Variational finite difference approach to buckling of plates of variable stiffness

Abstract

The total potential energy of buckling of a plate with variable stiffness has been discretized by the method of finite differences. According to the principle of minimum potential energy, by equating the partial derivative of total potential energy with respect to each grid point displacement to zero in succession, a set of linear homogeneous equations is obtained. This reduces to a standard characteristic value problem, the eigenvalues of which yield the buckling loads. Test problems of plates with uniform stiffness, gradually varying stiffness and abrupt variation of stiffness with different boundary conditions and a stepped column as a degenerate case of plate have been considered. Results are compared with those of analytical and numerical methods available. Good agreement has been observed in all cases. The proposed method has the advantage that the total number of equations is far less than in finite element method and application of boundary conditions is simple.