Page 161 - Mechanics of Microelectromechanical Systems
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148 Chapter 3
By arranging these compliances into a 3 by 3 symmetric compliance matrix,
the corresponding stiffness matrix can be obtained through inversion of this
compliance matrix. When the definition stiffnesses are needed, then simple
inversion of the individual compliances of Eqs. (3.46) through (3.51) will
produce these stiffnesses.
For designs where the circular segment is relatively short (R < 10 w),
Young and Budynas [1] recommend using the following bending energy:
where e is the eccentricity, which, for a rectangular cross-section, can be
calculated by means of Eq. (1.122). By applying again Castigliano’s
displacement theorem for the configuration of Fig. 3.16 in the presence of the
tip loads and (not shown in Fig. 3.16), the resulting displacements
and can be found by means of the following compliances:
