Perturbation Finite Element Method for Solving Geometrically Non-linear Problems of Axisymmetrical Shell

In analysing the geometrically nonlinear problem of an axisymmetrical thin-walled shell,the paper combines the perturbation method with the finite element method by introducing the former into the variational equation to obtain a series of linear equations of different orders and then solving the equations with the latter. It is well-known that the finite element method can be used to deal with difficult problems as in the case of structures with complicated shapes or boundary conditions,and the perturbation method can change the nonlinear problems into linear ones. Evidently the combination of the two methods will give an efficient solution to many difficult nonlinear problems and clear away some obstacles resulted from using any of the two methods solely.The paper derives all the formulas concerning an axisym-metric. shell of large deformation by means of the perturbation finite element method and gives two numerical examples,the results of which show good convergence characteristics.