Variational base and solution strategies for non-linear force-based beam finite elements

Date

2012-04-01

Author

Sarıtaş, Afşin

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This paper presents the variational bases for the non-linear force-based beam elements. The element state determination of these elements is obtained exactly from a two-field functional with independent stress and strain fields. The variational base of the non-linear force-based beam elements implemented in a general purpose displacement-based finite element program requires the inclusion of independent displacement field in the formulation. For this purpose, a three-field functional is considered with independent displacement, stress, and strain fields. Various local and global solution strategies come out from the mixed formulation of the beam element, and these are shown to yield the algorithms presented for non-linear force formulation beam elements in literature; thus removing any doubts on their variational bases. The presented numerical examples demonstrate the accuracy and robustness of the solution algorithms adapted for mixed formulation elements over popularly used displacement-based beam finite elements even for large structural systems.

Subject Keywords

Mixed methods, Flexibility method, Force formulation, Solution algorithm, Element state determination, Finite element

URI

https://hdl.handle.net/11511/36671

Journal

INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS

DOI

https://doi.org/10.1016/j.ijnonlinmec.2012.01.003

Collections

Department of Civil Engineering, Article

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Citation Formats

A. Sarıtaş, “Variational base and solution strategies for non-linear force-based beam finite elements,” INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, pp. 54–64, 2012, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/36671.