Page 328 - Mechanics of Microelectromechanical Systems

5. Static response of MEMS 315
(5.144) and (5.145), the maximum stress according to the large displacement
model is:

As a consequence, the following stress ratio can be formulated, based on Eqs.
(5.142) and (5.146):

The stress ratio of Eq. (5.147) is plotted against the force F in Fig. 5.48. It
can be seen that by using the small-displacement theory, the stresses are
always overevaluated, as compared to the large-displacement theory, up to
factors of approximately 2.5 for large values of F. However, at relatively
smaller loads, the predictions given by the two methods are almost identical,
as also shown in Fig. 5.48, where the stress ratio is very close to 1 for small
values of the force F.

Figure 5.48 Stress ratio as a function of the tip force – Eq. (5.147)

7. BUCKLING

7.1 Introduction

Buckling is associated with structural instability occurring at
statical/dynamical loads which are called critical and which can produce
either failure or large deformations that are unacceptable. The discussion
here will be restricted to statically-generated buckling. Figure 5.49 pictures
three different situations that are stability-related.