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A frame-invariant scheme for the geometrically exact beam using rotation vector parametrization

Ghosh, S and Roy, D (2009) A frame-invariant scheme for the geometrically exact beam using rotation vector parametrization. In: Computational Mechanics, 44 (1). pp. 103-118.

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Abstract

While frame-invariant solutions for arbitrarily large rotational deformations have been reported through the orthogonal matrix parametrization, derivation of such solutions purely through a rotation vector parametrization, which uses only three parameters and provides a parsimonious storage of rotations, is novel and constitutes the subject of this paper. In particular, we employ interpolations of relative rotations and a new rotation vector update for a strain-objective finite element formulation in the material framework. We show that the update provides either the desired rotation vector or its complement. This rules out an additive interpolation of total rotation vectors at the nodes. Hence, interpolations of relative rotation vectors are used. Through numerical examples, we show that combining the proposed update with interpolations of relative rotations yields frame-invariant and path-independent numerical solutions. Advantages of the present approach vis-a-vis the updated Lagrangian formulation are also analyzed.

Item Type: Journal Article
Additional Information: Copyright of this article belongs to Springer.
Keywords: Geometrically exact beam;Finite rotation;Rotation manifold; Tangent space;Relative rotation;Objective strain;Path-independence
Department/Centre: Division of Mechanical Sciences > Civil Engineering
Date Deposited: 22 Jul 2009 09:31
Last Modified: 19 Sep 2010 05:29
URI: http://eprints.iisc.ernet.in/id/eprint/19689

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