0
research-article

An Accurate and Robust Geometrically-exact Curved Beam Formulation for Multibody Dynamic Analysis

[+] Author and Article Information
Hui Ren

Division of Dynamics and Control, School of Astronautics, Harbin Institute of Technology, Harbin 150001, China
renhui@hit.edu.cn

Wei Fan

Division of Dynamics and Control, School of Astronautics, Harbin Institute of Technology, Harbin 150001, China
13B918015@hit.edu.cn

Weidong Zhu

Division of Dynamics and Control, School of Astronautics, Harbin Institute of Technology, Harbin 150001, China; Department of Mechanical Engineering, University of Maryland, Baltimore County, MD, 21250, USA
wzhu@umbc.edu

1Corresponding author.

ASME doi:10.1115/1.4037513 History: Received February 19, 2017; Revised July 22, 2017

Abstract

An accurate and robust geometrically-exact beam formulation (GEBF) is developed to simulate the dynamics of a beam with large deformations and large rotations. The undeformed configuration of the centroid line of the beam can be either straight or curved, and cross-sections of the beam can be either uniform or nonuniform with arbitrary shapes. The beam is described by the position of the centroid line and a local frame of a cross-section, and a rotation vector is used to characterize the rotation of the cross-section. The elastic potential energy of the beam is derived using continuum mechanics with the small-strain assumption and linear constitutive relation, and a factor naturally arises in the elastic potential energy, which can resolve the drawback of the traditional GEBF. Shape functions of the position vector and rotation vector are carefully chosen, and numerical incompatibility due to independent discretization of the position vector and rotation vector is resolved, which can avoid the shear locking problem. Numerical singularity of the rotation vector with its norm equal to zero is eliminated by Taylor polynomials. A rescaling strategy is adopted to resolve the singularity problem with its norm equal to 2m*pi, where m is a nonzero integer. The current formulation can be used to handle linear and nonlinear dynamics of beams under arbitrary concentrated and distributed loads. Several benchmark problems are simulated using the current formulation to validate its accuracy, adaptiveness, and robustness.

Copyright (c) 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

Figures

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In