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Third-order Time Integration Scheme for Structural Dynamics

Authors:
Eva Zupan
Dejan Zupan

Keywords: time integrators; three-dimensional rotations; quaternions; dynamics.

Abstract:
In this paper, we propose a new time integration scheme for rigid and flexible body dynamics, where rotational degrees of freedom are incorporated into the model. To properly consider the multiplicative and non-commutative nature of three-dimensional rotations, the integration scheme is designed in a special way. It employs the representation of rotations with quaternions and quaternion exponential to preserve the orthogonality condition. The scheme is implicit and its accuracy is of the third order. To gain the desired order of the scheme for rotational degrees of freedom, an additional correction function is introduced that compensates the non-commutativity of rotations. The performance of the scheme is demonstrated by several examples.

Pages: 56 to 61

Copyright: Copyright (c) IARIA, 2017

Publication date: November 12, 2017

Published in: conference

ISSN: 2308-4499

ISBN: 978-1-61208-599-9

Location: Barcelona, Spain

Dates: from November 12, 2017 to November 16, 2017