Development of Polynomial Based Program for Nonlinear Isotropic Rectangular Thin Plate

Abstract

The work is aim at the development of a computer program for the nonlinear analysis of rectangular thin isotropic plate on Ritz method. Twelve boundary conditions were analyzed which include: SSSS, CCCC, CSCS, CSSS, CCSS, CCCS, CCFC, SSFS, CCFS, SCFC, CSFS, and SCFS. 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. Polynomial function as shape function was on the decoupled Von Karman’s equations to obtain particular stress and displacement functions respectively. Non-linear total potential Energy was formulated using Von Karman equilibrium equation and Ritz method was deployed in this formulation. A computer based program was developed using Matlab programming language to circumvent the challenges involved in solving the governing differential equations of thin rectangular plates. The developed program is capable of determining deflection and stresses at any point of the plate against the usual method of evaluating deflection at the center. The results obtained were compared with those of previous researchers The comparison made are only for SSSS, CCCC and CCCS plates. It was so because the remaining boundary conditions considered in this work have not been researched upon by previous researchers. From results obtained, the average percentage differences recorded for SSSS, CCCC, and CCCS plates for the present and previous studies are 4.01978%, 3.7646%, and 5.02% respectively. The percentage differences for the three plates compared are within acceptable limit of 0.05 or 5% level of significance in statistics. From the comparison made, it was obvious that an excellent agreement was observed in all cases thus indicating applicability and validity of the polynomial function and computer program for solving exact plate bending problems.