Nonlinear structural analysis of a flexible multibody system using the classical Rayleigh-Ritz method

A new formulation based on the classical Rayleigh-Ritz method (CRRM) is proposed in this study to conduct a geometrically nonlinear analysis for flexible multibody structures (FMSs). The proposed formulation can employ various shape functions for global discretization. This feature renders the proposed formulation straight-forward and suitable for computer programming. The convergence characteristics of various shape functions for the proposed formulation were first examined with some numerical examples. Then we investigated the efficiency of the proposed formulation for obtaining converged solutions of the displacement, reaction force, maximum stress, and the location where the maximum stress occurs by comparing the degrees of freedom (DOFs) used for the proposed formulation and FEM formulation. The comparative study showed that the proposed formulation can be used to solve geometrically nonlinear FMS problems much more efficiently than the FEM formulation with the same level of accuracy.