Efficient Evaluation of the Elastic Forces and the Jacobian in the Absolute Nodal Coordinate Formulation

García-Vallejo, Daniel; Mayo, J.; Escalona, José L.; Domı́nguez, J.

doi:10.1023/b:nody.0000027747.41604.20

Cited by 118 publications

(55 citation statements)

References 15 publications

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“…Note that all stresses in the reference configuration, which can be curved or straight, are zero. Elastic deformations can be expressed as follows [12]:…”

Section: Background On Absolute Nodal Coordinate Formulationmentioning

confidence: 99%

“…As shown elsewhere [12], the elastic force vector can be evaluated as a function of a set of constant matrices that are integrated once in advance at the pre-processing stage.…”

Section: Background On Absolute Nodal Coordinate Formulationmentioning

confidence: 99%

“…3D beams and plates). In order to efficiently evaluate the damping forces involved, an invariantbased algorithm similar to a previous one presented in [12] for elastic forces was developed. As shown elsewhere [12], the computational cost of the simulations can be considerably decreased.…”

Section: Introductionmentioning

confidence: 99%

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An Internal Damping Model for the Absolute Nodal Coordinate Formulation

et al. 2005

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Introducing internal damping in multibody system simulations is important as real-life systems usually exhibit this type of energy dissipation mechanism. When using an inertial coordinate method such as the absolute nodal coordinate formulation, damping forces must be carefully formulated in order not to damp rigid body motion, as both this and deformation are described by the same set of absolute nodal coordinates. This paper presents an internal damping model based on linear viscoelasticity for the absolute nodal coordinate formulation. A practical procedure for estimating the parameters that govern the dissipation of energy is proposed. The absence of energy dissipation under rigid body motion is demonstrated both analytically and numerically. Geometric nonlinearity is accounted for as deformations and deformation rates are evaluated by using the Green-Lagrange strain-displacement relationship. In addition, the resulting damping forces are functions of some constant matrices that can be calculated in advance, thereby avoiding the integration over the element volume each time the damping force vector is evaluated.

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“…Note that all stresses in the reference configuration, which can be curved or straight, are zero. Elastic deformations can be expressed as follows [12]:…”

Section: Background On Absolute Nodal Coordinate Formulationmentioning

confidence: 99%

“…As shown elsewhere [12], the elastic force vector can be evaluated as a function of a set of constant matrices that are integrated once in advance at the pre-processing stage.…”

Section: Background On Absolute Nodal Coordinate Formulationmentioning

confidence: 99%

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An Internal Damping Model for the Absolute Nodal Coordinate Formulation

et al. 2005

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“…Fe denotes the element elastic force vector and Qe is the element external generalized force vector that can be deduced by continuum mechanism approach [43,44]. To improve the computational efficiency, the invariant matrix method [43] can be used to compute the element elastic force, which is computed by the following equation.…”

Section: Equations Of Motionmentioning

confidence: 99%

Dynamic computation of flexible multibody system with uncertain material properties

Luo

Zhang

et al. 2016

Nonlinear Dyn

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Based on the theory of Absolute Nodal Coordinate Formulation (ANCF), this paper proposes a new dynamic computation method to solve the flexible multibody system with uncertain material properties (Young's modulus and Poisson's ratio) that may be induced by the material asymmetric distribution.Rather than traditionally considering an uncertain factor as one single variable in the whole system, the material properties vary continuously in the space domain so that they are described by the random field, which is then discretized to countable random variables using the expansion optimization linear estimation (EOLE) method. The uncertain response of the system is approximated by the Polynomial Chaos (PC) expansion, numerically implemented by a collocation method. We propose and prove an important theory that the collocation method provides the same results as the Gaussian quadrature formula if the roots of the corresponding orthogonal polynomials are used as the collocation points. As a result, the proposed method is a non-intrusive technique that does not modify the original solver but only adds a pre-process and a post-process. The uncertain displacement of system is finally illustrated by an ellipse and ellipsoid, which visually show the uncertainty extent and correlation between different coordinates. The numerical examples show that the proposed method has almost an equivalent accuracy of Monte Carlo simulation but much higher efficiency.

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“…The non-linear Green-Lagrange strain tensor is calculated from the matrix of position vector gradients D, which can be written as follows [17] …”

Section: Continuum Mechanics Approach (Ancf-bc)mentioning

confidence: 99%

Use of the floating frame of reference formulation in large deformation analysis: Experimental and numerical validation

Nada

Hussein

Megahed

et al. 2009

Proceedings of the Institution of Mechanical Engineers, Part K:

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Abstract:The finite-element floating frame of reference (FFR) formulation is used, for the most part, in the small deformation analysis of flexible bodies that undergo large reference displacements. This formulation allows for filtering out systematically complex shapes associated with high frequencies that have no significant effect on the solution in the case of small deformations. The resulting low-order FFR models have been widely used to obtain efficient and accurate solutions for many engineering and physics applications. In this investigation, the use of the FFR formulation in the large deformation analysis is examined, and it is demonstrated that large deformation FFR models can be accurate in applications, where the deformation can be described using simple shapes as it is the case in robot system manipulators. In these cases, the standard finite-element FFR formulation must be used with non-linear strain-displacement relationships that account for the geometric non-linearities. The results obtained using the large deformation FFR models are compared with the results obtained using the large deformation absolute nodal coordinate formulation (ANCF), which does not allow for the use of linear modes. The ANCF models are developed using two different methods for formulating the elastic forces: the basic continuum mechanics approach (ANCF-BC) and the elastic line method (ANCF-EL). While the explicit Adams method can be used to obtain the numerical solution of the FFR model, two implicit integration methods are implemented in order to be able to obtain an efficient solution of the FFR and ANCF models. These implicit integration methods are the RADAU5 method and the Hilber-Hughes-Taylor (HHT) method. In the case of simple large deformation shapes, the simulation results obtained in this study show a good agreement between the FFR and the ANCF solutions. The results also show that, in the case of thin and stiff beams, the coupled deformation modes that result from the use of the ANCF-BC can be a source of numerical and locking problems, as reported in the literature. These ANCF-BC numerical problems can be circumvented using the implicit HHT integration method. Nonetheless, the HHT integrator does not capture high-frequency FFR axial modes which are necessary in order to obtain accurate solutions for high-speed rotating beams. In addition to the comparison with the ANCF solutions, experimental results of a forward dynamics model are used in this study to validate the large deformation FFR numerical solutions. The experimental set-up used in the validation of the numerical solutions is also described in this investigation.

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Efficient Evaluation of the Elastic Forces and the Jacobian in the Absolute Nodal Coordinate Formulation

Cited by 118 publications

References 15 publications

An Internal Damping Model for the Absolute Nodal Coordinate Formulation

An Internal Damping Model for the Absolute Nodal Coordinate Formulation

Dynamic computation of flexible multibody system with uncertain material properties

Use of the floating frame of reference formulation in large deformation analysis: Experimental and numerical validation

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