Stability of Equilateral Triangular Plates

Critical values of the middle plane forces for equilateral triangular plates that are determined for the clamped and simply supported edge conditions and for the cases of force parallel or perpendicular to a base show that accurate values for the lower modes of buckling may be obtained with relatively coarse grids and extrapolations. In certain cases, the pattern of convergence of the extrapolated values indicates the possibility of establishing bounds on the critical load values. In computing these, values, finite difference approximations to the governing differential equations are used. Four different approximations to the biharmonic operator are used, and solutions for the critical loads and corresponding mode shapes using several different grid spacings are obtained. The extrapolated values of the buckling loads may also be found. The use of successively finer grids results in convergence for the values of lowest critical load.