Buckling Analysis Of Plates Subjected To Biaxial Forces Using Galerkin’s Method

ABSTRACT

This work studied the buckling analysis of plates subject to biaxial forces using the Galerkin’s method. Twelve boundary conditions were considered. The plate deflection equations were obtained using the polynomial series, and from the plate deflection equations, the expression for the critical buckling loads of the different plate boundary conditions were obtained for different aspect ratios, ∝ using the Galerkin’s functional. The aspect ratios, considered throughout this work, ranged from 1 to 2. A linear relationship was obtained between the buckling load on the y axis and those on the x-axis. Results of the critical buckling loads for the twelve cases were Obtained For The Various Aspect Ratios (1 To 2) And K (I.E. A Constant Which Relates Forces On The Y- axis with forces on the x-axis) values (0.1 to 1). The Critical buckling load results of a square simply supported plate at k equal to unity was obtained as 19.754. When compared with the value (19.744) obtained by Iyengar, Ventsel and Krauthermmer and Chajes, a percentage difference of 0.047 was obtained. At k equal to zero (i.e. for SSSS plates) and for different aspect ratios, the results of the present study showed a maximum percentage difference of 0.069 when compared with those given by Ibearugbulem et al. For other plate conditions such as those plates clamped on opposite edges and simply supported on opposite edges; two adjacent edges clamped and the other two simply supported; and those completely clamped, the critical buckling load values differed on the average by 0.1705%, 0.047%, and 0.650% respectively from those given by Ibearugbulem et al. at K equals zero. The highest buckling load coefficients were realized for a square plate that is fully clamped on all the edges. At k equals zero the value was 108.0006, while 12.3488 was the least buckling load coefficient, which was obtained for an all-round simply supported plate at k equals unity and an aspect ratio of 2. The plates with two opposite edges clamped, and the other two edges simply supported, the CSCS plates gave the highest biaxial buckling load coefficients for all k values at an aspect ratio of 1 (i.e. square plate), but, for other aspect ratios greater than 1 (i.e. rectangular plates) the SCSC plates gave higher results for all k-values. From the results obtained and analyzed, it was therefore concluded that the orientation of the loads on the boundaries of the plates, affects its behavior.