A formulation of a plate element based on absolute nodal coordinate formulation using global and element coordinate systems

2016 ◽  
Vol 2016 (0) ◽  
pp. 413
Author(s):  
Hiroki KAMIYA ◽  
Kensuke HARA
Keyword(s):  
Absolute Nodal Coordinate Formulation ◽  
Plate Element ◽  
Coordinate Systems ◽  
Absolute Nodal Coordinate

Elastic Forces and Coordinate Systems in the Finite Element Formulations

1999 ◽  
Author(s):  
Marcello Berzeri ◽  
Marcello Campanelli ◽  
A. A. Shabana
Keyword(s):  
Finite Element ◽  
Absolute Nodal Coordinate Formulation ◽  
Frame Of Reference ◽  
Coordinate Systems ◽  
Absolute Nodal Coordinate ◽  
Floating Frame Of Reference ◽  
Elastic Forces ◽  
Floating Frame ◽  
The Absolute ◽  
Finite Element Formulations

Abstract The equivalence of the elastic forces of finite element formulations used in flexible multibody dynamics is the focus of this investigation. Two conceptually different finite element formulations that lead to exact modeling of the rigid body dynamics will be used. These are the floating frame of reference formulation and the absolute nodal coordinate formulation. It is demonstrated in this study that different element coordinate systems, which are used for the convenience of describing the element deformations in the absolute nodal coordinate formulation, lead to similar results as the element size is reduced. The equivalence of the elastic forces in the absolute nodal coordinate and the floating frame of reference formulations is shown. The result of this analysis clearly demonstrates that the instability observed in high speed rotor analytical models due to the neglect of the geometric centrifugal stiffening is not a problem inherent to a particular finite element formulation but only depends on the beam model that is used. Fourier analysis of the solutions obtained in this investigation also sheds new light on the fundamental problem of the choice of the deformable body coordinate system in the floating frame of reference formulation. A new method is presented and used to obtain a simple expression for the elastic forces in the absolute nodal coordinate formulation. This method, which employs a nonlinear elastic strain-displacement relationship, does not result in an unstable solution when the angular velocity is increased.

Analysis of Thin Plate Structures Using the Absolute Nodal Coordinate Formulation

2005 ◽  
Vol 219 (4) ◽  
pp. 345-355 ◽  
Author(s):  
K Dufva ◽  
A A Shabana
Keyword(s):  
Finite Element ◽  
Thin Plate ◽  
Absolute Nodal Coordinate Formulation ◽  
Mass Matrix ◽  
Plate Element ◽  
Shell Elements ◽  
Absolute Nodal Coordinate ◽  
Plate And Shell ◽  
Spatial Parameters ◽  
The Absolute

The absolute nodal coordinate formulation can be used in multibody system applications where the rotation and deformation within the finite element are large and where there is a need to account for geometrical non-linearities. In this formulation, the gradients of the global positions are used as nodal coordinates and no rotations are interpolated over the finite element. For thin plate and shell elements, the plane stress conditions can be applied and only gradients obtained by differentiation with respect to the element mid-surface spatial parameters need to be defined. This automatically reduces the number of element degrees of freedoms, eliminates the high frequencies due to the oscillations of some gradient components along the element thickness, and as a result makes the plate element computationally more efficient. In this paper, the performance of a thin plate element based on the absolute nodal coordinate formulation is investigated. The lower dimension plate element used in this investigation allows for an arbitrary rigid body displacement and large deformation within the element. The element leads to a constant mass matrix and zero Coriolis and centrifugal forces. The performance of the element is compared with other plate elements previously developed using the absolute nodal coordinate formulation. It is shown that the finite element used in this investigation is much more efficient when compared with previously proposed elements in the case of thin structures. Numerical examples are presented in order to demonstrate the use of the formulation developed in this paper and the computational advantages gained from using the thin plate element. The thin plate element examined in this study can be efficiently used in many applications including modelling of paper materials, belt drives, rotor dynamics, and tyres.

A novel absolute nodal coordinate formulation thin plate tire model with fractional derivative viscosity and surface integral-based contact algorithm

2018 ◽  
Vol 233 (3) ◽  
pp. 583-597
Author(s):  
Peng Lan ◽  
Yaqi Cui ◽  
Zuqing Yu
Keyword(s):  
Fractional Derivative ◽  
Contact Pressure ◽  
Thin Plate ◽  
Absolute Nodal Coordinate Formulation ◽  
Tire Model ◽  
Plate Element ◽  
Absolute Nodal Coordinate ◽  
Contact Patch ◽  
Contact Algorithm ◽  
The Absolute

A new absolute nodal coordinate formulation thin plate tire model, which includes the damping property of the rubber and an efficient tire–road contact algorithm is given. The fractional derivative viscosity constitutive model is proposed in this paper based on the complete form of the absolute nodal coordinate formulation thin plate element, which is created to describe the stress-free initially curved configuration of the tire. A new contact algorithm based on the integration of the contact pressure within the contact patch is developed. By solving the simultaneous equations of the tire geometry and road profile, the dimensionless coordinates for the boundary points of contact patch could be obtained directly. A self-adaptable Gauss integration strategy is introduced to perform the integration of the contact pressure within the varying region, so the integration could reach high precision by few integration points. The calculation of contact force is determined based on penalty method and smoothed Coulomb friction model. The application of fractional derivative viscosity on the absolute nodal coordinate formulation thin plate element is demonstrated by numerical results. A pressurized Golf tire model is given to show the feasibility of the proposed tire–ground contact algorithm.

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.

Improved Description of Elastic Forces for the Absolute Nodal Coordinate Based Plate Element

2005 ◽  
Author(s):  
Marko K. Matikainen ◽  
Aki M. Mikkola
Keyword(s):  
Finite Element ◽  
Continuum Mechanics ◽  
Absolute Nodal Coordinate Formulation ◽  
Three Dimensional ◽  
Plate Element ◽  
Absolute Nodal Coordinate ◽  
Finite Element Software ◽  
Elastic Forces ◽  
The Absolute ◽  
The Continuum

In this study, the improved description of elastic forces for the absolute nodal coordinate based plate element is introduced. The absolute nodal coordinate formulation, which utilizes global displacements and slope coordinates as nodal variables, can be used in large rotation and deformation dynamic analysis of beam and plate structures. The formulation avoids difficulties that arise when a rotation is interpolated in three-dimensional applications. In the absolute nodal coordinate formulation, a continuum mechanics approach has become the dominating procedure when elastic forces are defined. It has recently been perceived, however, that the continuum mechanics based absolute nodal coordinate elements suffer from serious shortcomings, including Poisson’s locking and poor convergence rate. These problems can be circumvented by modifying the displacement field of a finite element in the definition of elastic forces. This allows the use of the mixed type interpolation technique, leading to accurate and efficient finite element formulations. This approach has been previously applied to two- and three-dimensional absolute nodal coordinate based finite elements. In this study, the improved approach for elastic forces is extended to the absolute nodal coordinate plate element. The introduced plate element is compared in static examples to the continuum mechanics based absolute nodal coordinate plate element, as well as to commercial finite element software.

A New Plate Element Based on the Absolute Nodal Coordinate Formulation

2001 ◽  
Author(s):  
Aki M. Mikkola ◽  
Ahmed A. Shabana
Keyword(s):  
Absolute Nodal Coordinate Formulation ◽  
Mass Matrix ◽  
Body Motion ◽  
Deformation Analysis ◽  
Plate Element ◽  
Large Rotation ◽  
Shell Elements ◽  
Absolute Nodal Coordinate ◽  
Plates And Shells ◽  
The Absolute

Abstract In this investigation, a method for the finite rotation and large deformation analysis of plates is presented. The method, which is based on the absolute nodal coordinate formulation, leads to a plate element capable of representing exact rigid body motion. In this method, continuity conditions on all the displacement gradients are imposed. Therefore, non-smoothness of the plate mid-surface at the nodal points is avoided. By developing such a plate element, a constant mass matrix is obtained, and as a consequence, the centrifugal and Coriolis forces are equal to zero. Generalization of the formulation to the case of shell elements is discussed. Numerical results are presented in order to demonstrate the use of the proposed method in the large rotation and deformation analysis of plates and shells.

Development of Elastic Forces for a Large Deformation Plate Element Based on the Absolute Nodal Coordinate Formulation

2005 ◽  
Vol 1 (2) ◽  
pp. 103-108 ◽  
Author(s):  
Aki M. Mikkola ◽  
Marko K. Matikainen
Keyword(s):  
Finite Element ◽  
Dynamic Analysis ◽  
Continuum Mechanics ◽  
Absolute Nodal Coordinate Formulation ◽  
Three Dimensional ◽  
Plate Element ◽  
Absolute Nodal Coordinate ◽  
Elastic Forces ◽  
The Absolute ◽  
The Continuum

Dynamic analysis of large rotation and deformation can be carried out using the absolute nodal coordinate formulation. This formulation, which utilizes global displacements and slope coordinates as nodal variables, make it possible to avoid the difficulties that arise when a rotation is interpolated in three-dimensional applications. In the absolute nodal coordinate formulation, a continuum mechanics approach has become the dominating procedure when elastic forces are defined. It has recently been perceived, however, that the continuum mechanics based absolute nodal coordinate elements suffer from serious shortcomings, including Poisson’s locking and poor convergence rate. These problems can be circumvented by modifying the displacement field of a finite element in the definition of elastic forces. This allows the use of the mixed type interpolation technique, leading to accurate and efficient finite element formulations. This approach has been previously applied to two- and three-dimensional absolute nodal coordinate based finite elements. In this study, the improved approach for elastic forces is extended to the absolute nodal coordinate plate element. The introduced plate element is compared in static examples to the continuum mechanics based absolute nodal coordinate plate element, as well as to commercial finite element software. A simple dynamic analysis is performed using the introduced element in order to demonstrate the capability of the element to conserve energy.

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