Page 344 - Mechanics Analysis Composite Materials

Chapter 7. Environmental, special loading, and manufacturing effects 329

most difficult stage of the problem solution. There exist exact and approximate
analytical and numerical methods for performing inverse Laplace transformation
discussed, e.g., by Schapery (1974). The most commonly used approach is based on
approximation of the solution written in terms of transformation parameter p with
some functions for which the inverse Laplace transformation is known.
As an example, consider the problem of torsion for an orthotropic cylindrical
shell similar to shown in Figs. 5.19 and 5.21. The shear strain induced by torque T
is specified by Eq. (5.1 12). Using the elastic-viscoelastic analogy we can write the
corresponding equation for the creep problem as

(7.48)

Here, BM@)=A&(p)h, where h is the shell thickness.
Let the shell be made of glass+poxy composite whose mechanical properties are
listed in Table 3.5 and creep diagrams are shown in Fig. 7.15. To simplify the
analysis, we assume that for the unidirectional composite under study EZIEI = 0.22,
GI?/EI = 0.06, vi2 = v21 = 0 and introduce the normalized shear strain
7 = ".(&) -I .

Consider first a k45" angle-ply material discussed in Section 4.5 for which, with due
regard to Eqs. (4.72), and (7.46) we can write

Exponential approximation, Eq. (7.36), of the corresponding creep curve in
Fig. 7.15 (the lower broken line) is

where AI = 0.04 and a1 = 0.06 l/day. Using Eqs. (7.42), we arrive at the following
Laplace transforms of the creep compliance and the torque which is constant

AI T
C2*2(p)= - T*@)=- .
+P' P

The final expression for the Laplace transform of the normalized shear strain is

(7.49)