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Chapter 5. Mechanics of laminates 247
Then, Eq. (5.61) yields
-h/2 -h /2 -h/2
As can be seen from Eq. (5.60), Dll reaches its maximum value if J:;) = 0 or = 0
and All =Ai,. In this case, Eq. (5.59) gives e = h/2.
Thus, symmetric laminates provide the maximum bending stiffness for a given
number and mechanical properties of layers and, being referred to the middle-plane,
do not have membrane-bending coupling effects. This essentially simplifies behavior
of the laminate under loading and constitutive equations which have the form
specified by Eqs. (5.35). For a symmetric laminate with the layer coordinates shown
in Fig. 5.12, stiffness coefficients are calculated as
The transverse shear stiffness coefficients are given by Eq. (5.31) in which
To indicate symmetric laminates, contracted stacking-sequence notation is used,
e.g., [0"/90"/45"],~instead of [0"/90"/45"/45"/90'/0"].
Fig. 5.12. Layer coordinates of a symmetric laminate.
