Research Of Finit Element Perturbation Method About Inverse Problem Of The Differential Equation

From the equation of the beams`transverse vibration, through the deduct in mathematics to solve problems these become time-domain problems. In the basis of the perturbation method, to break down the differential equation that has been transformed, and according to the variational principle and the finite element method we can get a finite element equation, to understand the equation through the stable solution techniques, so we can get the inversion formula of finite element.In order to solve the problem, this paper introductions the regularization method, stable solution method and iterative Tikhonov regularization method. In regularization method, we introduction the theoretical basis of regularization meth- od and regularization parameter selection, regularization parameter selection has two important methods thoes are deviation principles and general deviation princip- les, and they have been widely used. Iterative Tikhonov regularization method is base on exact solutions ,that has a good convergence speed.For finite element method, through the beam structure we introduction the basic steps of the finite element method, these are discretization of the structure, analysis of the unit and integrated of the unit. In this paper, the discretization is conveyed that change freedom into finited, and use some special relationships thoes are nodal force and nodal displacements, throught the relationships we can get a equation and we work out the equation. By the superposition principle to establish the matrix of the overall structure, namely established a whole equation, and deal with the boundary conditions to summarize a overall finite element equation. To solve the equation through the stable solution techniques, so we can get the inversi- on formula of finite element, and doed numerical simulation.