Director-based beam finite elements relying on the geometrically exact beam theory formulated in skew coordinates

• Published in: International journal for numerical methods in engineering Vol. 97; no. 2; pp. 111 - 129
• Main Authors: Eugster, S.R., Hesch, C., Betsch, P., Glocker, Ch
• Format: Journal Article
• Language: English
• Published: Bognor Regis Blackwell Publishing Ltd 13-01-2014; Wiley Subscription Services, Inc
• Subjects: Beams (structural); constrained theories; Finite element method; Frames; geometrically exact beam; Interpolation; Mathematical analysis; Mathematical models; nonlinear beam elements; Numerical analysis; structural mechanics; virtual work
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.4586

SUMMARY
In the present work, a new director‐based finite element formulation for geometrically exact beams is proposed. The new beam finite element exhibits drastically improved numerical performance when compared with the previously developed director‐based formulations. This improvement is accomplished by adjusting the underlying variational beam formulation to the specific features of the director interpolation. In particular, the present approach does not rely on the assumption of an orthonormal director frame. The excellent performance of the new approach is illustrated with representative numerical examples. Copyright © 2013 John Wiley & Sons, Ltd.