Improved numerical dissipation for time integration algorithms in structural dynamics

Hilber, Hans M.; Hughes, Thomas J.R.; Taylor, Robert L.

doi:10.1002/eqe.4290050306

Cited by 2,058 publications

(1,071 citation statements)

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“…One possibility for the numerical implementation is to apply a time integration algorithm to the full system of differential algebraic equations. An example for such a time integration algorithm is the HHT integrator as presented in [30,31]. Therefore, the system's Jacobian must be computed, and the following system of equations must be solved:…”

Section: Contact and Friction Forces In The Framework Of Mbsmentioning

confidence: 99%

A complete strategy for efficient and accurate multibody dynamics of flexible structures with large lap joints considering contact and friction

2016

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This paper deals with the dynamics of jointed flexible structures in multibody simulations. Joints are areas where the surfaces of substructures come into contact, for example, screwed or bolted joints. Depending on the spatial distribution of the joint, the overall dynamic behavior can be influenced significantly. Therefore, it is essential to consider the nonlinear contact and friction phenomena over the entire joint. In multibody dynamics, flexible bodies are often treated by the use of reduction methods, such as component mode synthesis (CMS). For jointed flexible structures, it is important to accurately compute the local deformations inside the joint in order to get a realistic representation of the nonlinear contact and friction forces. CMS alone is not suitable for the capture of these local nonlinearities and therefore is extended in this paper with problem-oriented trial vectors. The computation of these trial vectors is based on trial vector derivatives of the CMS reduction base. This paper describes the application of this extended reduction method to general multibody systems, under consideration of the contact and friction forces in the vector of generalized forces and the Jacobian. To ensure accuracy and numerical efficiency, different contact and friction models are investigated and evaluated. The complete strategy is applied to a multibody system containing a multilayered flexible structure. The numerical results confirm that the method leads to accurate results with low computational effort.

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Section: Contact and Friction Forces In The Framework Of Mbsmentioning

confidence: 99%

A complete strategy for efficient and accurate multibody dynamics of flexible structures with large lap joints considering contact and friction

2016

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“…Implicit algorithms, which are unconditionally stable, are commonly preferred over explicit algorithms, which are generally limited by their intrinsic stability limit. Shing et al [15] developed an implicit algorithm based on the implicit algorithm by Hilber et al [16]. In this algorithm, a parameter was induced to control the value of the incremental displacement at each sub-step such that overshooting of the imposed displacement can be avoided.…”

Section: Introductionmentioning

confidence: 99%

Full operator algorithm for hybrid simulation

Hung

El‐Tawil

2009

Earthq Engng Struct Dyn

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SUMMARYOne of the weaknesses of the operator splitting method (OSM) is that its corrector step employs the approximation that incremental forces are linearly related to the tested structure's initial stiffness matrix. This paper presents a new predictor-corrector technique in which the assumptions about the tested structure's response are shifted to the predictor step, which results in an enhancement in overall simulation accuracy, especially for nonlinear structures. Unlike OSM, which splits the displacement and velocity operators into explicit and implicit terms, the new method uses predicted accelerations to compute fully explicit displacement and velocity values in the predictor step. Another advantage of the proposed technique, termed the full operator method (FOM) is that its formulation makes it suitable for both quasi-static and real-time hybrid simulation. The effectiveness of FOM is first evaluated by investigating error propagation in an undamped single degree-of-freedom model. It is shown that the corrector step in FOM is able to significantly suppress aberrant simulation results caused by incorrect estimation of the structure's stiffness matrix. The performance of FOM is demonstrated by exercising two additional models, which exhibit significant inelastic behavior under the prescribed excitation. The simulation results show that the proposed FOM algorithm is capable of producing accurate solutions and that the corrector step is influential in effectively reducing simulation errors. It is also shown that FOM suppresses actuator displacement control errors because of its reliance on measured quantities in the corrector step.

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“…Time-integration effects were considered to be an efficient remedy to prevent the solution from diverging in the vicinity of a bifurcation point. The HHT time integration method (named after the authors' surnames (Hilber et al, 1977)) was used for providing numerical damping in the higher frequency modes. At each time step, the Newton-Raphson iterative process (enhanced with the "Line Search" Method) was performed to solve the non-linear equations.…”

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confidence: 99%

Basic mechanisms of fluting formation and retention in paper

Kulachenko

Gradin

Uesaka

2007

Mechanics of Materials

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Out-of-plane deformations of paper, such as fluting, significantly deteriorate the quality of a printed product. There are several explanations of fluting presented in the literature but there is no unanimously accepted theory regarding fluting formation and retention which is consistent with all field observations. This paper first reviews the existing theories and proposes a mechanism that might give an answer to most of the questions regarding fluting. The fluting formation has been considered as a post-buckling phenomenon which has been analysed with the help of the finite element method. Fluting retention has been modelled by introducing an ink layer over the paper surface with the ink stiffness estimated from experimental results. The impact of fast drying on fluting has been assessed numerically and experimentally. The result of the study suggests that fluting occurs due to small-scale hygro-strain variations, which in turn are caused by the moisture variations created during fast convection (through-air) drying. The result also showed that ink stiffening alone cannot explain the fluting amplitudes observed in practice, but that high drying temperatures promote inelastic (irreversible) deformations in paper and this may itself preserve fluting.

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Improved numerical dissipation for time integration algorithms in structural dynamics

Cited by 2,058 publications

References 5 publications

A complete strategy for efficient and accurate multibody dynamics of flexible structures with large lap joints considering contact and friction

A complete strategy for efficient and accurate multibody dynamics of flexible structures with large lap joints considering contact and friction

Full operator algorithm for hybrid simulation

Basic mechanisms of fluting formation and retention in paper

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