Review on the Absolute Nodal Coordinate Formulation for Large Deformation Analysis of Multibody Systems

Gerstmayr, Johannes; Sugiyama, Hiroyuki; Mikkola, Aki

doi:10.1115/1.4023487

Cited by 154 publications

(78 citation statements)

References 102 publications

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“…While this objective was addressed in previous publications [23], the main contribution of this paper is to show the importance of volumetric locking elimination in the applications when bending-dominated models are considered. For a detailed overview of the locking phenomena occurring within ANCF framework as well as general review of developments in ANCF, consult [14,26]. Moreover, exemplary techniques that may reduce the locking influence on the results are presented and validated with several numerical examples.…”

Section: Introductionmentioning

confidence: 99%

Nearly incompressible nonlinear material models in the large deformation analysis of beams using ANCF

Orzechowski

Frączek

2015

Nonlinear Dyn

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Many modern applications of the flexible multibody systems require formulations that can effectively solve problems that include large displacements and deformations having the ability to model nonlinear materials. One method that allows dealing with such systems is continuum-based absolute nodal coordinate formulation (ANCF). The objective of this study is to formulate an efficient method of modeling nonlinear nearly incompressible materials with polynomial Mooney-Rivlin models and volumetric energy penalty function in the framework of the ANCF. The main part of this paper is dedicated to the examination of several ANCF fully parameterized beam elements under incompressible regime. Moreover, two volumetric suppression methods, originating in the finite element analysis, are proposed: a well-known selective reduced integration and F-bar projection. It is also presented that the use of these methods is crucial for performing reliable analysis of models with bending-dominated loads when lower-order elements are employed. The results of the simulations carried on with considered elements and proposed methods are compared with the results obtained from commercial finite element package and existing ANCF implementation. The results

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Section: Introductionmentioning

confidence: 99%

Nearly incompressible nonlinear material models in the large deformation analysis of beams using ANCF

Orzechowski

Frączek

2015

Nonlinear Dyn

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“…In the literature, C 1 continuity is mentioned as a theoretically indispensable requirement when the element stiffness properties are calculated based on element curvature [101,29]. This is due to the fact that the curvature of the overall displacement field will be infinite at the boundary between two adjacent elements if there is a discontinuity in the slope.…”

Section: Discussion On the Kinematics Of Thin Ancf Shell Elementsmentioning

confidence: 99%

“…The ANCF is based in the multibody dynamics community and uses a more consistent kinematic description based on nodal positions and slope vectors defined with respect to a fixed global reference frame. The ANCF has certain advantages when it comes to implementation in the multibody dynamics framework [29]. Due to this, the method has gained much attention in the multibody dynamics research community.…”

Section: Flexible Multibody Dynamicsmentioning

confidence: 99%

“…The calculation of the curvatures κ of ANCF elements has been subject to much discussion and several approaches have been suggested [19,27,29]. In this study, the curvature of the thin ANCF shell elements is calculated as suggested in the original papers regarding thin ANCF shell elements [19,21]:…”

Section: Structural Mechanics Approachmentioning

confidence: 99%

“…For that element, the curvature is calculated using second order derivatives of the position field. As mentioned earlier, C 1 continuous interpolation is recommended when the element curvature is calculated using higher order derivatives [101,29]. However, the interpolation used for the quadratic shear and thickness deformable elements ensures only C 0 continuous interpolation, which is the reason that this different approach is chosen.…”

Section: Elastic Forcesmentioning

confidence: 99%

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Rectangular shell elements based on the absolute nodal coordinate formulation

Hyldahl¹

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This thesis concerns the development of tools that are useful for designing machine systems and components in an virtual environment using flexible multibody dynamics. Initially, flexible multibody dynamics is briefly reviewed to explain available formalisms and possible applications of this method. Subsequently, attention is turned towards the analysis of structures that undergo large deformations and rotations using shell finite elements based on the absolute nodal coordinate formulation, ANCF. This topic is the focus for the remainder of the thesis.The thesis is divided into three main parts. The first part acts as a general introduction to ANCF based shell finite elements and sums up available elements found in the research literature. In the end, a new ANCF element developed during this PhD project is presented which gives enhanced modeling capabilities of problems including e.g. moving boundary conditions. The second part concerns the performance and behavior of a certain class of ANCF shell elements that are developed for analysis of thin shell structures. This includes discussions on differences concerning their kinematic descriptions and disclosure of certain issues regarding their performance. Those being sensitivity to irregular mesh, pour representation of curved structures and load dependent convergence when analyzing curved structures.The final part concerns the development of a new versatile ANCF shell element. This element is distinguished by being able to describe both thin and thick curved structures. This part contains a thorough derivation of its kinematics and stiffness description, as well as numerical examples to demonstrate its performance. However, this part of the study is not yet complete.Finally, the findings of this PhD project are summed up in a conclusion and possibilities for further studies and perspectives are outlined.v ResuméDenne afhandling omhandler udviklingen af vaerktøjer, som er nyttige til at designe maskiner og maskindele i et virtuelt miljø vha. fleksibel flerlegemedynamik. Indledningsvist gives der en kort gennemgang af den fleksible flerlegeme-dynamik, for at give et overblik over metoden og dens mulige anvendelser. Dernaest flyttes opmaerksomheden over på analyse af strukturer som udsaettes for store deformationer og rotationer vha. endelige skalelementer (eng: shell finite elements) baseret på absolutte knude koordinater (eng: absolute nodal coordinate formulation, ANCF). Dette emne vil vaere fokus i resten af afhandlingen.Afhandlingen er inddelt i 3 dele. Den første del giver en general introduktion til ANCF skal-elementer, og opsummerer de forskellige elementklasser som kan findes i litteraturen. Mod slutningen introduceres der et nyt ANCF skal-element, som er udviklet under dette ph.d.-projekt. Dette element muliggør forbedret modellering af problemer med mobile randbetingelser.Anden del omhandler effektiviteten og egenskaberne hos en saerlig klasse af ANCF skal-elementer, som er udviklet specielt til analyse af tynde skalstrukturer. Heri diskuteres der...

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Explicit free‐floating beam element

Nielsen

Krenk

2014

Numerical Meth Engineering

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SUMMARYA two-node free-floating beam element capable of undergoing arbitrary large displacements and finite rotations is presented in explicit form. The configuration of the beam in three-dimensional space is represented by the global components of the position of the beam nodes and an associated set of convected base vectors (directors). The local constitutive stiffness is derived from the complementary energy of a set of six independent deformation modes, each corresponding to an equilibrium state of constant internal force or moment. The deformation modes are characterized by generalized strains, formed via scalar products of the element related vectors. This leads to a homogeneous quadratic strain definition in terms of the generalized displacements, whereby the elastic energy becomes at most bi-quadratic. Additionally, the use of independent equilibrium modes to set up the element stiffness avoids interpolation of kinematic variables, resulting in a locking-free formulation in terms of three explicit matrices. A set of classic benchmark examples illustrates excellent performance of the explicit beam element.

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Review on the Absolute Nodal Coordinate Formulation for Large Deformation Analysis of Multibody Systems

Cited by 154 publications

References 102 publications

Nearly incompressible nonlinear material models in the large deformation analysis of beams using ANCF

Nearly incompressible nonlinear material models in the large deformation analysis of beams using ANCF

Rectangular shell elements based on the absolute nodal coordinate formulation

Explicit free‐floating beam element

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