Nonlinear Structural Dynamic Finite Element Analysis Using Ritz Vector Reduced Basis Method | Zendy

M.S. Yao | Zendy

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Nonlinear Structural Dynamic Finite Element Analysis Using Ritz Vector Reduced Basis Method

Author(s) -

M.S. Yao

Publication year - 1996

Publication title -

shock and vibration

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.418

H-Index - 45

eISSN - 1875-9203

pISSN - 1070-9622

DOI - 10.1155/1996/769484

Subject(s) - finite element method , nonlinear system , basis (linear algebra) , mathematics , equations of motion , transformation (genetics) , idealization , dynamic problem , mathematical analysis , ritz method , finite set , mathematical optimization , geometry , classical mechanics , structural engineering , engineering , physics , biochemistry , chemistry , quantum mechanics , gene , boundary value problem

The large number of unknown variables in a finite element idealization for dynamic structural analysis is represented by a very small number of generalized variables, each associating with a generalized Ritz vector known as a basis vector. The large system of equations of motion is thereby reduced to a very small set by this transformation and computational cost of the analysis can be greatly reduced. In this article nonlinear equations of motion and their transformation are formulated in detail. A convenient way of selection of the generalized basis vector and its limitations are described. Some illustrative examples are given to demonstrate the speed and validity of the method. The method, within its limitations, may be applied to dynamic problems where the response is global in nature with finite amplitude.

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