Three-Dimensional Fully Parameterized Triangular Plate Element Based on the Absolute Nodal Coordinate Formulation

2013 ◽  
Vol 8 (4) ◽  
Author(s):  
Abdel-Nasser A. Mohamed
Keyword(s):  
Rectangular Plate ◽  
Absolute Nodal Coordinate Formulation ◽  
Plate Theory ◽  
Three Dimensional ◽  
Plate Element ◽  
Shape Functions ◽  
Absolute Nodal Coordinate ◽  
Triangular Plate ◽  
The Absolute ◽  
Rectangular Plate Element

In this work, a new three-dimensional fully parameterized triangular plate element based on the absolute nodal coordinate formulation (ANCF) is introduced. This plate element has 12 coordinates per node; therefore, it can be used in thick plate applications. The proposed 12 shape functions are obtained by adding three shape functions to the nine shape functions that were previously used with the ANCF thin triangular plate element. Unlike the existing ANCF thin triangular plate element, which allows only the use of classical Kirchoff's plate theory, the fully parameterized ANCF triangular plate element proposed in this work allows for the use of a general continuum mechanics approach and also allows for a straight forward implementation of general nonlinear constitutive equations. Moreover, all deformation modes including thickness deformation can be captured using the fully parameterized ANCF triangular plate element proposed in this paper. The numerical results obtained in this investigation show that in case of negligible deformation, the fully parameterized ANCF triangular plate element behaves like a rigid body. Moreover, it is found that there is a good agreement between the solutions obtained using the proposed fully parameterized ANCF triangular plate element and the theoretical model in the case of small deformations. Furthermore, it is shown that the results of the proposed element agree well with the results obtained using the existing fully parameterized ANCF rectangular plate element when large deformation conditions are applied. The twist behavior of the proposed element is verified by comparison with the results obtained using a conventional nonlinear rectangular plate element.

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.

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.

Two Simple Triangular Plate Elements Based on the Absolute Nodal Coordinate Formulation

2008 ◽  
Vol 3 (4) ◽  
Author(s):  
Oleg Dmitrochenko ◽  
Aki Mikkola
Keyword(s):  
Finite Element ◽  
Numerical Solutions ◽  
Absolute Nodal Coordinate Formulation ◽  
Plate Theory ◽  
Body Motion ◽  
Absolute Nodal Coordinate ◽  
Triangular Plate ◽  
Plate Elements ◽  
Important Addition ◽  
The Absolute

In this paper, two triangular plate elements based on the absolute nodal coordinate formulation (ANCF) are introduced. Triangular elements employ the Kirchhoff plate theory and can, accordingly, be used in thin plate problems. As usual in ANCF, the introduced elements can exactly describe arbitrary rigid body motion when their mass matrices are constant. Previous plate developments in the absolute nodal coordinate formulation have focused on rectangular elements that are difficult to use when arbitrary meshes need to be described. The elements introduced in this study have overcome this problem and represent an important addition to the absolute nodal coordinate formulation. The two elements introduced are based on Specht’s and Morley’s shape functions, previously used in conventional finite element formulations. The numerical solutions of these elements are compared with previously proposed rectangular finite element and analytical results.

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.

Large Deformation Triangular Plate Elements for Multibody Problems

2007 ◽  
Author(s):  
Oleg Dmitrochenko ◽  
Aki Mikkola
Keyword(s):  
Numerical Solutions ◽  
Absolute Nodal Coordinate Formulation ◽  
Plate Theory ◽  
Body Motion ◽  
Absolute Nodal Coordinate ◽  
Plate Elements ◽  
Mass Matrices ◽  
Important Addition ◽  
The Absolute ◽  
Thin Plate Bending

In this paper, triangular finite elements based on the absolute nodal coordinate formulation are introduced. Triangular elements employ the Kirchhoff plate theory and can, accordingly, be used in thin plate bending problems. These elements can exactly describe arbitrary rigid body motion while their mass matrices are constant. Previous plate developments in the absolute nodal coordinate formulation have focused on rectangular elements that are difficult to use when arbitrary meshes need to be described. The elements introduced in this study have overcome this problem and represent an important addition to the absolute nodal coordinate formulation. The two elements introduced are based on Specht’s and Morley’s shape functions. The numerical solutions of these elements are compared with results obtained using the previously proposed rectangular finite element and analytical results.

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