A new locking-free formulation for planar, shear deformable, linear and quadratic beam finite elements based on the absolute nodal coordinate formulation

Nachbagauer, Karin; Pechstein, Astrid S.; Irschik, Hans; Gerstmayr, Johannes

doi:10.1007/s11044-011-9249-8

Cited by 92 publications

(32 citation statements)

References 15 publications

(65 reference statements)

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“…Following the work of , the work of elastic forces can be based on Reissner's nonlinear rod theory, see Reissner (1972), as implemented by Simo and Vu-Quoc (1986a), and a continuum mechanics based formulation, using a St. Venant-Kirchhoff material. For the 3D case, see Nachbagauer et al (2011).…”

Section: Virtual Work Of Elastic Forces For Thick Beams With Shear Anmentioning

confidence: 99%

“…The idea of the structural mechanics formulation is to incorporate the strain energy of classical nonlinear rod theories into the ANCF, for details see and Nachbagauer et al (2011). The planar case of Eq.…”

Section: Structural Mechanics Formulationmentioning

confidence: 99%

“…The interested reader is referred to the works by Gerstmayr and Irschik (2008), , Nachbagauer et al (2011 and Gruber et al (2013), in which each of the proposed ANC beam finite elements is tested separately.…”

Section: Evaluation Of the Accuracy And Performance Of Anc Finite Elementioning

confidence: 99%

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The Absolute Nodal Coordinate Formulation

Gerstmayr

Humer

Gruber

et al. 2016

Structure-Preserving Integrators in Nonlinear Structural Dynamics and Flexible Multibody Dynamics

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The key idea of the absolute nodal coordinate formulation (ANCF) is to use slope vectors in order to describe the orientation of the cross-section of structural mechanics components, such as beams, plates or shells. This formulation relaxes the kinematical assumptions of Bernoulli-Euler and Timoshenko beam theories and enables a deformation of the cross-sections. The present contribution shows how to create 2D and 3D structural finite elements based on the ANCF by employing different sets of slope vectors for approximating the cross-sections' orientation. A specific aim of this chapter is to present a unified notation for structural mechanics and continuum mechanics ANC formulations. Particular focus is laid on enhanced formulations for such finite elements that circumvent severe issues like Poisson or shear locking. The performance of these elements is evaluated and a detailed assessment comprising the convergence order, the number of iterations, and Jacobian updates for large deformation benchmark problems is provided.

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Section: Virtual Work Of Elastic Forces For Thick Beams With Shear Anmentioning

confidence: 99%

Section: Structural Mechanics Formulationmentioning

confidence: 99%

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The Absolute Nodal Coordinate Formulation

Gerstmayr

Humer

Gruber

et al. 2016

Structure-Preserving Integrators in Nonlinear Structural Dynamics and Flexible Multibody Dynamics

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“…In general, the stiffness description of ANCF elements is quite cumbersome and several different techniques have been applied to derive the internal elastic forces. Techniques ranging from simple structural mechanics [28] to advanced beam theories [55] or full continuum mechanics [86].…”

Section: Absolute Nodal Coordinate Formulationmentioning

confidence: 99%

“…In previous studies, Lobatto quadrature has been applied for addressing the curvature locking in ANCF beam elements (e.g. [55]). Here, the term in the elastic force vector associated to thickness straining is evaluated using Lobatto quadrature instead of Gaussian quadrature.…”

Section: Numerical Examplesmentioning

confidence: 99%

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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A condensed algorithm for adaptive component mode synthesis of viscoelastic flexible multibody dynamics

Tang

Tian

2020

Numerical Meth Engineering

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A condensed algorithm for adaptive component mode synthesis is proposed to compute the dynamics of viscoelastic flexible multibody systems efficiently and accurately. As studied, the continuous use of modes derived from the initial configuration will lead to poor convergence when dealing with geometric nonlinearity caused by large deformations and overall rotations. The modal reduction at a series of quasi-static equilibrium configurations should be updated accordingly. According to the loss rate of system energy in the updating process of modal bases, an adaptive mode selection is proposed to reserve the optimal modal bases with their modal number automatically so as to achieve a high-accuracy simulation. In the proposed condensed iteration algorithm, the order of reduced dynamic equations in the Newton-Raphson is far less than the number of the unknowns to be discrete in generalized-α scheme. Using an analytical mapping between the two parts of unknowns, the new algorithm solves a small part of the unknowns iteratively and solves the others noniteratively. Therefore, the saving of time cost comes not only from the proposed adaptive component mode synthesis, but also from the proposed condensed iteration algorithm. The modal bases of subsystems are updated by a series of frame-like quasi-static equilibrium configurations independently, in conjunction with the Craig-Bampton method. Thus, the challenges in the model reduced of extensive ranges of stiffness and damping are removed via the successively updated modal bases. Finally, three numerical tests are made to illuminate the high accuracy and efficiency of the new algorithm proposed. K E Y W O R D S absolute nodal coordinate formulation, condensed algorithm for adaptive component mode synthesis, flexible multibody dynamics, modal reductions, viscoelastic damping 1 INTRODUCTION The past few decades have witnessed the development 1-4 of the computational dynamics of flexible multibody systems (FMBS). The geometrically exact beam formulation (GEBF) 2,3 and the absolute nodal coordinate formulation (ANCF) 4 are two promising formulations to handle the complexities of both large deformations and overall rotations. Simo and Vu-Quoc 2,3 developed the GEBF based on Reissner's theory, and the main problem of the GEBF is how to handle the

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A new locking-free formulation for planar, shear deformable, linear and quadratic beam finite elements based on the absolute nodal coordinate formulation

Cited by 92 publications

References 15 publications

The Absolute Nodal Coordinate Formulation

The Absolute Nodal Coordinate Formulation

Rectangular shell elements based on the absolute nodal coordinate formulation

A condensed algorithm for adaptive component mode synthesis of viscoelastic flexible multibody dynamics

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