Page 86 - Mechanics of Microelectromechanical Systems

2. Microcantilevers, microhinges, microbridges 73
Equations (2.23) prove that the stiffnesses obtained by inverting the bending-
related compliance matrix are different from the stiffnesses that define the
three different springs and that are calculated as the algebraic inverses of the
corresponding compliances. It is useful to express one set of stiffnesses in
terms of the other set as:

or as:

Example 2.1
The tip deflection and slope are available for a constant cross-
section rectangular microcantilever. Find the errors of calculating the tip
force according to the approximate equation:
with respect to the force calculated by means of the exact equation:

Solution:
The relative error is:

Figure 2.5 Errors in evaluating the tip force by approximate versus exact equations