On The Finite Difference Method Based On The Principle Of Variation Of The Bending Problem Of Plate With Beam-strengthened Edges

The balance equation model of the bending problem of plate with beam-strengthened edges, where the natural boundary conditions are related to the higher order derivatives of the boundary tangent and normal, is the boundary value problem of the fourth-order elliptic partial differential equations. For the plate that is non-homogenous and has variable thickness, the problem has the characteristics of variable coefficients. In this thesis, starting from the variation model, the finite difference scheme of the boundary problem was constructed with FDM based on the principle of variation. The method incorporated the boundary condition of the balance equation to resolve the higher order derivative items in the boundary, so the difference operator that only relied on the network nodes of the plate. Moreover, the symmetry and positive definiteness of the difference operator were kept. At the same time, according to the difference equations, the Matlab program is programmed and developed to do numerical simulation. In comparison with the available document, comparing calculation was processed .The result showed the algorithm has satisfying accuracy. This algorithm can show quantitatively the international law of the plate and the boundary beam. At the same time, the algorithm can provide reference for engineering design.