Page 22 - Mechanics of Microelectromechanical Systems
P. 22
1. Stiffness basics 9
Because of the three Eqs. (1.24), which enforce the rotation equilibrium, only
6 stresses are independent. The equilibrium (or Navier’s) equations are:
where X, Y and Z are body force components acting at the center of the
isolated element.
Six strains correspond to the six stress components, as expressed by the
generalized Hooke’s law:
The strain-displacement (or Cauchy’s) equations relate the strains to the
displacements as:
It should be noted that for normal strains (and stresses), the subscript
indicates the axis the stress is parallel to, whereas for shear strains (and
stresses), the first subscript indicates the axis which is parallel to the strain,
