Page 44 - Mechanics of Microelectromechanical Systems
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1. Stiffness basics 31
which is the known equation for the axial stiffness of a constant cross-section
bar.
Example 1.7
Design a microcantilever of constant rectangular cross-section which
needs to have a minimum stiffness while having maximum stiffnesses
and
Solution:
The following objective function can be constructed:
which has to be minimized in order to satisfy the requirements of the
example. By using Eqs. (1.95) and (1.106), the function of Eq. (1.107)
becomes:
It is assumed that the length l and width w can be expressed as fractions of
the thickness t as:
By substituting Eqs. (1.109) into Eq. (1.108), the objective function changes
into:
In order to minimize f, and have to be maximum, which means that w
and l have to be maximum.
5.2.3 Torsion
The tip moment that produces torsion is expressed in terms of the
rotation angle by means of Castigliano’s first theorem as:
where the torsion-related strain energy is formulated from Eq. (1.71) as:
