01111i01122(=02211） 01133(=93311水92222 02233（=93322i93333 02323（=93232=02332=p3223】 01313（=p3131=01331=03113) 01212（=02121=01221=02112） 1.l Figure 13.2 Transversely Isotropic Material 13.2 ELASTIC COEFFICIENTS FOR A TRANSVERSELY ISOTROPIC MATERIAL Recall:By definition,a transversely isotropic material (Figure 13.2)is such that any plane including a preferred axis is a plane of mechanical symmetry.We have already noted that this is a particular case of orthotropic materials.Therefore,the only nonzero elastic constants are shown in Figure 13.2. The preferred direction is axis 1 in Figure 13.2.Considering that the coordinates 1,2,3 and I,II,III can be obtained from each other by a rotation of 0.One then has [10 [cosT]= -S with c=cos0 s=sine 0 s From the definition of material,the matrix of elastic coefficients has to remain invariant in this rotation.The Relation 13.1 allows one to write 。Φ1111=p111 ·中1mm=91122c2+91332=91122 3 See Section 9.3. Using the symmetries in Equation 9.1 and also using the discussion of the previous paragraph. 2003 by CRC Press LLC13.2 ELASTIC COEFFICIENTS FOR A TRANSVERSELY ISOTROPIC MATERIAL Recall: By definition,3 a transversely isotropic material (Figure 13.2) is such that any plane including a preferred axis is a plane of mechanical symmetry. We have already noted that this is a particular case of orthotropic materials. Therefore, the only nonzero elastic constants are shown in Figure 13.2. 4 The preferred direction is axis 1 in Figure 13.2. Considering that the coordinates 1,2,3 and I,II,III can be obtained from each other by a rotation of q. One then has From the definition of material, the matrix of elastic coefficients has to remain invariant in this rotation. The Relation 13.1 allows one to write Figure 13.2 Transversely Isotropic Material 3 See Section 9.3. 4 Using the symmetries in Equation 9.1 and also using the discussion of the previous paragraph. cosI m [ ] 10 0 0 c s – 0 s c = with c = cosq s = sinq • FI I I I = j1111 • FI I II II j1122c 2 j1133s 2 = = + j1122 TX846_Frame_C13 Page 262 Monday, November 18, 2002 12:29 PM © 2003 by CRC Press LLC