Page 40 - Mechanics of Microelectromechanical Systems
P. 40
1. Stiffness basics 27
remain plane and perpendicular on this surface after the load has been
applied. These assumptions are at the basis of the Euler-Bernoulli model, as
mentioned previously.
Figure 1.18 Cantilever with full three-dimensional loading
According to Castigliano’s first theorem, the force or moment producing
bending at a point on a beam can be found by evaluating the partial
derivatives of the strain energy generated through bending in terms of the
corresponding deflection or rotation (slope) at that point in the form:
where the subscript b,y indicates bending about the y-axis. Within the small-
displacement (engineering) beam theory, the strain energy which is produced
through bending about the y-axis is expressed as:
