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

Abstract

formulated by Saini, et al. [6]. Apparently, the scenario of edge effect and the behavior of mechanical sensitivity for a simply The problem of large deflection of a simply supported layered supported sensor plate is worth note for both design and application plate under initial tension is studied. The approach is based on von concerns. Karman plate theory for large deflection in deriving the nonlinear governing equations for the lateral slope and radial force resultant, With this regard, the work of Sheplak and Dugundji [2] is followed by a non-dimensional scheme. To have a preliminary extended to a simply supported symmetrically layered case in the insight, however, only the linear problem is considered by neglecting present study To have an informative insight, however, only the the arising nonlinear terms, yielding a modified Bessel equation for linear case of the posed problem is considered. The approach the lateral slope. This equation is solved analytically by considering developed by Sheplak & Dugundji [2] is modified to solve for the the boundary conditions of simply supported ends along the edge. present simply-supported symmetrically-layered case. In this The related geometrical responses are then obtained by utilizing the manner, the nonlinear governing equations are established first but re-occurrence relationships between the modified Bessel functions. the arising nonlinear terms are neglected, resulting in a modified Emphasis is placed upon the investigation of the effects of initial Bessel equation for the lateral slope. The associated complete tension and deviation in layer moduli upon the transition behavior solution is thus expressible in terms of modified Bessel functions between a plate and a membrane as well as the deviation in the edge with unknown coefficients to be solved by imposing the zone behavior near the boundary of the plate, between a simply corresponding boundary conditions of the problem. Subsequently, supported case and a clamped one, for typical micro-plates made of the geometrical responses including the central and overall lateral common silicon-based materials. deflections, lateral curvatures; and the radial stress on the top surface along the radial direction of the plate are obtained. The structural behavior that differs from a clamped plate, particularly near the edge