Higher-order beam elements based on the absolute nodal coordinate formulation for three-dimensional elasticity

This study thoroughly examines various higher-order three and four-node beam elements for use in the absolute nodal coordinate formulation (ANCF). The paper carefully investigates which potential benefits and drawbacks the utilization of higher-order ANCF beam elements without in-slope vectors has in the case of the usage of full three-dimensional elasticity. When the elastic forces for shear-deformable ANCF beam elements are calculated using full three-dimensional elasticity—especially in the form of the St. Venant–Kirchhoff material law—Poisson locking severely deteriorates the accuracy of the numeric results. As shown in this paper, an existing approach to preventing this locking phenomenon for three-node beam elements can still produce unsatisfying results in load cases involving bidirectional bending. The results of this study show that enriching the polynomial basis used to approximate the beam kinematics provides a natural solution to this issue. As will be seen, these findings for three-node elements can also be extended to four-node elements. When using a sufficient approximation order in transverse directions, satisfying accuracy can be achieved both in conventional one-dimensional bending and in the above-mentioned bidirectional load case.

[1]  Daniel García-Vallejo,et al.  Modeling of Belt-Drives Using a Large Deformation Finite Element Formulation , 2006 .

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

[3]  Johannes Gerstmayr,et al.  Analysis of higher and lower order elements for the absolute nodal coordinate formulation , 2005 .

[4]  Aki Mikkola,et al.  Digital Nomenclature Code for Topology and Kinematics of Finite Elements Based on the Absolute Nodal Co-Ordinate Formulation , 2011 .

[5]  Aki Mikkola,et al.  Meshing strategies in the absolute nodal coordinate formulation-based Euler–Bernoulli beam elements , 2016 .

[6]  A. Shabana,et al.  EFFICIENT INTEGRATION OF THE ELASTIC FORCES AND THIN THREE-DIMENSIONAL BEAM ELEMENTS IN THE ABSOLUTE NODAL COORDINATE FORMULATION , 2005 .

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

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

[9]  J. J. Traybar,et al.  An Experimental Study of the Nonlinear Stiffness of a Rotor Blade Undergoing Flap, Lag and Twist Deformations , 1975 .

[10]  Aki Mikkola,et al.  Beam Elements with Trapezoidal Cross Section Deformation Modes Based on the Absolute Nodal Coordinate Formulation , 2010 .

[11]  A. Shabana.  Definition of the Slopes and the Finite Element Absolute Nodal Coordinate Formulation , 1997 .

[12]  Aki Mikkola,et al.  A study of moderately thick quadrilateral plate elements based on the absolute nodal coordinate formulation , 2013, Multibody System Dynamics.

[13]  Johannes Gerstmayr,et al.  A 3D Shear Deformable Finite Element Based on the Absolute Nodal Coordinate Formulation , 2013 .

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

[15]  Janusz Frączek,et al.  Nearly incompressible nonlinear material models in the large deformation analysis of beams using ANCF , 2015 .

[16]  Aki Mikkola,et al.  A two-dimensional shear deformable beam element based on the absolute nodal coordinate formulation , 2005 .

[17]  A. Mikkola,et al.  A geometrically exact beam element based on the absolute nodal coordinate formulation , 2008 .

[18]  Aki Mikkola,et al.  Experimental validation of flexible multibody dynamics beam formulations , 2013 .

[19]  Gengkai Hu,et al.  A finite element beam model including cross-section distortion in the absolute nodal coordinate formulation , 2014 .

[20]  Alexander Humer.  Dynamic modeling of beams with non-material, deformation-dependent boundary conditions , 2013 .

[21]  Chang-Wan Kim,et al.  Three-Dimensional Solid Brick Element Using Slopes in the Absolute Nodal Coordinate Formulation , 2014 .