Symplectic Difference Format Of Elasticity Problems With Mixed Boundary

Since Hamiltonian system was introduced into elasticity, quite great progress was made on its theories and methods. Brilliant fruit of research was harvested in this area. Symplectic FDM was presented as a numerical method to solve the problems of elasticity recently. In this paper, the method is applied to elasticity problems with displacement boundary and mixed boundary and the pilot study is made. Several number calculation method for elasticity is introduced in Lagrange system and Hamiltonian system. From the Hamilton's dual equations in the plane rectangle coordinates system, the symplectic difference formats are established for elasticity problems with displacement boundary and mixed boundary. Interpolating integral method is used in the deriving process. The programs corresponding to these problems are designed. The numerical results are expected. The formats extended the application of symplictic FDM. The trend of its further development was discussed. The research shows that the sympleetic FDM can treat various boundaries better because of its adoption of the dual variables of displacement and stress. The sympleetic FDM has a wide prospect in future.