Page 343 - Mechanics Analysis Composite Materials

328 Mechanics and analysis of composite materials

Applying Laplace transformation to these equations we can reduce them to the
form analogous to Hooke’s law, Eqs. (4.59, Le.

(7.45)

where

For the unidirectional composite ply whose typical creep diagrams are shown in
Fig. 7.15, the foregoing equations can be simplified neglecting material creep in the
longitudinal direction (CII= 0) and assuming that Poisson’s effect is linear elastic
and symmetric, i.e. that

Then, Eqs. (7.45) acquire the form:

E,@) =---a;@> v12a;@),
*
El E2
* a;@) v21
E2@) =--- 07 (7.47)
E; El 7

Supplementing constitutive equations, Eqs. (7.45) or (7.47), with strain-displace-
ment and equilibrium equations written in terms of Laplace transforms of stresses,
strains, displacements, and external loads, and solving the problem of elasticity we
can find Laplace transforms of all the variables. To write thus obtained solution in
terms of time t, we need to take the inverse Laplace transformation, and this is the