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A finite element formulation for sliding beams, Part I
Author(s) -
Behdinan K.,
Tabarrok B.
Publication year - 1998
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19981215)43:7<1309::aid-nme456>3.0.co;2-2
Subject(s) - discretization , finite element method , beam (structure) , mathematical analysis , mathematics , domain (mathematical analysis) , equations of motion , mixed finite element method , geometry , physics , classical mechanics , optics , thermodynamics
We use the updated Lagrangian and the co‐rotational finite element methods to obtain solutions for geometrically non‐linear flexible sliding beams. Finite element formulations are normally carried out for fixed domains. Since the sliding beam is a system of changing mass, first we discretize the system by introducing a variable‐domain beam element and model the sliding beam by a fixed number of elements with changing length. Second, we transform the system governing equations of motion to a fixed domain and use conventional finite elements (fixed size and number) to discretize the system. Then our investigation is followed by a comparison between two formulations. Finally, we use the co‐rotational method in conjunction with a variable domain beam element to obtain the discretized system equations. To do so, we consider the beam to slide with respect to a fixed channel and later we consider a formulation in which the beam remains at rest and the channel slides with a prescribed velocity. We show that both formulations end up with identical discretized equations of motion. © 1998 John Wiley & Sons, Ltd.