An exact conserving algorithm for nonlinear dynamics with rotational DOFs and general hyperelasticity. Part 1

Rods

authored by

P. M. Pimenta, E. M.B. Campello, Peter Wriggers

Abstract

A fully conserving algorithm is developed in this paper for the integration of the equations of motion in nonlinear rod dynamics. The starting point is a re-parameterization of the rotation field in terms of the so-called Rodrigues rotation vector, which results in an extremely simple update of the rotational variables. The weak form is constructed with a non-orthogonal projection corresponding to the application of the virtual power theorem. Together with an appropriate time-collocation, it ensures exact conservation of momentum and total energy in the absence of external forces. Appealing is the fact that nonlinear hyperelastic materials (and not only materials with quadratic potentials) are permitted without any prejudice on the conservation properties. Spatial discretization is performed via the finite element method and the performance of the scheme is assessed by means of several numerical simulations.

Organisation(s)

Institute of Continuum Mechanics

External Organisation(s)

Universidade de Sao Paulo

Type

Article

Journal

Computational mechanics

Volume

42

Pages

715-732

No. of pages

18

ISSN

0178-7675

Publication date

02.04.2008

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Computational Mechanics, Ocean Engineering, Mechanical Engineering, Computational Theory and Mathematics, Computational Mathematics, Applied Mathematics

Sustainable Development Goals

SDG 7 - Affordable and Clean Energy

Electronic version(s)

https://doi.org/10.1007/s00466-008-0271-5 (Access: Unknown)