Page 233 - Mechanics Analysis Composite Materials

218 Mechanics and analysis of composite materials

angles with the global structural axes x, y, z (see Fig. 4.96). In the principal material
coordinates, constitutive equations have the form of Eqs. (4.53)or Eqs. (4.54).
Introducing directional cosines Ixi, l~, which are cosines of the angles that the
l,i
i-axis (i = 1, 2, 3) makes with axes i,y, z, respectively, applying Eqs. (2.8), (2.9)
and (2.31) to transform stresses and strains in coordinates 1, 2, 3 to stresses and
strains referred to coordinates x, y, z, and using the procedure described in Section
4.3.1 we finally arrive at the following constitutive equations in the global structural
coordinate frame

(4.171)

sllll SI122 SI133 SI112 SI113 SI123
32222 s2233 s2212 s2213 s2223
s3333 S3312 S3313 s3323
IS1 =
SI212 SI213 SI223
SYm SI313 SI323
s2323
is the stiffness matrix in which

J
Y
Fig. 4.96. Material elements referred to the global structural coordinate frame x, y, z and to the principal
material axes I, 2. 3.