Buckling Analysis Of Isotropic Rectangular Plates Using Ritz Method

ABSTRACT

This research work presents the buckling analysis of isotropic rectangular plates using Ritz method. The Ritz method and polynomial series were used in the analysis. The various boundary conditions covered in this research work includes SSFS, CCFC, CSFS, CCFS, SCFC and SCFS. The polynomial series was truncated at the fifth term, which satisfied all the boundary conditions of the plate and resulted to a peculiar shape function. The resulting shape function were substituted into the total potential energy functional of the Ritz method and upon minimization, the critical buckling load equations were obtained. The critical buckling loads were obtained by substituting different aspect ratios ranging from 0.1 to 2.0. The buckling loads obtained were compared with those of earlier researchers. The critical buckling loads K for SSFS, CCFC, CSFS, CCFS, SCFC and SCFS for aspect ratio of 1.0 are respectively: 12.97 ஽ ௕మ , 47.625 ஽ ௕మ , 16.07 ஽ ௕మ , 45.104 ஽ ௕మ , 16.074 ஽ ௕ మ , and 26.771 ஽ ௕ మ . The comparison showed that the result of the average percentage differences recorded for SSFS, CCFC and CSFS plates are 2.95623267%, 0.003197633136% and 4.200645529%. The behavior of the graph shows that as the aspect ratio increases from 0.1 to 2.0, the critical buckling load decreased. The closeness shows that the shape functions derived using polynomial series is a very good approximation of the exact values of the isotropic rectangular plate.