Nonlinear Analysis of SSSS Thin Isotropic Rectangular Plate Using Polynomial as Shape Function

Abstract

This paper presents non¬linear analysis of isotropic rectangular plate with all edges simply supported (SSSS) under a uniform distributed load using polynomial series as shape function, and under the application of Ritz method. There are several analytical tools available for analyzing isotropic rectangular plate. Among all the available analytical methods, polynomial offers a better approach. Earlier researchers on SSSS plate were, however, centered on the use trigonometric series and approximate method in form of numerical and energy method. General expressions for displacement and stress functions for large deflection of isotropic thin rectangular plate under uniformly distributed transverse loading were obtained by direct integration of Von Karman’s non- linear governing differential compatibility and equilibrium equations. Total potential energy functional was formulated based on the derived displacement and stress functions. Subsequently, the formulated total potential energy functional was minimized and resulted to 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 4.0198%. The percentage difference for the plate was within acceptable limit of 0.05 or 5% level of significance in statistics. From the comparison, an excellent agreement exist between the present and previous works. Thus, this indicate applicability and validity of the polynomial function for solving exact plate bending problem.