Page 125 - Mechanics Analysis Composite Materials

110 Mechanics and analysis of composite materials

(3.1 16)

which can be in turn expressed in terms of displacements with the aid of Eqs. (2.22),
i.e.,

(3.1 17)

Substituting Eqs. (3.1 16) into Eqs. (3.1 17) and integrating we can determine the
displacements as

Here, u(x) and u(x) are functions of integration which, as well as functions z(x) and
~(x),should be found using compatibility conditions at fiber-matrix interfaces.
Using Fig. 3.63 we can write these conditions in the following form:

d d
uxk= 0) = -Tu+), ux(y= a) = -u:(x))
2-
u,o, = 0) = u, (x), UV(y = a) = u2(x) .

Satisfying them we can find U(X) and u(x) directly as

Fig. 3.63. Compatible fiber-matrix deformation.