Access the full text.
Sign up today, get DeepDyve free for 14 days.
D. Logan (2001)
A First Course in the Finite Element Method
Q. Tian, Yanlei Sun, Cheng Liu, Haiyan Hu, P. Flores (2013)
ElastoHydroDynamic lubricated cylindrical joints for rigid-flexible multibody dynamicsComputers & Structures, 114
AA Shabana (2018)
10.1002/9781119293248
Q. Tian, L. Chen, Yunqing Zhang, Jingzhou Yang (2009)
An Efficient Hybrid Method for Multibody Dynamics Simulation Based on Absolute Nodal Coordinate FormulationJournal of Computational and Nonlinear Dynamics, 4
G. Farin (2001)
Curves and Surfaces for Cagd: A Practical Guide
A. Kłodowski, T. Rantalainen, A. Mikkola, A. Heinonen, H. Sievänen (2011)
Flexible multibody approach in forward dynamic simulation of locomotive strains in human skeleton with flexible lower body bonesMultibody System Dynamics, 25
T. Belytschko, L. Glaum (1979)
Applications of higher order corotational stretch theories to nonlinear finite element analysisComputers & Structures, 10
Imad Khan, K. Anderson (2013)
Divide-and-Conquer-Based Large Deformation Formulations for Multi-Flexible Body Systems
A. Shabana (2015)
ANCF Tire Assembly Model for Multibody System ApplicationsJournal of Computational and Nonlinear Dynamics, 10
Jialiang Sun, Q. Tian, Haiyan Hu, N. Pedersen (2019)
Axially variable-length solid element of absolute nodal coordinate formulationActa Mechanica Sinica, 35
Zhigang Zhang, Tengfei Wang, A. Shabana (2019)
Development and implementation of geometrically accurate reduced-order models: Convergence properties of planar beamsJournal of Sound and Vibration
A. Goetz (1970)
Introduction to differential geometry
A. Shabana (2018)
Geometrically accurate infinitesimal-rotation spatial finite elementsProceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics, 233
A. Boresi, Ken Chong, James Lee (1974)
Elasticity in engineering mechanics
G. Holzapfel (2000)
Nonlinear Solid Mechanics: A Continuum Approach for Engineering ScienceMeccanica, 37
J. Cottrell, Thomas Hughes, Y. Bazilevs (2009)
Isogeometric Analysis: Toward Integration of CAD and FEA
Jeremy Laflin, K. Anderson, Imad Khan, M. Poursina (2014)
New and Extended Applications of the Divide-and-Conquer Algorithm for Multibody DynamicsJournal of Computational and Nonlinear Dynamics, 9
Gaute Fotland, C. Haskins, T. Rølvåg (2019)
Trade study to select best alternative for cable and pulley simulation for cranes on offshore vesselsSystems Engineering, 23
T. Chandrupatla, A. Belegundu (1990)
Introduction to Finite Elements in Engineering
Shujia Li, Yongxing Wang, Xunxun Ma, Shengze Wang (2019)
Modeling and Simulation of a Moving Yarn Segment: Based on the Absolute Nodal Coordinate FormulationMathematical Problems in Engineering
Dimitris Metaxas, Demetri Terzopoulos (1993)
Shape and Nonrigid Motion Estimation Through Physics-Based SynthesisIEEE Trans. Pattern Anal. Mach. Intell., 15
A. Shabana (2017)
Geometrically accurate floating frame of reference finite elements for the small deformation problemProceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics, 232
J. Gallier (2011)
Geometric Methods and Applications
A. Shabana (1985)
Automated Analysis of Constrained Systems of Rigid and Flexible BodiesJournal of Vibration and Acoustics-transactions of The Asme, 107
(2007)
Flexible robotic manipulators: modeling, simulation and control with experimentation, [PhD Thesis
Demetri Terzopoulos, Dimitris Metaxas (1990)
Dynamic 3D models with local and global deformations: deformable superquadrics[1990] Proceedings Third International Conference on Computer Vision
J. Hewlett, Siamak Arbatani, J. Kövecses (2020)
A fast and stable first-order method for simulation of flexible beams and cablesNonlinear Dynamics, 99
A. Shabana (2015)
Definition of ANCF Finite ElementsJournal of Computational and Nonlinear Dynamics, 10
Yuechen Duan, Dingguo Zhang, Jia-zhen Hong (2013)
Partition method for impact dynamics of flexible multibody systems based on contact constraintApplied Mathematics and Mechanics, 34
L. Piegl, W. Tiller (1995)
The NURBS Book
D. Hutton (2003)
Fundamentals of Finite Element Analysis
A. Shabana, Hao Ling (2019)
Noncommutativity of Finite Rotations and Definitions of Curvature and TorsionJournal of Computational and Nonlinear Dynamics
Thant Htun, Hiroyoshi Suzuki, D. García-Vallejo (2020)
Dynamic modeling of a radially multilayered tether cable for a remotely-operated underwater vehicle (ROV) based on the absolute nodal coordinate formulation (ANCF)Mechanism and Machine Theory, 153
A. Bower (2009)
Applied Mechanics of Solids
Grzegorz Orzechowski, J. Frączek (2012)
INTEGRATION OF THE EQUATIONS OF MOTION OF MULTIBODY SYSTEMS USING ABSOLUTE NODAL COORDINATE FORMULATIONActa Mechanica et Automatica, 6
P. Pilvin (2019)
Continuum MechanicsMechanics - Microstructure - Corrosion Coupling
A. Shabana (2016)
ANCF Consistent Rotation-Based Finite Element FormulationJournal of Computational and Nonlinear Dynamics, 11
D Terzopoulos (1991)
10.1109/34.85659IEEE Trans. Pattern Anal. Mach. Intell., 13
Grzegorz Orzechowski (2012)
Analysis of beam elements of circular cross section using the absolute nodal coordinate formulationArchive of Mechanical Engineering, 59
J. Gerstmayr, J. Schöberl (2006)
A 3D Finite Element Method for Flexible Multibody SystemsMultibody System Dynamics, 15
Mohamed Omar, A. Shabana (2001)
A TWO-DIMENSIONAL SHEAR DEFORMABLE BEAM FOR LARGE ROTATION AND DEFORMATION PROBLEMSJournal of Sound and Vibration, 243
T. Belytschko, L. Schwer, M. Klein (1977)
Large displacement, transient analysis of space framesInternational Journal for Numerical Methods in Engineering, 11
A. Yamano, A. Shintani, Tomohiro Ito, C. Nakagawa, H. Ijima (2020)
Influence of boundary conditions on a flutter-millJournal of Sound and Vibration, 478
D. Rogers (2011)
An Introduction to NURBS: With Historical Perspective
L. Segerlind (1976)
Applied Finite Element Analysis
A. Cammarata, C. Pappalardo (2020)
On the use of component mode synthesis methods for the model reduction of flexible multibody systems within the floating frame of reference formulationMechanical Systems and Signal Processing, 142
B. Specht (1988)
Modified shape functions for the three‐node plate bending element passing the patch testInternational Journal for Numerical Methods in Engineering, 26
T. Belytschko, B. Hsieh (1973)
Non-Linear Transient Finite Element Analysis with Convected Co--ordinatesInternational Journal for Numerical Methods in Engineering, 7
O. Zienkiewicz, R. Taylor, J. Zhu, Elsevier Bl, Ttfrworth Hhintalann (1977)
The finite element method
AA Shabana (2020)
10.1017/9781108757553
O. Dmitrochenko, A. Mikkola (2011)
Digital Nomenclature Code for Topology and Kinematics of Finite Elements Based on the Absolute Nodal Co-Ordinate FormulationProceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics, 225
R. Cook, D. Malkus, M. Plesha, R. Witt (1974)
Concepts and Applications of Finite Element Analysis
J. Bonet, R. Wood (1997)
Nonlinear Continuum Mechanics for Finite Element Analysis
A. Shabana (2008)
Computational Continuum Mechanics: Computational Geometry and Finite Element Analysis
L. Piegl, W. Tiller (1997)
The NURBS book (2nd ed.)
Grzegorz Orzechowski, J. Frączek (2015)
Nearly incompressible nonlinear material models in the large deformation analysis of beams using ANCFNonlinear Dynamics, 82
O. Zienkiewicz, R. Taylor, J. Zhu (2005)
The Finite Element Method: Its Basis and Fundamentals
A. Noor (1990)
Bibliography of Monographs and Surveys on ShellsApplied Mechanics Reviews, 43
Dimitris Metaxas (1996)
Physics-Based Deformable Models: Applications to Computer Vision, Graphics, and Medical Imaging
Curing ill surfaces, SIAM News
Richard Mould (1994)
Differential Geometry I
Xian Guo, Dingguo Zhang, Liang Li, Le Zhang (2018)
Application of the two-loop procedure in multibody dynamics with contact and constraintJournal of Sound and Vibration
Irving Shames, C. Dym (2017)
Energy and Finite Element Methods In Structural Mechanics : SI Units
S. Gibson, B. Mirtich (1997)
A Survey of Deformable Modeling in Computer Graphics
Yuanzhao Chen, Dingguo Zhang, Liang Li (2019)
Dynamic analysis of rotating curved beams by using Absolute Nodal Coordinate Formulation based on radial point interpolation methodJournal of Sound and Vibration
J. Gallier (2000)
Geometric Methods and Applications: For Computer Science and Engineering
A. Shabana (2005)
Dynamics of Multibody Systems: Contents
Yue Zhang, Cheng Wei, Yang Zhao, Chunlin Tan, Yongjian Liu (2018)
Adaptive ANCF method and its application in planar flexible cablesActa Mechanica Sinica, 34
Hong Qin, Demetri Terzopoulos (1996)
D-NURBS: A Physics-Based Framework for Geometric DesignIEEE Trans. Vis. Comput. Graph., 2
(2019)
Methods for real-time simulation of systems of rigid and flexible bodies with unilateral contact and friction, [PhD Thesis
K. Nachbagauer, A. Pechstein, H. Irschik, J. Gerstmayr (2011)
A new locking-free formulation for planar, shear deformable, linear and quadratic beam finite elements based on the absolute nodal coordinate formulationMultibody System Dynamics, 26
Yinhuan Zheng, A. Shabana (2017)
A two-dimensional shear deformable ANCF consistent rotation-based formulation beam elementNonlinear Dynamics, 87
D. Vallejo, A. Alcayde, J. López-Martínez, F. Montoya (2019)
Detection of Communities within the Multibody System Dynamics Network and Analysis of Their RelationsSymmetry, 11
Lei Yu, Zhihua Zhao, Jiali Tang, Gexue Ren (2010)
Integration of absolute nodal elements into multibody systemNonlinear Dynamics, 62
S. Chu, K. Pan (1975)
Dynamic Response of a High-Speed Slider-Crank Mechanism With an Elastic Connecting RodJournal of Engineering for Industry, 97
A. Noor, T. Belytschko, J. Simo (1989)
Analytical and computational models of shells; Proceedings of the Symposium, ASME Winter Annual Meeting, San Francisco, CA, Dec. 10-15, 1989
J. Altenbach (1979)
Segerlind, L. J., Applied Finite Element Analysis. New York‐London‐Sydney‐Toronto, John Wiley & Sons 1976. XIII, 422 S., £ 12.60Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik, 59
(2004)
Textbook of Finite Element Analysis, 1st edn. PHI Learning Private Limited
J. Guilie, P. Tallec (2013)
Influence of strain-induced crystallization on the crack driving force in fracture behavior of rubber
R. Wait, A. Mitchell (1985)
Finite Element Analysis and Applications
R. Ogden (1984)
Non-Linear Elastic Deformations
Infinitesimal-rotation finite elements allow creating a linear problem that can be exploited to systematically reduce the number of coordinates and obtain efficient solutions for a wide range of applications, including those governed by nonlinear equations. This paper discusses the limitations of conventional infinitesimal-rotation finite elements (FE) in capturing correctly the initial stress-free reference-configuration geometry, and explains the effect of these limitations on the definition of the inertia used in the motion description. An alternative to conventional infinitesimal-rotation finite elements is a new class of elements that allow developing inertia expressions written explicitly in terms of constant coefficients that define accurately the reference-configuration geometry. It is shown that using a geometrically inconsistent (GI) approach that introduces the infinitesimal-rotation coordinates from the outset to replace the interpolation-polynomial coefficients is the main source of the failure to capture correctly the reference-configuration geometry. On the other hand, by using a geometrically consistent (GC) approach that employs the position gradients of the absolute nodal coordinate formulation (ANCF) to define the infinitesimal-rotation coordinates, the reference-configuration geometry can be preserved. Two simple examples of straight and tapered beams are used to demonstrate the basic differences between the two fundamentally different approaches used to introduce the infinitesimal-rotation coordinates. The analysis presented in this study sheds light on the differences between the incremental co-rotational solution procedure, widely used in computational structural mechanics, and the non-incremental floating frame of reference formulation (FFR), widely used in multibody system (MBS) dynamics.Graphic Abstract[graphic not available: see fulltext]
"Acta Mechanica Sinica" – Springer Journals
Published: Feb 5, 2021
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.