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Figure 13.3 Rotation above an Orthotropic Transverse Axis with (see Figure 13.3): cos(E,x)cos(E,y) cos(化， Tc-s [cos"] cos(t,x)cos(t,y) cos(t,z) 0 cos(z,x)cos(z,y)cos(z,z) 00 1 Noting that the only nonzero coefficientsare those that appear in Equation 13.4,one obtains: ·④11=cp1111+c22p1122+c2s2p1212+c232p1221… …+c2p212+c2sp2121+c2p211+sp2222 ·中1m=cp1111+sp2222+2c232(p1122+2p1212） Expressing this coefficient as a function of the "technical"constants which appear in Equation 13.5,one obtains: m"后*言+信-哈) ·电1mm=c2s29111+cp1122-c2gp1212-c232p1221… …-52c2p2112-32c2p2121+sp2211+s2c2p2222 ·④mm=(c+s)91122+c2s(9111+p2222-4c2sp1212) or in the "technical"form: m=尝e++信+远动) 。④1mm=cp1133+sp2233 and as91133=911226 ④11mm=cp1122+Sp2233 6 Because this is a transversely isotropic material;see Equations 9.2 and 13.4. 2003 by CRC Press LLCwith (see Figure 13.3): Noting that the only nonzero coefficients jmnpq are those that appear in Equation 13.4, one obtains: Expressing this coefficient as a function of the “technical” constants which appear in Equation 13.5, one obtains: or in the “technical” form: 6 Figure 13.3 Rotation above an Orthotropic Transverse Axis 6 Because this is a transversely isotropic material; see Equations 9.2 and 13.4. [cosI m] cos( ) , x cos( ) , y cos( ) , z cos( ) t, x cos( ) t, y cos( ) t, z cos( ) z, x cos( ) z, y cos( ) z, z c s – 0 s c 0 001 = = • FIIII c 4 j1111 c 2 s 2 j1122 c 2 s 2 j1212 c 2 s 2 = +++ j1221º º c 2 s 2 j2112 c 2 s 2 j2121 c 2 s 2 j2211 s 4 ++++ j2222 • FIIII c 4 j1111 s 4 j2222 2c 2 s 2 j1122 + 2j1212 = + + ( ) FIIII c 4 E ---- s 4 Et ---- s 2 c 2 1 Gt ------- 2 nt Et – ------ Ë ¯ Ê ˆ = + + • FI I II II c 2 s 2 j1111 c 4 j1122 c 2 s 2 – j1212 c 2 s 2 = + – j1221º º s 2 c 2 – j2112 s 2 c 2 – j2121 s 4 j2211 s 2 c 2 + + j2222 • FI I II II c 4 s 4 ( ) + j1122 c 2 s 2 j1111 j2222 4c 2 s 2 + – j1212 = + ( ) FI I II II nt Et ------ c 4 s 4 ( ) + c 2 s 2 1 E ---- 1 Et ---- 1 Gt + – ------- Ë ¯ Ê ˆ = – + • FI I III III c 2 j1133 s 2 = = + j2233 and as j1133 j1122 FI I III III c 2 j1122 s 2 = + j2233 TX846_Frame_C13 Page 265 Monday, November 18, 2002 12:29 PM © 2003 by CRC Press LLC