Buckling of Plates of Abruptly Varying Stiffnesses

By replacing the continuous system of the plate with a discrete system of beams and torsional panels with finite degrees-of-freedom, a grid framework model is formulated for obtaining the critical buckling load of plates whose stiffness changes abruptly in two directions. This approach is then generalized to consider the effect of lateral deformations by a mathematically consistent first order finite-difference method. However, it is found that the effect of Poisson's ratio on the critical buckling load is negligible. The advantage in the discrete formulation is that no fictitious points need be considered, thereby making it possible to easily deal with cases of nonhomogeneity, complex boundary conditions, etc. An advantage over the finite element method is that the number of equations are far less, since there is only one unknown at a grid point. Numerical examples for different boundary conditions are presented to show the convergence and versatility of the method.