Possible simplifications of the general model

The general model formulated in the previous section can be simplified by introducing further assumptions about the geometric and mechanical assumptions.

Possible simplifications of the general model Possible simplifications of the general model

In particular, a key simplification derives in the case of negligible thickness tf of the FRP laminate, if compared, for instance, with a suitable reference value of the length. In particular, it is possible to demonstrate that the height-order equation (32) can be reduced by uncoupling the equations (30) and (31):

Under the mathematical point of view, the above simplification derives from the condition <atf^0 for whichever value of the non dimensional parameters listed at the end of section 2.1. It means that the thickness of the FRP laminate is much smaller than the characteristic length of the problem <a, which is the main argument of the solutions of the general equation (32). The uncoupled boundary conditions for eq. (42) simplify as a consequence of the condition rotf^0, turning in a completely uncoupled expressions:

Possible simplifications of the general model
Подпись: (44)

A sound demonstration about how equation (32) reduces to (42)-(43) in the case of rotf^0, can be obtained by means of some mathematical transformations of both the equation (32) and the boundary conditions (34)-(37) in dimensionless form. These transformations, as well as the discussion about the slight modifications in the out-of-plane stress regime, are omitted herein for the sake of brevity.