ANCF Consistent Rotation-Based Finite Element Formulation

2015 ◽  
Vol 11 (1) ◽  
Author(s):  
Ahmed A. Shabana
Keyword(s):  
Rotation Vector ◽  
Element Formulation ◽  
General Description ◽  
Centrifugal Forces ◽  
Large Rotation ◽  
Plate And Shell ◽  
Shell Models ◽  
Deformation Modes ◽  
Inertia Forces ◽  
The Continuum

In this technical brief, a consistent rotation-based formulation is proposed using the absolute nodal coordinate formulation (ANCF) kinematic description. The proposed formulation defines a unique rotation field, employs one interpolation, captures shear deformations, does not suffer from the redundancy problem encountered when using large rotation vector formulations, allows for systematically describing curved geometry, and leads to elastic force definitions that eliminate high-frequency modes associated with the deformation of the cross section. The drawback of this formulation, as it is the case with the large rotation vector formulations, is the nonlinearity of the inertia forces including nonzero Coriolis and centrifugal forces. Furthermore, the formulation does not capture deformation modes that can be captured using the more general ANCF finite elements. Nonetheless, the proposed method is consistent with the continuum mechanics general description, can be related to computational geometry methods, and can be used to develop beam, plate, and shell models without violation of basic mechanics principles.

Absolute Nodal Coordinate Formulation

1997 ◽  
Author(s):  
Ahmed A. Shabana ◽  
Hussien A. Hussien ◽  
José L. Escalona
Keyword(s):  
Finite Element ◽  
Rigid Body ◽  
Rigid Bodies ◽  
Rotation Vector ◽  
Finite Rotations ◽  
Large Rotation ◽  
Finite Element Procedure ◽  
Floating Frame ◽  
Inertia Forces ◽  
Body Inertia

Abstract There are three basic finite element formulations, which are used in multibody dynamics. These are the floating frame reference approach, the incremental method and the large rotation vector approach. In the floating frame of reference and incremental formulations, the slopes are assumed small in order to define infinitesimal rotations that can be treated and transformed as vectors. This description, however, limits the use of some important elements such as beams and plates in a wide range of large displacement applications. As demonstrated in some recent publications, if infinitesimal rotations are used as nodal coordinates, the use of the finite element incremental formulation in the large reference displacement analysis does not lead to exact modeling of the rigid body inertia when the structures rotate as rigid bodies. In this paper, a new and simple finite element procedure that employs the mathematical definition of the slope and uses it to define the element coordinates instead of the infinitesimal and finite rotations is developed for large rotation and deformation problems. By using this description and by defining the element coordinates in the global system, not only the need for performing coordinate transformation is avoided, but also a simple expression for the inertia forces is obtained. Furthermore, the resulting mass matrix is constant and it is the same matrix that appears in linear structural dynamics. It is demonstrated in this paper, that this coordinate description leads to exact modeling of the rigid body inertia when the structure rotate as rigid bodies. Nonetheless, the stiffness matrix becomes nonlinear function of time even in the case of small displacements. The method presented in this paper differs from previous large rotation vector formulations in the sense that the inertia forces, the kinetic energy, and the strain energy are not expressed in terms of any orientation coordinates, and therefore, the method does not require interpolation of finite rotations. While the use of the formulation is demonstrated using a simple planar beam element, the generalization of the method to other element types and to the three dimensional case is straightforward. Using the finite element procedure presented in this paper, beams and plates can be treated as isoparametric elements.

Improved Bilinear Degenerated Shell Element

2015 ◽  
Vol 12 (02) ◽  
pp. 1550004 ◽  
Author(s):  
N. V. Swamy Naidu ◽  
B. Sateesh
Keyword(s):  
Shell Element ◽  
Shell Structures ◽  
Thin Plates ◽  
Element Formulation ◽  
Rigid Body Modes ◽  
Test Requirements ◽  
Degenerated Shell Element ◽  
Deformation Modes ◽  
Torsional Rotation ◽  
Transverse Shear Strains

The development of a new four node 24 degree of freedom bilinear degenerated shell element is presented for the analysis of shell structures. The present finite element formulation considers the assumed covariant transverse shear strains to avoid the shear locking problem and the assumed covariant membrane strains, which are separated from covariant in-plane strains, to overcome the membrane locking problem. The formulation also includes the deviation of the normal torsional rotation of the mid surface in the governing equation. This element is free from serious shear and membrane locking problems and undesirable spurious kinematic deformation modes. The element is tested for rigid body modes and distorted edges to meet the patch test requirements. The versatility and accuracy of this new degenerated shell element is demonstrated by solving several numerical examples for thick and thin plates.

Locking and Stability of 3D Woven Composite Reinforcements

2014 ◽  
Vol 611-612 ◽  
pp. 292-299 ◽  
Author(s):  
Sylvain Mathieu ◽  
Philippe Boisse ◽  
Nahiene Hamila ◽  
Florent Bouillon
Keyword(s):  
Finite Element ◽  
Strain Energy ◽  
Constitutive Law ◽  
Element Formulation ◽  
Woven Composite ◽  
Anisotropic Behavior ◽  
Stabilization Procedure ◽  
Bias Extension ◽  
Deformation Modes ◽  
Composite Reinforcements

3D woven composite reinforcements preforming simulations are an unavoidable step of composite part processing. The present paper deals with thick composite fabric behavior modelling and issues arising during the numerical simulation of preforming. After the description of the independent deformation modes of initially orthotropic reinforcements, a physically motivated and invariant based hyperelastic strain energy density is introduced. This constitutive law is used to show the limitations of a classical finite element formulation in 3D fabric simulations. Tension locking is highlighted in bias extension tests and a reduced integration hexahedral finite element with specific physical hourglass stabilization is proposed. Instabilities due to the highly anisotropic behavior law, witnessed in bending dominated situations, are exposed and a stabilization procedure is initiated.

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