Transition behavior in large deflection of elastically-bossed unsymmetrically layered plate under initial tension

The transition behavior of an elastically-bossed un-symmetrically layered plate in large deflection due to lateral load is studied. von Karman plate theory for large deflection is utilized and extended to the case of a pre-stressed un-symmetrically layered plate with an elastic boss. The governing equations are simplified to a modified Bessel equation for the lateral slope, by neglecting the arising nonlinear terms following a linear consideration. Analytical solution is developed by imposing the interface continuity and the clamped-end boundary condition, which is expressible via modified Bessel functions of the first and the second kinds, rather than only the first kind for a flat plate. A subsequent integration is performed to evaluate the deflection at the center of the plate for studying the transition behavior as a function of pretension. For a nearly monolithic plate with a shallow boss, the results agree well with those of a flat plate available in literature, thus validates the presented approach. For two-layered un-symmetric plates made of typical silicon based materials, various radial sizes and thickness for the center boss are implemented. The solutions show that, widening the center boss may appreciably extend the range of pretension for the plate mode and thus enlarge the pretension for transferring to a membrane behavior.