An improvement of the discrete method for analyzing the bending problem of plates

Abstract

An improved method is proposed to analyze the bending problem of plates. The fundamental differential equations are satisfied for the whole plate. By transforming these differential equations into integral equations in a small area, the quantities of an appointed point can be expressed by those of the other three points. By choosing the appointed point according to a regular order, the quantities of these three points can be replaced by the quantities of the boundary points. Finally, the quantities of any point can be expressed by those of the boundary points and the unknown quantities are only on the boundary. That makes the number of the unknown quantities and the computer time of the coefficient reduce greatly. The comparision of the present method with that used early is presented and the advantages of the present method are shown. Some numerical results are given by using uniform or non-uniform divisions. By comparing the numerical results obtained by the present method with those previously published, the efficiency and accuracy of the present method are investigated.