Bipenalty method from a frequency domain perspective

Ilanko, Sinniah; Monterrubio, Luis E.

doi:10.1002/nme.4266

Cited by 8 publications

(9 citation statements)

References 27 publications

(56 reference statements)

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“…The critical time step for these schemes is given by (16) where crit is the critical sampling frequency, and ! max is the maximum eigenfrequency of the system [12].…”

Section: Eigenvalue Analysis Of the Bipenalised Systemmentioning

confidence: 99%

“…Estimating the maximum eigenvalue of a system is a well-known problem in explicit FE analysis because, from (16), it is required for the selection of a suitable time step. A simple and efficient method of achieving this is to use direct iteration (also known as power iteration), which may be used to compute the maximum eigenvalue without solving the full eigenvalue problem.…”

Section: Choosing a Penalty Ratio Without Computing The Maximum Eigenmentioning

confidence: 99%

“…However, if we assume that reliable methods are already available for computing a stable time step we can choose a safe penalty ratio directly. Equations (16) and (30) show that by choosing a ratio such that…”

Section: Choosing a Penalty Ratio Without Computing The Maximum Eigenmentioning

confidence: 99%

“…An alternative treatment of the bipenalty method, focussed mainly (although not exclusively) on frequency domain analysis, can also be found in Reference [15], whereas recent work by Ilanko and Monterrubio [16] highlights some of the advantages of the bipenalty method for computing the eigenvalues of constrained systems.…”

Section: Introductionmentioning

confidence: 99%

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The bipenalty method for arbitrary multipoint constraints

Hetherington

Ferran

Askes

2012

Numerical Meth Engineering

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SUMMARYIn finite element (FE) analysis, traditional penalty methods impose constraints by adding virtual stiffness to the FE system. In dynamics, this can decrease the critical time step of the system when conditionally stable time integration schemes are used by introducing spurious modes with high eigenfrequencies. Recent studies have shown that using mass penalties alongside traditional stiffness penalties can mitigate this effect for systems with a one single-point constraint. In the present work, we extend this finding to include systems with an arbitrary set of multipoint constraints. By analysing the generalised eigenvalue problem, we show that the values of spurious eigenfrequencies may be controlled by the choice of stiffness and mass penalty parameters. The method is demonstrated using numerical examples, including a one-dimensional contact-impact formulation and a two-dimensional crack propagation analysis. The results show that constraint imposition using the bipenalty method can be employed such that the critical time step of an analysis is unaffected, whereas also displaying superiority over the mass penalty method in terms of accuracy and versatility.

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“…The critical time step for these schemes is given by (16) where crit is the critical sampling frequency, and ! max is the maximum eigenfrequency of the system [12].…”

Section: Eigenvalue Analysis Of the Bipenalised Systemmentioning

confidence: 99%

Section: Choosing a Penalty Ratio Without Computing The Maximum Eigenmentioning

confidence: 99%

Section: Choosing a Penalty Ratio Without Computing The Maximum Eigenmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The bipenalty method for arbitrary multipoint constraints

Hetherington

Ferran

Askes

2012

Numerical Meth Engineering

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show abstract

“…The bipenalty method initially gained popularity for frequency domain problems, see Ilanko and Ilanko and Monterrubio . In contrast to the stiffness penalty approach, it significantly reduces one or more eigenfrequencies.…”

Section: Introductionmentioning

confidence: 99%

On stability and reflection‐transmission analysis of the bipenalty method in contact‐impact problems: A one‐dimensional, homogeneous case study

Kopačka

Tkachuk

Gabriel

et al. 2017

Numerical Meth Engineering

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Summary The stability and reflection‐transmission properties of the bipenalty method are studied in application to explicit finite element analysis of one‐dimensional contact‐impact problems. It is known that the standard penalty method, where an additional stiffness term corresponding to contact boundary conditions is applied, attacks the stability limit of finite element model. Generally, the critical time step size rapidly decreases with increasing penalty stiffness. Recent comprehensive studies have shown that the so‐called bipenalty technique, using mass penalty together with standard stiffness penalty, preserves the critical time step size associated to contact‐free bodies. In this paper, the influence of the penalty ratio (ratio of stiffness and mass penalty parameters) on stability and reflection‐transmission properties in one‐dimensional contact‐impact problems using the same material and mesh size for both domains is studied. The paper closes with numerical examples, which demonstrate the stability and reflection‐transmission behavior of the bipenalty method in one‐dimensional contact‐impact and wave propagation problems of homogeneous materials.

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Bibliography

2014

The Rayleigh–Ritz Method for Structural Analysis

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Bipenalty method from a frequency domain perspective

Cited by 8 publications

References 27 publications

The bipenalty method for arbitrary multipoint constraints

The bipenalty method for arbitrary multipoint constraints

On stability and reflection‐transmission analysis of the bipenalty method in contact‐impact problems: A one‐dimensional, homogeneous case study

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