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

• Published in: International journal of non-linear mechanics 2019-04, Vol.110, p.69-80
• Main Authors: Jeong, Sinwoo, Yoo, Hong Hee
• Format: Article
• Language: English
• Subjects: Classical Rayleigh–Ritz method; Comparative studies; Computer programming; Convergence; Finite element method; Flexible multibody structure; Global discretization; Multibody systems; Nonlinear analysis; Ritz method; Shape functions; Structural analysis
• ISSN: 0020-7462; 1878-5638
• DOI: 10.1016/j.ijnonlinmec.2019.01.011

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 straightforward 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. •The classical Rayleigh–Ritz method is used for geometrically nonlinear analyses.•With this formulation, the governing equations can be generated systematically.•The Legendre polynomial, as a shape function, is employed to obtain solutions.•The degrees of freedom for obtaining converged solutions are compared.