ABSTRACT
This difficulty is overcome in an approximate sense by a bilinear contact element. In particular, we introduce a new spring, kg, as shown in Figure 15.2.
The stiffness of the middle spring (B in series with the contact spring) is now denoted as km, and
(15.2)
It is desirable for the middle spring to be soft when the gap is open (g>δ) and to be stiff when the gap is closed (g≤δ):
(15.3)
Elementary algebra serves to demonstrate that
(15.4)
Consequently, the model with the contact is too stiff by 0.5% when the gap is open, and too soft by 0.33% when the gap is closed (contact). One conclusion that can be drawn
from this example is that the stiffness of the gap element should be related to the stiffnesses of the contactor and target in the vicinity of the contact point.
