Page 303 - Mechanics Analysis Composite Materials
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288 Mechanics and analysis of composite materials
2
1
t
Fig. 6.18. A special orthotropic material with equal strength in directions 1 and 2 referred to coordinates
(1, 2) and (l', 2').
Now, present Eq. (6.25) in the following matrix form:
(6.27)
where
(6.28)
Superscript "T" means transposition converting the column vector {CJ}into the
row vector {c}~.Let us transform stresses referred to axes (1, 2) into stresses
corresponding to axes (l', 2') shown in Fig. 6.18. Such transformation can be
performed with the aid of Eqs. (4.68) if we put o.~= 01,c,, = CJZ, zxJ,= qz,
crl = 02 = 0i5,512 = 7;; and take Cp = 45".The matrix form. of this transfor-
mation is
= (6.29)
where
[TI = 1/2 1/2
1/2
r21/2 "I0 .
-1/2
Substitution of stresses in Eq. (6.29) into Eq. (6.27) yields
{CJ~~)~[T]~[R~][TI{CT~~}
1
=
