New Analytical Solutions for Orthotropic Rectangular Clamped Plates Under Pressure Loading

Abstract

Abstract The exact solution of a clamped rectangular orthotropic plate with pressure loading is presented. Unlike isotropic materials which behave equally in all directions, composites are strongly orthotropic due to the presence of stiff fibers in a relatively soft matrix. Similarly, metals with a definitive grain direction also exhibit a pronounced orthotropic behavior. The presence of aircraft cabin pressure induces bending of orthotropic panels used for example on doors and pressure bulkheads. Therefor the analysis of orthotropic rectangular clamped plates under pressure loading is needed in the sizing of modern aircraft structures. Existing methods for calculating the bending deformation of a clamped rectangular plate are commonly based on the Rayleigh-Ritz method, or Finite Element Analysis, which are approximate methods. In contrast the solutions presented in this paper exactly satisfy the resulting governing differential equation. The solution procedure presented in this paper is an expansion of Timoshenko’s[1][2] superposition method to orthotropic materials. This solutions method leads to more accurate results particularly for the stresses and strains. The solution procedure is presented in this paper, along with the resulting final equations. Additionally we present comparisons of a convergence study comparing to other commonly used approximate analysis methods.