Development of a Shear Deformable Element Using the Absolute Nodal Coordinate Formulation

2000 ◽  
Author(s):  
Mohamed A. Omar ◽  
Ahmed A. Shabana
Keyword(s):  
Absolute Nodal Coordinate Formulation ◽  
Absolute Nodal Coordinate ◽  
The Absolute ◽  
Shear Deformable

A Procedure for the Inclusion of Transverse Shear Deformation in a Beam Element Based on the Absolute Nodal Coordinate Formulation

2007 ◽  
Author(s):  
Aki Mikkola ◽  
Oleg Dmitrochenko ◽  
Marko Matikainen
Keyword(s):  
Shear Deformation ◽  
Transverse Shear ◽  
Absolute Nodal Coordinate Formulation ◽  
Beam Element ◽  
Transverse Shear Deformation ◽  
High Frequencies ◽  
Absolute Nodal Coordinate ◽  
Numerical Performance ◽  
The Absolute ◽  
Shear Deformable

In this study, a procedure to account for transverse shear deformation in the absolute nodal coordinate formulation is presented. In the absolute nodal coordinate formulation, shear deformation is usually defined by employing the slope vectors in the element transverse direction. This leads to the description of deformation modes that are, in practical problems, associated with high frequencies. These high frequencies, in turn, complicate the time integration procedure burdening numerical performance. In this study, the description of transverse shear deformation is accounted for in a two-dimensional beam element based on the absolute nodal coordinate formulation without the use of transverse slope vectors. In the introduced shear deformable beam element, slope vectors are replaced by vectors that describe the rotation of the beam cross-section. This procedure represents a simple enhancement that does not decrease the accuracy or numerical performance of elements based on the absolute nodal coordinate formulation. Numerical results are presented in order to demonstrate the accuracy of the introduced element in static and dynamic cases. The numerical results obtained using the introduced element agree with the results obtained using previously proposed shear deformable beam elements.

Shear Correction for Thin Plate Finite Elements Based on the Absolute Nodal Coordinate Formulation

2009 ◽  
Author(s):  
Oleg Dmitrochenko ◽  
Aki Mikkola
Keyword(s):  
Shear Deformation ◽  
Absolute Nodal Coordinate Formulation ◽  
Beam Element ◽  
Transverse Shear Deformation ◽  
High Frequencies ◽  
Absolute Nodal Coordinate ◽  
Plate Elements ◽  
Numerical Performance ◽  
The Absolute ◽  
Shear Deformable

This study is an extension of a newly introduced approach to account transverse shear deformation in absolute nodal coordinate formulation. In the formulation, shear deformation is usually defined by employing slope vectors in the element transverse direction. This leads to the description of deformation modes that, in practical problems, may be associated with high frequencies. These high frequencies, in turn, could complicate the time integration procedure, burdening numerical performance of shear deformable elements. In a recent study of this paper’s authors, the description of transverse shear deformation is accounted for in a two-dimensional beam element, based on the absolute nodal coordinate formulation without the use of transverse slope vectors. In the introduced shear deformable beam element, slope vectors are replaced by vectors that describe the rotation of the beam cross-section. This procedure represents a simple enhancement that does not decrease the accuracy or numerical performance of elements based on the absolute nodal coordinate formulation. In this study, the approach to account for shear deformation without using transverse slopes is implemented for a thin rectangular plate element. In fact, two new plate elements are introduced: one within conventional finite element and another using the absolute nodal coordinates. Numerical results are presented in order to demonstrate the accuracy of the introduced plate element. The numerical results obtained using the introduced element agree with the results obtained using previously proposed shear deformable plate elements.

Inclusion of Transverse Shear Deformation in a Beam Element Based on the Absolute Nodal Coordinate Formulation

2008 ◽  
Vol 4 (1) ◽  
Author(s):  
Aki Mikkola ◽  
Oleg Dmitrochenko ◽  
Marko Matikainen
Keyword(s):  
Shear Deformation ◽  
Transverse Shear ◽  
Absolute Nodal Coordinate Formulation ◽  
Beam Element ◽  
Transverse Shear Deformation ◽  
High Frequencies ◽  
Absolute Nodal Coordinate ◽  
Numerical Performance ◽  
The Absolute ◽  
Shear Deformable

In this study, a procedure to account for transverse shear deformation in the absolute nodal coordinate formulation is presented. In the absolute nodal coordinate formulation, shear deformation is usually defined by employing the slope vectors in the element transverse direction. This leads to the description of deformation modes that are, in practical problems, associated with high frequencies. These high frequencies, in turn, complicate the time integration procedure burdening numerical performance. In this study, the description of transverse shear deformation is accounted for in a two-dimensional beam element based on the absolute nodal coordinate formulation without the use of transverse slope vectors. In the introduced shear deformable beam element, slope vectors are replaced by vectors that describe the orientation of the beam cross-section. This procedure represents a simple enhancement that does not decrease the accuracy or numerical performance of elements based on the absolute nodal coordinate formulation. Numerical results are presented in order to demonstrate the accuracy of the introduced element in static and dynamic cases. The numerical results obtained using the introduced element agree with the results obtained using previously proposed shear deformable beam elements.

A Linear Beam Finite Element Based on the Absolute Nodal Coordinate Formulation

2004 ◽  
Vol 127 (4) ◽  
pp. 621-630 ◽  
Author(s):  
Kimmo S. Kerkkänen ◽  
Jussi T. Sopanen ◽  
Aki M. Mikkola
Keyword(s):  
Absolute Nodal Coordinate Formulation ◽  
Longitudinal Direction ◽  
Beam Element ◽  
Computational Effort ◽  
Two Dimensional ◽  
Absolute Nodal Coordinate ◽  
Beam Elements ◽  
Shear Deformable Beam ◽  
The Absolute ◽  
Shear Deformable

In this paper, a new two-dimensional shear deformable beam element based on the absolute nodal coordinate formulation is proposed. The nonlinear elastic forces of the beam element are obtained using a continuum mechanics approach, without employing a local element coordinate system. In this study, linear polynomials are used to interpolate both the transverse and longitudinal components of the displacement. This is different from other absolute nodal-coordinate-based beam elements where cubic polynomials are used in the longitudinal direction. The use of linear interpolation polynomials leads to the phenomenon known as shear locking. This defect is avoided through the adoption of selective integration within the numerical integration method. The proposed element is verified using several numerical examples. The results of the proposed element are compared to analytical solutions and the results for an existing shear deformable beam element. It is shown that by using the proposed element, accurate linear and nonlinear static deformations, as well as realistic dynamic behavior including the capturing of the centrifugal stiffening effect, can be achieved with a smaller computational effort than by using existing shear deformable two-dimensional beam elements.

Performance of the Incremental and Non-Incremental Finite Element Formulations in Flexible Multibody Problems

1999 ◽  
Vol 122 (4) ◽  
pp. 498-507 ◽  
Author(s):  
Marcello Campanelli ◽  
Marcello Berzeri ◽  
Ahmed A. Shabana
Keyword(s):  
Finite Element ◽  
Multibody Systems ◽  
Absolute Nodal Coordinate Formulation ◽  
Flexible Multibody Systems ◽  
Large Displacement ◽  
Body Motion ◽  
Absolute Nodal Coordinate ◽  
Flexible Multibody ◽  
The Absolute ◽  
Finite Element Formulations

Many flexible multibody applications are characterized by high inertia forces and motion discontinuities. Because of these characteristics, problems can be encountered when large displacement finite element formulations are used in the simulation of flexible multibody systems. In this investigation, the performance of two different large displacement finite element formulations in the analysis of flexible multibody systems is investigated. These are the incremental corotational procedure proposed in an earlier article (Rankin, C. C., and Brogan, F. A., 1986, ASME J. Pressure Vessel Technol., 108, pp. 165–174) and the non-incremental absolute nodal coordinate formulation recently proposed (Shabana, A. A., 1998, Dynamics of Multibody Systems, 2nd ed., Cambridge University Press, Cambridge). It is demonstrated in this investigation that the limitation resulting from the use of the infinitesmal nodal rotations in the incremental corotational procedure can lead to simulation problems even when simple flexible multibody applications are considered. The absolute nodal coordinate formulation, on the other hand, does not employ infinitesimal or finite rotation coordinates and leads to a constant mass matrix. Despite the fact that the absolute nodal coordinate formulation leads to a non-linear expression for the elastic forces, the results presented in this study, surprisingly, demonstrate that such a formulation is efficient in static problems as compared to the incremental corotational procedure. The excellent performance of the absolute nodal coordinate formulation in static and dynamic problems can be attributed to the fact that such a formulation does not employ rotations and leads to exact representation of the rigid body motion of the finite element. [S1050-0472(00)00604-8]

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