Sensitivity in Large Deflection of Bossed and Pre-Tensioned Layered Plate under Lateral Load

Mechanical sensitivity of a bossed and clamped layered isotropic circular plate with pretension in large deflection is evaluated. The approach extends Von-Karman’s plate theory for large deflection to a symmetrically layered plate with a center boss. The derived nonlinear governing equations are solved using a finite difference method incorporating a numerical iteration scheme in finding the lateral slope and radial force resultant. The obtained geometrical responses are further manipulated to calculate the associated mechanical sensitivity. For a 3-layered plate with nearly the same layer moduli, the results correlate well with those following available formulation for a single-layer isotropic plate. The developed approach is then implemented for various initial tensions, lateral pressures as well as different boss sizes and ratios between the layer moduli. The obtained numerical results show that, initial tension appears to have the strongest influence upon the radial variation of mechanical sensitivity over the top surface of the bossed layered plate. While both the size of center boss and magnitude of lateral pressure can still have a significant effect, the mechanical sensitivity seems to be insensitive to the change of the ratio between layer moduli for a bossed and symmetrically layered plate.