Macromechanical analysis of 3-D textile reinforced composites 107 4.6 Displacement field in a thick plate. Table 4.1.Stiffness properties as a function of the theory used Theory Needed stiffness properties Beams theory Ex Gxy and Vxy Laminated plates theory Ex Ey,Gxy and Vxy Irons's theory Ex Ey,Gxy Gxz Gyz and VxY First-order shear theory Ex Ey,Gxy,Gxz Gyz and Vxy Higher-order shear theory Ex Ey,Gxy,Gxz Gyz and Vxy Elasticity theory Ex Ey,Ez,Gxy,Gxz Gvz,VxY,Vxz and Vyz The following stiffness properties are needed:Ex,Ey,Ez,Gxy,Gxz.Gyz, Vxy,Vxz and vyz. Table 4.1 represents the stiffness properties needed as a function of the theory applied. 4.2.2 Stiffness and strength properties as a function of the 3-D textile preform The 3-D textile preform used as a reinforcement for the composite ma- terial affects the needed stiffness and strength properties for two reasons [18-23: On the one hand,every 3-D textile technology is associated with one or more theories among the ones described in Section 4.2.1.Each of these theories requires a specific list of stiffness properties for an appropriate implementation. On the other hand,every 3-D textile technology requires one or more specific strength criteria and,therefore,a number of strength properties.Macromechanical analysis of 3-D textile reinforced composites 107 The following stiffness properties are needed: EX, EY, EZ, GXY, GXZ, GYZ, vXY, vXZ and vYZ. Table 4.1 represents the stiffness properties needed as a function of the theory applied. 4.2.2 Stiffness and strength properties as a function of the 3-D textile preform The 3-D textile preform used as a reinforcement for the composite ma￾terial affects the needed stiffness and strength properties for two reasons [18–23]: • On the one hand, every 3-D textile technology is associated with one or more theories among the ones described in Section 4.2.1. Each of these theories requires a specific list of stiffness properties for an appropriate implementation. • On the other hand, every 3-D textile technology requires one or more specific strength criteria and, therefore, a number of strength properties. Table 4.1. Stiffness properties as a function of the theory used Theory Needed stiffness properties Beams theory EX, GXY and vXY Laminated plates theory EX, EY, GXY and vXY Irons’s theory EX, EY, GXY, GXZ, GYZ and vXY First-order shear theory EX, EY, GXY, GXZ, GYZ and vXY Higher-order shear theory EX, EY, GXY, GXZ, GYZ and vXY Elasticity theory EX, EY, EZ, GXY, GXZ, GYZ, nXY, nXZ and vYZ 4.6 Displacement field in a thick plate. RIC4 7/10/99 7:43 PM Page 107 Copyrighted Material downloaded from Woodhead Publishing Online Delivered by http://woodhead.metapress.com Hong Kong Polytechnic University (714-57-975) Saturday, January 22, 2011 12:30:21 AM IP Address: 158.132.122.9