Remarks: For each ply having orthotropic axes x,y,z,the constitutive Equation 13.3 can be written as,taking into account the simplification o,0: Ey 0 0 Ey 1马 0 0 E 0 y x 0 0 0 0 Yxz 0 0 0 Txz 0 0 0 0 1 or under inverse form Ox [E E12 0 0 0 9 E22 0 0 0 S 人分 0 0 Es=Gxy 0 0 (17.2) 0 0 0 E4=G知 0 Yz 0 0 0 Ess =Gy Yyz where: Eu=1-VxVxs Ey E22=1-VxyVyx The transverse shear is at the origin of distortions as illustrated in Figure 17.1 for the shear stress T As a consequence,the displacements due to flexion discussed in Section 12.2.1 can be adapted as shown in Figure 17.2. yz orthotropic plate sandwich plate laminated plate in x,y,z axes Figure 17.1 Distortion of Section due to Transverse Shear Tyz 2003 by CRC Press LLCRemarks:
For each ply having orthotropic axes x, y, z, the constitutive Equation 13.3 can be written as, taking into account the simplification sz # 0: or under inverse form (17.2) where:
The transverse shear is at the origin of distortions as illustrated in Figure 17.1 for the shear stress tyz. As a consequence, the displacements due to flexion discussed in Section 12.2.1 can be adapted as shown in Figure 17.2. Figure 17.1 Distortion of Section due to Transverse Shear tyz ex e y g xy g xz g yz Ó ˛ Ô Ô Ô Ô Ô Ô Ô Ô Ô Ô Ì ˝ Ô Ô Ô Ô Ô Ô Ô Ô Ô Ô Ï ¸ 1 Ex --- nyx Ey –----- 00 0 n xy Ex –----- 1 Ey --- 00 0 0 0 1 Gxy ------ 0 0 0 00 1 Gxz ------ 0 0 000 1 Gyz ------ sx sy txy txz t yz Ó ˛ Ô Ô Ô Ô Ô Ô Ô Ô Ô Ô Ì ˝ Ô Ô Ô Ô Ô Ô Ô Ô Ô Ô Ï ¸ = sx sy txy txz Ót yz ˛ Ô Ô Ô Ô Ô Ô Ì ˝ Ô Ô Ô Ô Ô Ô Ï ¸ E11 E21 0 0 0 E12 E22 0 0 0 0 0 E33 = Gxy 0 0 0 0 0 E44 = Gxz 0 0 0 0 0 E55 = Gyz ex e y g xy g xz Óg yz ˛ Ô Ô Ô Ô Ô Ô Ì ˝ Ô Ô Ô Ô Ô Ô Ï ¸ = E11 Ex 1 – nxynyx = -----------------------; E12 nyxEx 1 – nxynyx = -----------------------; E22 Ey 1 – nxynyx = ----------------------- TX846_Frame_C17 Page 319 Monday, November 18, 2002 12:33 PM © 2003 by CRC Press LLC