Analytical Linear study of Large Deflection of Simply Supported Layered-Plate under Initial Tension

The problem of large deflection of a simply supported layered plate under initial tension is studied. The approach is based on von Karman plate theory for large deflection in deriving the nonlinear governing equations for the lateral slope and radial force resultant, followed by a non-dimensional scheme. To have a preliminary insight, however, only the linear problem is considered by neglecting the arising nonlinear terms, yielding a modified Bessel equation for the lateral slope. This equation is solved analytically by considering the boundary conditions of simply supported ends along the edge. The related geometrical responses are then obtained by utilizing the re-occurrence relationships between the modified Bessel functions. Emphasis is placed upon the investigation of the effects of initial tension and deviation in layer moduli upon the transition behavior between a plate and a membrane as well as the deviation in the edge zone behavior near the boundary of the plate, between a simply supported case and a clamped one, for typical micro-plates made of common silicon-based materials.