Flexural stiffness of leaf springs for compliant micromechanisms

Von Kármán equations have been used to evaluate the flexural behaviour of rectangular leaf springs with constant thickness. A closed form solution is obtained, showing that flexural stiffness varies continuously from that obtained by considering a beam model to the value given by the linear plate theory. This behaviour depends on section geometry, Poisson's ratio, and main curvature. A new characterizing parameter, whose relation with flexural stiffness allows a typical non-linear behaviour to be emphasized, is introduced in this work. In particular, for a given geometry and material, the flexural stiffness increases with the deflection and consequently with the load.