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.

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.

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.

Study on Application of Numerical Manifold Method

2012 ◽  
Vol 182-183 ◽  
pp. 1194-1199
Author(s):  
Lei Zheng ◽  
Zheng Zhong Shen
Keyword(s):  
Continuum Mechanics ◽  
Discontinuous Deformation Analysis ◽  
Deformation Analysis ◽  
Numerical Manifold Method ◽  
Analysis Method ◽  
Continuous Problems ◽  
Discontinuous Deformation ◽  
Numerical Manifold ◽  
Cover Function ◽  
The Continuum

Numerical manifold method (NMM) is based on the blocky theory which absorbed the advantages of finite element method based on the continuum mechanics, discontinuous deformation analysis method based on the non-continuum mechanics and analytic method. According to the finite covering technology of modern manifold analysis method, uniform solving format on continuous-non-continuous problems is established by taking the continuous and discontinuous cover function which can be used for the numerical simulation of large deformation and continuous-discontinuous deformation. The calculation program is worked out based on the method above and it is applied to the actual project.

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.

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