Page 327 - Mechanics of Microelectromechanical Systems
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314 Chapter 5
Figure 5.47 Tip deformation about the longitudinal axis according to the large-displacement
theory
Example 5.20
Analyze the maximum stresses that are produced through bending of the
microcantilever in the preceding example when calculated by both the small-
and large-displacement theories.
Solution:
According to the small-displacement theory, the maximum stresses,
which are located on the upper fibers of the microcantilever, are calculated
as:
It has been shown that represents the true curvature, and this fact was
used in the large-displacement theory. The radius of curvature is therefore:
The maximum strain (on the upper fibers) can be calculated as:
By way of Eq. (5.133), which gives the space derivative of the slope
according to the large displacement theory, the maximum value invoked in
Eq. (5.144) is:
For materials with linearly-elastic behavior, the stress is the product of the
Young’s modulus and the corresponding strain, and therefore, by using Eqs.
