The Symplectic Difference Method Of Elasticity Based On The Hamilton System

Today symplectic difference method and the theory of elasticity in the system of Hamilton have been developed more than before, but it was not published that symplectic difference method was used in the solution of elastic problem. So, it is the first attempt to find out that the symplectic difference method in Hamilton system is used in the solution of elastic problem, and an anticipated solution is gained in this paper. To begin with, the theory of Hamilton system that is started with is introduced and the numerical methods of elastic problem are discussed summarily. Then the equations of elastic problem are imported into the Hamilton system in the plane right-angle coordinate system and a new symplectic numerical method, the symplectic difference method of elasticity in Hamilton system, is put up based on the mixed equation of elastic problem. The arithmetic of the method is programmed and used in the solution of three problems of elasticity, which is sheet problem, simply girder problem and deep girder problem that is pressed equally in the right-angle coordinate system. In the same way, the symplectic difference method is put up in pole coordinate system. It is programmed and applied in the solution of cylinder problem and bent girder problem successfully, too. When the solutions of examples are achieved, the superiorities of the method is embodied which are big pace and good stability even when net meter ratio is bigger than 1, which is a greatly breakthrough in the limit of stabilization in the finity difference method ago. At last, the direction in the future research and current problems left behind is pointed out. In short, this paper shows that it is feasible that the symplectic difference method in Hamilton system is applied in the solution of elastic problem and the basic exploring is successful.