Numerical Analysis of Initial Deflected Shapes by the Buckling Equation in Rectangular Thin Plates

Abstract

To find a numerical solution to the two-dimensional buckling equation, we use Richardson's second-order extrapolation formulae with the finite-difference methods. The two-dimensional buckling equation is treated and rewritten as follows : forth-order partial derivatives + unknown coefficient·second-order partial derivatives = eigenvalue·warp function. When the eigenvalues become zero by searching for the corresponding values of unknown coefficients, we can obtain the numerical solutions as the warp functions with arbitrary scale.