A new absolute nodal coordinate formulation beam element with multilayer circular cross section

A systematic numerical integration method is applied to the absolute nodal coordinate formulation (ANCF) fully parameterized beam element with smooth varying and continuous cross section. Moreover, the formulation for the integration points and weight coefficients are given in the method which is used to model the multilayer beam with a circular cross section. To negate the effect of the bending stiffness for the element used to model the high-voltage electrical wire, the general continuum mechanical approach is adjusted. Additionally, the insulation cover for some particular types of the wire is described by the nearly incompressible Mooney–Rivlin material model. Finally, a static problem is presented to prove the accuracy and convergence properties of the element, and a dynamic problem of a flexible pendulum is simulated whereby the balance of the energy can be ensured. An experiment is carried out in which a wire is released as a pendulum and falls on a steel rod. The configurations of the wire are captured by a high-speed camera and compared with the simulation results. The feasibility of the wire model can therefore be demonstrated.

[1]  Johannes Gerstmayr,et al.  Analysis of Thin Beams and Cables Using the Absolute Nodal Co-ordinate Formulation , 2006 .

[2]  R. S. Rivlin,et al.  Large elastic deformations of isotropic materials. I. Fundamental concepts , 1948, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[3]  Carmine Maria Pappalardo,et al.  Contact force control in multibody pantograph/catenary systems , 2016 .

[4]  Grzegorz Orzechowski.  Analysis of beam elements of circular cross section using the absolute nodal coordinate formulation , 2012 .

[5]  Cheng Liu,et al.  Computational dynamics of soft machines , 2017 .

[6]  R. Rivlin.  LARGE ELASTIC DEFORMATIONS OF ISOTROPIC MATERIALS. I. FUNDAMENTAL CONCEPTS , 1997 .

[7]  M. Mooney.  A Theory of Large Elastic Deformation , 1940 .

[8]  Alexander Konyukhov,et al.  Geometrically exact covariant approach for contact between curves , 2010 .

[9]  A. Shabana.  Computational Continuum Mechanics: Computational Geometry and Finite Element Analysis , 2008 .

[10]  Ahmed A. Shabana,et al.  Analysis of warping deformation modes using higher order ANCF beam element , 2016 .

[11]  R. Rivlin.  Large Elastic Deformations of Isotropic Materials , 1997 .

[12]  Aki Mikkola,et al.  A Non-Incremental Nonlinear Finite Element Solution for Cable Problems , 2003 .

[13]  Yoshihiro Suda,et al.  A curved beam element in the analysis of flexible multi-body systems using the absolute nodal coordinates , 2007 .

[14]  R. Rivlin.  Large elastic deformations of isotropic materials. II. Some uniqueness theorems for pure, homogeneous deformation , 1948, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[15]  Ahmed A. Shabana,et al.  Pantograph/Catenary Contact Formulations , 2017 .

[16]  R. Y. Yakoub,et al.  Three Dimensional Absolute Nodal Coordinate Formulation for Beam Elements: Implementation and Applications , 2001 .

[17]  Peter Betsch,et al.  A mortar method for energy‐momentum conserving schemes in frictionless dynamic contact problems , 2009 .

[18]  Barbara I. Wohlmuth,et al.  A Mortar Finite Element Method Using Dual Spaces for the Lagrange Multiplier , 2000, SIAM J. Numer. Anal..

[19]  Przemysław Litewka.  Enhanced multiple-point beam-to-beam frictionless contact finite element , 2013 .

[20]  Qiping Xu,et al.  An improved dynamic model for a silicone material beam with large deformation , 2018 .

[21]  A. Mikkola,et al.  Inclusion of Transverse Shear Deformation in a Beam Element Based on the Absolute Nodal Coordinate Formulation , 2009 .

[22]  Aki Mikkola,et al.  A Linear Beam Finite Element Based on the Absolute Nodal Coordinate Formulation , 2005 .

[23]  Ahmed A. Shabana,et al.  A new multibody system approach for tire modeling using ANCF finite elements , 2016 .

[24]  A. Shabana,et al.  Definition of the Elastic Forces in the Finite-Element Absolute Nodal Coordinate Formulation and the Floating Frame of Reference Formulation , 2001 .

[25]  Qiang Tian,et al.  Deployment dynamics of a simplified spinning IKAROS solar sail via absolute coordinate based method , 2013 .

[26]  Giorgio Zavarise,et al.  Isogeometric treatment of frictional contact and mixed mode debonding problems , 2017 .

[27]  Wing Kam Liu,et al.  Nonlinear Finite Elements for Continua and Structures , 2000 .

[28]  Johannes Gerstmayr,et al.  Analysis of Stress and Strain in the Absolute Nodal Coordinate Formulation , 2006 .

[29]  Qiang Tian,et al.  Contact dynamics of elasto-plastic thin beams simulated via absolute nodal coordinate formulation , 2016 .

[30]  Ronald Cools,et al.  A survey of known and new cubature formulas for the unit disk , 2000 .

[31]  R. Y. Yakoub,et al.  Three Dimensional Absolute Nodal Coordinate Formulation for Beam Elements: Theory , 2001 .

[32]  Q. Tian,et al.  Dynamic simulation of frictional contacts of thin beams during large overall motions via absolute nodal coordinate formulation , 2014 .

[33]  Jia-Zhen Hong,et al.  Nonlinear formulation for flexible multibody system with large deformation , 2007 .

[34]  A. Shabana,et al.  DEVELOPMENT OF SIMPLE MODELS FOR THE ELASTIC FORCES IN THE ABSOLUTE NODAL CO-ORDINATE FORMULATION , 2000 .

[35]  A. Mikkola,et al.  A new locking-free shear deformable finite element based on absolute nodal coordinates , 2007 .

[36]  Mohamed A. Omar,et al.  A TWO-DIMENSIONAL SHEAR DEFORMABLE BEAM FOR LARGE ROTATION AND DEFORMATION PROBLEMS , 2001 .

[37]  Janusz Frączek,et al.  Volumetric locking suppression method for nearly incompressible nonlinear elastic multi-layer beams using ANCF elements , 2017 .

[38]  Aki Mikkola,et al.  Three-Dimensional Beam Element Based on a Cross-Sectional Coordinate System Approach , 2006 .

[39]  Peter Wriggers,et al.  Three-dimensional mortar-based frictional contact treatment in isogeometric analysis with NURBS , 2012 .

[40]  Yang Zhao,et al.  Adaptive ANCF method and its application in planar flexible cables , 2018 .

[41]  Ahmed A. Shabana,et al.  Computational Continuum Mechanics , 2008 .

[42]  Qiang Tian,et al.  Dynamics of a large scale rigid–flexible multibody system composed of composite laminated plates , 2011 .