Page 54 - Mechanics of Microelectromechanical Systems

1. Stiffness basics 41
where is given in the first Eq. (1.126). By taking the partial derivatives
of the strain energy, Eq. (1.155), in terms of and respectively, the
compliances of Eq. (1.127) become:

5.3.2.2 Out-of-the-Plane Compliances

Similar to the case of a thick curved beam, the out-of-the-plane
compliances can be formulated as arranged in Eq. (1.137). The strain energy
for a thin (relatively-long) curved beam is formed by contributions from the
bending moment and the torsion moment only, namely:

with and being defined in Eqs. (1.134). By performing the partial
derivatives of the strain energy given in Eq. (1.162) in terms of and
respectively (according to the first two sides of Eqs. 91.135)), the only
compliance that is different from the ones already derived for a thick curved
beam is:

It can be seen that Eq. (1.163) can be obtained from Eq. (1.138) by
considering that the shearing effects are negligible