Page 27 - Mechanics of Microelectromechanical Systems
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14 Chapter 1
The stress-strain Eqs. (1.26) have been utilized to derive Eqs. (1.37) and
(1.38).
4. MEMBERS, LOADS AND BOUNDARY
CONDITIONS
MEMS components are designed in various geometric configurations,
and the states of external load, together with the constraining boundary
conditions, can be diverse as well. These factors affect the
stiffness/compliance properties of flexible mechanical microcomponents.
The elastic members can be one-dimensional (such as bars, rods, beams
or columns), two-dimensional (such as membranes or plates) and three-
dimensional (such as blocks). For each of them, specific equations that
describe the state of deformation or stress apply. There are four different
types of loading/deformations, namely: normal, torsion, shearing and
bending. They are briefly characterized here in terms of stresses,
deformations and strain energy for one-dimensional members.
4.1 Normal Loading
In the case of normal loading, the stresses and strains (deformations) are
perpendicular to the surface where the axial (normal) force is applied. Figure
1.1 is the physical model of a fixed-free bar of constant cross-section that is
acted upon by an axial force at its free end. The constant normal stress that is
generated by an axial load N over an area A is:
The total axial deformation which is registered at the free end (where the
axial force is being applied) with respect to the fixed end, spaced at a
distance l, is:
and the strain is:
