ì Ï = – º c 2 s 2 ( ) – nt Et ------ 1 2Gt – ---------- Ë ¯ Ê ˆ ˛ ˝ ¸ – zxy Gxy -------- 2cs n n – t ( ) Et = – -------------------- zxz Gxz -------- cs 1 Gt ------- 2 1( ) + n Et – -------------------- Ë ¯ Ê ˆ = – e et Óg t˛ Ô Ô Ô Ô Ì ˝ Ô Ô Ô Ô Ï ¸ 1 E ---- –nt Et --------- 0 –nt E --------- 1 Et ---- 0 0 0 1 Gt ------- s st Ót t˛ Ô Ô Ô Ô Ì ˝ Ô Ô Ô Ô Ï ¸ = TX846_Frame_C13 Page 270 Monday, November 18, 2002 12:29 PM © 2003 by CRC Press LLC