Nonlinear analysis of large deflection of bossed layered-plate under initial tension

The nonlinear problem of large deflection of a bossed and laterally loaded circular layered plate with clamped end under initial tension is studied. The approach follows Von Karman plate theory for large deflection for an isotropic symmetrically layered case simulating a typical micro-pressure sensing device. The thus derived nonlinear governing equations for lateral slope and radial force resultant were solved using a numerical finite difference method incorporated with the boundary conditions along the central boss and the clamped edge. A three-layered symmetric plate with nearly monolithic material properties and a narrowed boss was considered first and the results correlate well with available solutions for an isotropic single-layered problem. Typical bossed and layered plates are then implemented and the results show that, changing the boss width may sensibly affect the structural behavior of the layered sensing plate, in general, in a comparatively low initial tension condition. As the initial tension becomes relatively large, on the other hand, the effect of pretension appears to be dominant, rendering nearly the same results for the structural responses regardless of the boss size and the deviation in the layer moduli.