Continuum Mechanics Based Bi-linear Shear Deformable Shell Element Using Absolute Nodal Coordinate Formulation

2014 ◽  
Author(s):  
Hiroki Yamashita ◽  
Antti I. Valkeapaa ◽  
Paramsothy Jayakumar ◽  
Hiroyuki Sugiyama
Keyword(s):  
Continuum Mechanics ◽  
Absolute Nodal Coordinate Formulation ◽  
Shell Element ◽  
Absolute Nodal Coordinate ◽  
Linear Shear ◽  
Shear Deformable

Continuum Mechanics Based Bilinear Shear Deformable Shell Element Using Absolute Nodal Coordinate Formulation

2015 ◽  
Vol 10 (5) ◽  
Author(s):  
Hiroki Yamashita ◽  
Antti I. Valkeapää ◽  
Paramsothy Jayakumar ◽  
Hiroyuki Sugiyama
Keyword(s):  
Continuum Mechanics ◽  
Numerical Solutions ◽  
Absolute Nodal Coordinate Formulation ◽  
Shell Element ◽  
Deformation Analysis ◽  
Normal Strain ◽  
Absolute Nodal Coordinate ◽  
Assumed Strain ◽  
Shear Deformable ◽  
The Continuum

In this investigation, a continuum mechanics based bilinear shear deformable shell element is developed using the absolute nodal coordinate formulation (ANCF) for the large deformation analysis of multibody shell structures. The element consists of four nodes, each of which has the global position coordinates and the transverse gradient coordinates along the thickness introduced for describing the orientation and deformation of the cross section of the shell element. The global position field on the middle surface and the position vector gradient at a material point in the element are interpolated by bilinear polynomials. The continuum mechanics approach is used to formulate the generalized elastic forces, allowing for the consideration of nonlinear constitutive models in a straightforward manner. The element lockings exhibited in the element are eliminated using the assumed natural strain (ANS) and enhanced assumed strain (EAS) approaches. In particular, the combined ANS and EAS approach is introduced to alleviate the thickness locking arising from the erroneous transverse normal strain distribution. Several numerical examples are presented in order to demonstrate the accuracy and the rate of convergence of numerical solutions obtained by the continuum mechanics based bilinear shear deformable ANCF shell element proposed in this investigation.

Bi-Linear Shear Deformable ANCF Shell Element Using Continuum Mechanics Approach

2014 ◽  
Author(s):  
Hiroki Yamashita ◽  
Antti I. Valkeapää ◽  
Paramsothy Jayakumar ◽  
Hiroyuki Sugiyama
Keyword(s):  
Continuum Mechanics ◽  
Numerical Solutions ◽  
Shell Element ◽  
Material Point ◽  
Deformation Analysis ◽  
Position Vector ◽  
Normal Strain ◽  
Assumed Strain ◽  
Linear Shear ◽  
Shear Deformable

In this investigation, a bi-linear shear deformable shell element is developed using the absolute nodal coordinate formulation for the large deformation analysis of multibody shell structures. The element consists of four nodes, each of which has the global position coordinates and the gradient coordinates along the thickness introduced for describing the orientation and deformation of the cross section of the shell element. The global position field on the mid-plane and the position vector gradient at a material point in the element are interpolated by bi-linear polynomials. The continuum mechanics approach is used to formulate the generalized elastic forces, allowing for the consideration of nonlinear constitutive models in a straightforward manner. The element locking exhibited in this type of element can be eliminated using the assumed natural strain (ANS) and enhanced assumed strain (EAS) approaches. In particular, the combined ANS and EAS approach is introduced to alleviate the thickness locking arising from the erroneous transverse normal strain distribution. Several numerical examples are presented in order to demonstrate the accuracy and the rate of convergence of numerical solutions obtained by the bi-linear shear deformable ANCF shell element proposed in this investigation.

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.

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.

Nondimensional analysis of a two-dimensional shear deformable beam in absolute nodal coordinate formulation

2017 ◽  
Vol 232 (7) ◽  
pp. 1236-1246 ◽  
Author(s):  
Kun-Woo Kim ◽  
Jae-Wook Lee ◽  
Jin-Seok Jang ◽  
Joo-Young Oh ◽  
Ji-Heon Kang ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Absolute Nodal Coordinate Formulation ◽  
Equation Of Motion ◽  
Central Processing Unit ◽  
Processing Unit ◽  
Two Dimensional ◽  
Absolute Nodal Coordinate ◽  
Central Processing ◽  
Dimensional Equation ◽  
Shear Deformable

Absolute nodal-coordinate formulation is a technique that was developed in 1996 for expressing the large rotation and deformation of a flexible body. It utilizes global slopes without a finite rotation in order to define nodal coordinates. The method has a shortcoming in that the central processing unit time increases because of increases in the degrees of freedom. In particular, when considering the deformation of a cross section, the shortcoming due to the increase in the degrees of freedom becomes clear. Therefore, in the present research, the dimensional equation of motion concerning a two-dimensional shear deformable beam, developed by Omar and Shabana, is converted into a nondimensional equation of motion in order to reduce the central processing unit time. By utilizing an example of a cantilever beam, wherein an exact solution for the static deflection exists, the nondimensional equation of motion was verified. Moreover, by using an example of a free-falling flexible pendulum, the efficiency of the nondimensional equation of motion gained by increasing the number of elements was compared with that of the dimensional equation of motion.

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