Large Deflection Analysis of Clamped Thin Rectangular Isotropic Plate under the Action of a Uniform Distributed Load

Abstract

This present paper deals with large deflection of clamped thin rectangular isotropic plate under uniformly distributed load. The analysis of clamped plates is of great important and its structural behavior has not been completely understood. Previous studies have made a great in road in the analysis of clamped plates through varied approaches mostly assuming trigonometric series as displacement field. A variational method based on the principle of minimization of total potential energy has been employed through assumed displacement field. Therefore, the von Karman differential equation was decoupled through direct integration retaining its non-linear character. The aim of this present studies is to provide solution to analysis structural behavior of clamped (CCCC) thin rectangular isotropic plate under uniform distributed. The analysis was accomplished through a theoretical formulation of shape function based on polynomial series and subsequently, the formulated shape function was used on Ritz energy method. The resulting functional was minimized to obtain a general amplitude equation of the form K1∆3+K2∆+K3. Where K1, K2 and K3 are coefficients of amplitude equation and ∆ is the deflection coefficient (factor). Newton-Raphson method was used to evaluate the deflection coefficient. Values of ∆ from Timoshenko and that from present study were compared with an aspect ratios ranging from 1.0 to 1.5 with an increment of 0.1. From results obtained, the average percentage difference for the pervious and present studies is 3.7646%, The percentage difference for the plate was within acceptable limit of 0.05 or 5% level of significance in statistics. It is shown from the comparison that good agreement exists between the present and previous works and that this approach provides simply, direct, straightforward and highly accurate solutions for this family of problems.