Higher-order beam elements based on the absolute nodal coordinate formulation for three-dimensional elasticity

Ebel, Henrik; Matikainen, Marko K.; Hurskainen, Vesa-Ville; Mikkola, Aki

doi:10.1007/s11071-016-3296-x

Cited by 44 publications

(30 citation statements)

References 16 publications

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“…Numerical examples show that these two beam elements of ANCF are all locking-alleviated 12,14 and have the same order of convergence compared with Reissner's shear deformation beam. 11,12 Henrik Ebel et al 16 and Patel et al 8 recently proposed several higher-order beam elements of locking alleviation, and Patel et al 8 pointed out that the linear interpolation considered in the transverse direction is one of the main reasons for the poor performance of the standard formulation based on continuum mechanics. Because the use of Hooke's law in this case leads to a stiff behavior in the response to nonuniform strain distribution like bending.…”

Section: Modeling Approach and Criterion Of Truncation Errorsmentioning

confidence: 99%

“…The Princeton beam of concern is a cantilevered beam undergoing large static displacement and rotation of a gravitational tip load. 13,16,71,72 The beam has served as a benchmark to assess the accuracy of the model formulations. Figure 5 shows the configuration, geometric parameters and material parameters of the beam, respectively.…”

Section: Dynamics Of a Princeton Beammentioning

confidence: 99%

“…[9][10][11][12][13] A variety of locking mechanisms have been thoroughly studied in the community of finite elements, because many classical finite elements may also suffer from locking problems. 8 For a detailed discussion or quantification about the locking alleviation techniques for ANCF, one can refer to the work of Nachbagauer, 12,14 Bauchau et al, 13 Gerstmayr et al, 15 Henrik Ebel et al, 16 and Patel et al 8 In addition, the ANCF 11,12,14 can be modified according to the strain energy defined by Simo and Vu-Quoc with fully equivalent static and dynamics behaviors compared with Reissner's shear deformation beam. 11,12 Both formulations above have seen successful applications in the field of flexible multibody dynamics.…”

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confidence: 99%

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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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Section: Modeling Approach and Criterion Of Truncation Errorsmentioning

confidence: 99%

Section: Dynamics Of a Princeton Beammentioning

confidence: 99%

mentioning

confidence: 99%

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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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“…In conclusion, these elements suffer from Poisson locking, and similar to the findings for beam elements in previous studies, approximations of at least second order in all directions seem to be a functional remedy for Poisson locking. 8 The linear element 3423, however, suffers from a variety of severe locking phenomena and hence delivers results with absolute values that are approximately an order of magnitude smaller than the reference value.…”

Section: Cantilevered Platementioning

confidence: 99%

“…In previous studies, an approach that does not employ in-plane slope vectors has delivered promising results for three-node ANCF beam elements that make use of the St. Venant-Kirchhoff material law. 8 The objective of this article is to extend this recently introduced approach of the usage of a high polynomial order in all three directions without the use of in-plane slopes to plate applications. This extension makes it possible to employ full three-dimensional elasticity in the definition of the elastic forces.…”

Section: Introductionmentioning

confidence: 99%

Analysis of high-order quadrilateral plate elements based on the absolute nodal coordinate formulation for three-dimensional elasticity

Ebel

Matikainen

Hurskainen

et al. 2017

Advances in Mechanical Engineering

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The absolute nodal coordinate formulation is a computational approach to analyze the dynamic performance of flexible bodies experiencing large deformations in multibody system dynamics applications. In the absolute nodal coordinate formulation, full three-dimensional elasticity can be used in the definition of the elastic forces. This approach makes it straightforward to implement advanced material models known from general continuum mechanics in the absolute nodal coordinate formulation. As, however, pointed out in the literature, the use of full three-dimensional elasticity can lead to severe locking problems, already present in simple, static tests. To overcome these drawbacks and to get a better understanding of these behaviors in the case of absolute nodal coordinate formulation elements, this study introduces and carefully analyses several high-order three-dimensional plate elements based on the absolute nodal coordinate formulation, primarily in meaningful static scenarios. The proposed elements are put to test in various numerical experiments intended to bring forward possible locking phenomena and to evaluate the accuracy attainable with the considered element formulations. The proposed eight-and nine-node elements that incorporate polynomial approximations of second order in all three directions prove to be advantageous both with respect to the actual performance and with regard to the numerical efficiency when compared to other absolute nodal coordinate formulation plate elements. A comparison with a four-node high-order element corroborates the supposition that the usage of in-plane slopes as nodal coordinates has a negative effect on numerical convergence properties in thin-plate use cases. An additional example showcases the functioning of two of the higher-order elements in a dynamic simulation.

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Locking alleviation in the large displacement analysis of beam elements: the strain split method

Patel

Shabana

2018

Acta Mech

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This paper proposes a new locking alleviation technique for absolute nodal coordinate formulation (ANCF) beam and plate elements based on a strain split approach. The paper also surveys classical finite element (FE) and ANCF locking alleviation techniques discussed in the literature. Because ANCF beam elements, which allow for the cross section stretch, fully capture the Poisson effect, Poisson locking is an issue when such beam elements are considered. The two-dimensional fullyparameterized ANCF beam element is primarily used in this investigation because such an element can serve as a good surrogate model for three-dimensional ANCF beams and plates as far as membrane, bending and transverse shearing behavior is concerned. In addition to proposing the strain split method (SSM) for ANCF locking alleviation, this work assesses the ANCF FE performance in the cases of higher-order interpolation, enhanced assumed strain method, elastic line method, and the enhanced continuum mechanics approach; and demonstrates the design of the enhanced strain interpolation function by using the shape functions of higher-order ANCF elements. Additionally, a new higher-order ANCF two-dimensional beam element is proposed in order to compare its performance with other finite elements that require the use of other locking alleviation techniques proposed and reviewed in the paper. Finally, several numerical examples are shown to demonstrate the effectiveness of the locking alleviation methods applied to ANCF elements. The purpose of this investigation, apart from proposing a new locking alleviation technique, a new higher-order beam element, and comparing several existing locking alleviation techniques, is to show that dealing with locking in fully-parameterized ANCF elements is feasible and that several methods exist to effectively improve the ANCF element performance without sacrificing important ANCF element properties and features including position vector gradient continuity. Because of the use of ANCF position vector gradients as nodal coordinates, complex stress-free initially-curved geometries can be systematically obtained. Such initially-curved geometries require special attention when attempting to solve locking problems, as will be discussed in this paper.

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Higher-order beam elements based on the absolute nodal coordinate formulation for three-dimensional elasticity

Cited by 44 publications

References 16 publications

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

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

Analysis of high-order quadrilateral plate elements based on the absolute nodal coordinate formulation for three-dimensional elasticity

Locking alleviation in the large displacement analysis of beam elements: the strain split method

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