Modeling and Verification of a RANCF Fluid Element Based on Cubic Rational Bezier Volume

2020 ◽  
Vol 15 (4) ◽  
Author(s):  
Liang Ma ◽  
Cheng Wei ◽  
Chao Ma ◽  
Yang Zhao
Keyword(s):  
Absolute Nodal Coordinate Formulation ◽  
Three Dimensional ◽  
Mesh Size ◽  
Constraint Equation ◽  
Liquid Column ◽  
Position Vector ◽  
Fluid Element ◽  
Absolute Nodal Coordinate ◽  
Better Than ◽  
Good Agreement

Abstract This investigation is focused on developing a novel three-dimensional rational absolute nodal coordinate formulation (RANCF) fluid element based on cubic rational Bezier volume. The new fluid element can describe liquid columns with initially curved configurations precisely, performing better than the conventional absolute nodal coordinate formulation (ANCF) fluid element. A new kinematic description, which employs a different interpolation function to describe the displacement field, makes this element a true difference. The shape function is no longer calculated by an incomplete polynomial or nonrational B-spline function, replaced by the rational Bezier function. Dynamical model or governing equation of the RANCF fluid element is built based on the constitutive equation of fluid, momentum, and constraint equation. One liquid column with initially cylindrical configuration is established by the RANCF fluid element, the position vector of control points and their weights are calculated to achieve the specific initial configuration. A simulation of the cylindrical liquid column collapsing on a plane is implemented to verify the validity of the RANCF fluid element, and numerical results are in good agreement with those obtained in the literature. The convergence of the RANCF fluid element is also checked and proved not to be influenced by mesh size. Finally, the precise description ability of the RANCF fluid element is compared with that of the conventional ANCF fluid element, the former shows a great advantage.

Comparison of Three-Dimensional Flexible Beam Elements for Dynamic Analysis: Classical Finite Element Formulation and Absolute Nodal Coordinate Formulation

2009 ◽  
Vol 5 (1) ◽  
Author(s):  
A. L. Schwab ◽  
J. P. Meijaard
Keyword(s):  
Dynamic Analysis ◽  
Absolute Nodal Coordinate Formulation ◽  
Three Dimensional ◽  
Flexible Beam ◽  
Element Formulation ◽  
Shear Locking ◽  
Elastic Line ◽  
Absolute Nodal Coordinate ◽  
Beam Elements ◽  
Bending Mode

Three formulations for a flexible spatial beam element for dynamic analysis are compared: a Timoshenko beam with large displacements and rotations, a fully parametrized element according to the absolute nodal coordinate formulation (ANCF), and an ANCF element based on an elastic line approach. In the last formulation, the shear locking of the antisymmetric bending mode is avoided by the application of either the two-field Hellinger–Reissner or the three-field Hu–Washizu variational principle. The comparison is made by means of linear static deflection and eigenfrequency analyses on stylized problems. It is shown that the ANCF fully parametrized element yields too large torsional and flexural rigidities, and shear locking effectively suppresses the antisymmetric bending mode. The presented ANCF formulation with the elastic line approach resolves most of these problems.

An improved variable-length beam element with a torsion effect based on the absolute nodal coordinate formulation

2017 ◽  
Vol 232 (1) ◽  
pp. 69-83
Author(s):  
Shuai Yang ◽  
Zongquan Deng ◽  
Jing Sun ◽  
Yang Zhao ◽  
Shengyuan Jiang
Keyword(s):  
Absolute Nodal Coordinate Formulation ◽  
Beam Element ◽  
Variable Length ◽  
Ball Screw ◽  
Position Vector ◽  
Drilling Process ◽  
Rotational Angle ◽  
Absolute Nodal Coordinate ◽  
One Dimensional ◽  
Torsion Effect

This paper proposes an improved variable-length beam element based on absolute nodal coordinate formulation and arbitrary Lagrangian–Eulerian description to build dynamic model of a one-dimensional medium with mass transportation and a non-ignorable torsion effect. The rotational angle of the presented element is interpolated using the same Hermite polynomials as the position vector such that the change rate of the rotational angles of the two nodes are also introduced into generalized coordinates of the element, which ensures the continuity of the nodal torque. Numerical examples demonstrate that the proposed element can precisely describe the dynamic behaviour of a one-dimensional medium. Furthermore, its ability to describe the torsion effect is significantly enhanced compared to earlier element in the literature. In engineering applications, the proposed element can be used in the dynamic analysis of drill stems in the drilling process, slender workpieces of cylinder shafts in turning processes and leading screws in ball screw mechanisms.

Application of Plasticity Theory and Absolute Nodal Coordinate Formulation to Flexible Multibody System Dynamics

2003 ◽  
Vol 126 (3) ◽  
pp. 478-487 ◽  
Author(s):  
Hiroyuki Sugiyama ◽  
Ahmed A. Shabana
Keyword(s):  
Finite Element ◽  
Absolute Nodal Coordinate Formulation ◽  
Plasticity Theory ◽  
Position Vector ◽  
Element Formulation ◽  
Absolute Nodal Coordinate ◽  
Flexible Multibody ◽  
The Absolute ◽  
Return Algorithm ◽  
Finite Element Formulations

The objective of this investigation is to develop a nonlinear finite element formulation for the elastic-plastic analysis of flexible multibody systems. The Lagrangian plasticity theory based on J2 flow theory is used to account for the effect of plasticity in flexible multibody dynamics. It is demonstrated that the principle of objectivity that is an issue when existing finite element formulations using rate-type constitutive equations are used is automatically satisfied when the stress and strain rate are directly calculated in the Lagrangian descriptions using the absolute nodal coordinate formulation employed in this investigation. This is attributed to the fact that, in the finite element absolute nodal coordinate formulation, the position vector gradients can completely define the state of rotation and deformation within the element. As a consequence, the numerical algorithm used to determine the plastic deformations such as the radial return algorithm becomes much simpler when the absolute nodal coordinate formulation is used as compared to existing finite element formulations that employ incrementally objective algorithms. Several numerical examples are presented in order to demonstrate the use of the formulations presented in the paper.

Three Dimensional Absolute Nodal Coordinate Formulation for Beam Elements: Theory

2000 ◽  
Vol 123 (4) ◽  
pp. 606-613 ◽  
Author(s):  
Ahmed A. Shabana ◽  
Refaat Y. Yakoub
Keyword(s):  
Coordinate System ◽  
Absolute Nodal Coordinate Formulation ◽  
Mass Matrix ◽  
Local Coordinate System ◽  
Three Dimensional ◽  
Deformation Analysis ◽  
Large Element ◽  
Absolute Nodal Coordinate ◽  
Beam Elements ◽  
Highly Nonlinear

The description of a beam element by only the displacement of its centerline leads to some difficulties in the representation of the torsion and shear effects. For instance such a representation does not capture the rotation of the beam as a rigid body about its own axis. This problem was circumvented in the literature by using a local coordinate system in the incremental finite element method or by using the multibody floating frame of reference formulation. The use of such a local element coordinate system leads to a highly nonlinear expression for the inertia forces as the result of the large element rotation. In this investigation, an absolute nodal coordinate formulation is presented for the large rotation and deformation analysis of three dimensional beam elements. This formulation leads to a constant mass matrix, and as a result, the vectors of the centrifugal and Coriolis forces are identically equal to zero. The formulation presented in this paper takes into account the effect of rotary inertia, torsion and shear, and ensures continuity of the slopes as well as the rotation of the beam cross section at the nodal points. Using the proposed formulation curved beams can be systematically modeled.

Modeling and Analysis of Wire Rope in the Drilling Device Using ANCF Method

2014 ◽  
Vol 1006-1007 ◽  
pp. 30-33 ◽  
Author(s):  
Yue Zhang ◽  
Cheng Wei ◽  
Jiang Zhang ◽  
Yang Zhao
Keyword(s):  
Computational Efficiency ◽  
Absolute Nodal Coordinate Formulation ◽  
Three Dimensional ◽  
Wire Rope ◽  
Large Rotation ◽  
Modeling And Analysis ◽  
Absolute Nodal Coordinate ◽  
Flexible Cable ◽  
Deformation Problem ◽  
The Wire

The wire rope of drilling device is modeled by using absolute nodal coordinate formulation (ANCF) which is presented for the analysis of three dimensional flexible cable in this paper. This formulation is suited for the analysis of large rotation and deformation problem. Only axial and bending deformations are taken into account in this paper, which increases the computational efficiency without affecting the precision. Vibrations of the drilling mechanism and the wire rope under different preloads are simulated. It can be seen from the emulational results that resonance will occur when the preload increases to a certain value and the amplitude is the largest in this case.

Coupled Deformation Modes in the Large Deformation Finite Element Analysis: Generalization

2009 ◽  
Vol 4 (2) ◽  
Author(s):  
Oleg N. Dmitrochenko ◽  
Bassam A. Hussein ◽  
Ahmed A. Shabana
Keyword(s):  
Continuum Mechanics ◽  
Absolute Nodal Coordinate Formulation ◽  
Flexible Structures ◽  
Three Dimensional ◽  
Numerical Results ◽  
Elastic Line ◽  
Absolute Nodal Coordinate ◽  
Plate Elements ◽  
General Continuum ◽  
Deformation Modes

The effect of the absolute nodal coordinate formulation (ANCF)–coupled deformation modes on the accuracy and efficiency when higher order three-dimensional beam and plate finite elements are used is investigated in this study. It is shown that while computational efficiency can be achieved in some applications by neglecting the effect of some of the ANCF-coupled deformation modes, such modes introduce geometric stiffening/softening effects that can be significant in the case of very flexible structures. As shown in previous publications, for stiff structures, the effect of the ANCF-coupled deformation modes can be neglected. For such stiff structures, the solution does not strongly depend on some of the ANCF-coupled deformation modes, and formulations that include these modes lead to numerical results that are in good agreement with formulations that exclude them. In the case of a very flexible structure, on the other hand, the inclusion of the ANCF-coupled deformation modes becomes necessary in order to obtain an accurate solution. In this case of very flexible structures, the use of the general continuum mechanics approach leads to an efficient solution algorithm and to more accurate numerical results. In order to examine the effect of the elastic force formulation on the efficiency and the coupling between different modes of deformation, three different models are used again to formulate the elastic forces in the absolute nodal coordinate formulation. These three methods are the general continuum mechanics approach, the elastic line (midsurface) approach, and the elastic line (midsurface) approach with the Hellinger–Reissner principle. Three-dimensional absolute nodal coordinate formulation beam and plate elements are used in this study. In the general continuum mechanics approach, the coupling between the cross section deformation and the beam centerline or plate midsurface displacement is considered, while in the approaches based on the elastic line and the Hellinger–Reissner principle, this coupling is neglected. In addition to the fully parametrized beam element used in this study, three different plate elements, two fully parametrized and one reduced order thin plate elements, are used. The numerical results obtained using different finite elements and elastic force formulations are compared in this study.

Rational ANCF Thin Plate Finite Element

2016 ◽  
Vol 11 (5) ◽  
Author(s):  
Carmine M. Pappalardo ◽  
Zuqing Yu ◽  
Xiaoshun Zhang ◽  
Ahmed A. Shabana
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Thin Plate ◽  
Geometric Modeling ◽  
Absolute Nodal Coordinate Formulation ◽  
Position Vector ◽  
Plate Element ◽  
Conic Sections ◽  
Absolute Nodal Coordinate ◽  
Linear Algebraic Equations

In this paper, a rational absolute nodal coordinate formulation (RANCF) thin plate element is developed and its use in the analysis of curved geometry is demonstrated. RANCF finite elements are the rational counterpart of the nonrational absolute nodal coordinate formulation (ANCF) finite elements which employ rational polynomials as basis or blending functions. RANCF finite elements can be used in the accurate geometric modeling and analysis of flexible continuum bodies with complex geometrical shapes that cannot be correctly described using nonrational finite elements. In this investigation, the weights, which enter into the formulation of the RANCF finite element and form an additional set of geometric parameters, are assumed to be nonzero constants in order to accurately represent the initial geometry and at the same time preserve the desirable ANCF features, including a constant mass matrix and zero centrifugal and Coriolis generalized inertia forces. A procedure for defining the control points and weights of a Bezier surface defined in a parametric form is used in order to be able to efficiently create RANCF/ANCF FE meshes in a straightforward manner. This procedure leads to a set of linear algebraic equations whose solution defines the RANCF coordinates and weights without the need for an iterative procedure. In order to be able to correctly describe the ANCF and RANCF gradient deficient FE geometry, a square matrix of position vector gradients is formulated and used to calculate the FE elastic forces. As discussed in this paper, the proposed finite element allows for describing exactly circular and conic sections and can be effectively used in the geometry and analysis modeling of multibody system (MBS) components including tires. The proposed RANCF finite element is compared with other nonrational ANCF plate elements. Several numerical examples are presented in order to demonstrate the use of the proposed RANCF thin plate element. In particular, the FE models of a set of rational surfaces, which include conic sections and tires, are developed.

A New Higher-Order Euler-Bernoulli Beam Element of Absolute Nodal Coordinate Formulation

2020 ◽  
Author(s):  
Peng Zhang ◽  
Jianmin Ma ◽  
Menglan Duan
Keyword(s):  
Absolute Nodal Coordinate Formulation ◽  
Strain Tensor ◽  
Beam Element ◽  
Higher Order ◽  
Position Vector ◽  
Traditional Theory ◽  
Bernoulli Beam ◽  
Geometrically Nonlinear Analysis ◽  
Absolute Nodal Coordinate ◽  
Euler Bernoulli Beam

Abstract In this study, a new higher-order Euler-Bernoulli beam element of Absolute Nodal Coordinate Formulation (ANCF) is developed for geometrically nonlinear analysis of planar structures. The strain energy of the beam element is derived by applying the definition of the Green–Lagrange strain tensor in continuum mechanics. The first contribution of this research is to realize the accurate calculation of curvature on the beam element node by additionally considering the second derivative of the position vector obtained by quintic Hermite interpolation function. Furthermore, in traditional theory, the independent variable of finite formulation is arc-length coordinate s, while in this work, a correction is come up with and proven that it is actually an equivalent parameter. Some benchmark problems of straight beams are solved by the proposed element and accurate results are obtained by just fewer elements when compared with the other works including the traditional ANCF element and B23 element of ABAQUS. What leads to this accuracy result is that the precise calculation of nodal curvature is obtained from higher order interpolation scheme. The correctness and accuracy of the proposed element are validated in this work and it can be further developed for tackling large deformation and large rotation problems of spatial curved beams.

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