An averaged lagrangian-finite element technique for the solution of nonlinear vibration problems

In this paper, a technique for the dynamic analysis of geometrically nonlinear structures is developed. A Lagrangian function is employed to construct the structural Hamiltonian. The temporal variation of the response is then expressed in terms of the spatial variables through the use of the Hamiltonian function. To demonstrate the proposed technique, the nonlinear vibration of certain axisymmetric shells is analyzed. A variational formulation is presented and implemented by the finite element method. An incremental-iterative scheme is then developed to solve the governing set of discrete equations. Numerical computations are presented for a circular plate and various spherical caps.