期刊
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
卷 48, 期 19, 页码 2764-2777出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ijsolstr.2011.06.001
关键词
Geometrically exact beam theories; Highly flexible beams and cables; Jaumann strains; Nonlinear structural mechanics
类别
资金
- National Science Foundation [CMMI 1039433]
Presented here are three kinematic representations of large rotations for accurate modeling of highly flexible beam-like structures undergoing arbitrarily large three-dimensional elastic deformation and/or rigid-body motion. Different methods of modeling torsional deformation result in different beam theories with different mathematical characteristics. Each of these three geometrically exact beam theories fully accounts for geometric nonlinearities and initial curvatures by using Jaumann strains, exact coordinate transformations, and orthogonal virtual rotations. The derivations are presented in detail, a finite element formulation is included, fully nonlinear governing equations and boundary conditions are presented, and the corresponding form for numerically exact analysis using multiple shooting methods is also derived. These theories are compared in terms of their appropriate application areas, possible singular problems, and easiness for use in modeling and analysis of multibody systems. Nonlinear finite element analysis of a rotating beam and nonlinear multiple shooting analysis of a torsional bar are performed to demonstrate the capability and accuracy of these beam theories. (C) 2011 Elsevier Ltd. All rights reserved.
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