Page 246 - Mechanics Analysis Composite Materials

Chapter 5. Mechanies of laminates 23 1

‘3

a
Fig. 5.6. Reduction of transverse shear stresses to stress resultants (transverse shear forces).

(5.12)
-e -e

Because the particular distribution of txzand z, does not influence the displace-
ments, we can introduce some average stresses having the same resultants as the
actual ones, i.e.,

However, according to Eqs. (5.11), shear strains are linear combinations of shear
stresses. So we can use the same law to introduce average shear strains as

(5.13)

Average shear strains ’yx and yv can be readily expressed in terms of displacements
if we substitute Eqs. (5.9) into Eqs. (5.13), i.e.,

These equations, in contrast to Eqs. (5.9), do not include derivatives with respect
to z. So we can substitute Eqs. (5.1) and (5.2) to get the final result
aw aw
y.y = e, +-, y), = e, +- . (5.14)
ax aY