A new family of explicit time integration methods for linear and non‐linear structural dynamics

Chung, Jintai; Lee, Jang Moo

doi:10.1002/nme.1620372303

Cited by 143 publications

(101 citation statements)

References 18 publications

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“…These are commercial FE packages that use an explicit time integra-593 tion scheme [261,[264][265][266][267][268][269][270][271][272][273][274] during the solution phase to solve for time-varying acceleration, velocity, and 594 displacement results.…”

Section: Explicit Dynamic Fe Models 590mentioning

confidence: 99%

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An extensive review of vibration modelling of rolling element bearings with localised and extended defects

Singh

Howard

Hansen

2015

Journal of Sound and Vibration

124

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This paper presents a review of literature concerned with the vibration modelling of rolling element bearings that have localised and extended defects. An overview is provided of contact fatigue, which initiates subsurface and surface fatigue spalling, and subsequently leads to reducing the useful life of rolling element bearings. A review is described of the development of all analytical and finite element (FE) models available in the literature for predicting the vibration response of rolling element bearings with localised and extended defects. Low-and high-frequency vibration signals are generated at the entry and exit of the rolling elements into and out of a bearing defect, respectively. The development of this finding is described along with analytical models to approximate these vibration signals. Algorithms to estimate the size of bearing defects are reviewed and their limitations are discussed. A summary of the literature is presented followed by recommendations for future research.

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Section: Explicit Dynamic Fe Models 590mentioning

confidence: 99%

“…Unlike the analytical 537 models, one can minimise the assumptions in FE methods and achieve comparatively better results; however, schemes. These schemes include implicit [256][257][258][259][260][261][262][263] and explicit [261,[264][265][266][267][268][269][270][271][272][273][274] time integration methods.…”

mentioning

confidence: 99%

An extensive review of vibration modelling of rolling element bearings with localised and extended defects

Singh

Howard

Hansen

2015

Journal of Sound and Vibration

124

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“…(1), additional relations, the so-called time integration scheme equations, which express relations between displacements, velocities and accelerations at the current time and at the next time are also needed. They should also be consistent [4,[6][7][8]. This leads to the set of equations which constitute the system or the problem to be solved:…”

Section: Time Integration Of a Finite-elements Discretizationmentioning

confidence: 99%

“…To control these spurious frequencies, numerical dissipation can be introduced in time integration schemes. Although numerical dissipation has been widely used in combination with implicit scheme to enhance the convergence of the iterations, some recent works have shown interest in numerical dissipation when dealing with explicit schemes and non-linear dynamics [4][5][6][7][8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Comparative study of numerical explicit schemes for impact problems

Nsiampa

Ponthot

Noels

2008

International Journal of Impact Engineering

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Explicit numerical schemes are used to integrate in time finite element discretization methods. Unfortunately, these numerical approaches can induce high-frequency numerical oscillations into the solution. To eliminate or to reduce these oscillations, numerical dissipation can be introduced. The paper deals with the comparison of three different explicit schemes: the central difference scheme which is a nondissipative method, the Hulbert Chung dissipative explicit scheme and the Tchamwa-Wielgosz dissipative scheme. Particular attention is paid to the study of these algorithms' behavior in problems involving high-velocity impacts like Taylor anvil impact and bullet-target interactions. It has been shown that Tchamwa-Wielgosz scheme is efficient in filtering the high-frequency oscillations and is more dissipative than Hulbert Chung explicit scheme. Although its convergence rate is only first order, the loss of accuracy remains limited to acceptable values.

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“…In order to develop the Green/Newmark method (ImGA/Newmark), Newmark method expressions are employed initially to establish expressions that permit to compute the model Green's function as well as its time derivatives at time t. Subsequently the expressions obtained are introduced in the recurrence relations shown by Equation (10).…”

mentioning

confidence: 99%

A time domain FEM approach based on implicit Green's functions for non‐linear dynamic analysis

Soares

Mansur

2004

Numerical Meth Engineering

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SUMMARYThe present paper describes an unconditionally stable algorithm to integrate the equations of motion in time. The standard FEM displacement model is employed to perform space discretization, and the time-marching process is carried out through an algorithm based on the Green's function of the mechanical system in nodal co-ordinates. In the present 'implicit Green's function approach' (ImGA), mechanical system Green's functions are not explicitly computed; rather they are implicitly considered through an iterative pseudo-forces process. Under certain simplifying hypothesis, iterations are not necessary and the ImGA becomes cheaper than standard Newmark/Newton-Raphson algorithm. At the end of the paper numerical examples are presented in order to illustrate the accuracy of the present approach.

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A new family of explicit time integration methods for linear and non‐linear structural dynamics

Cited by 143 publications

References 18 publications

An extensive review of vibration modelling of rolling element bearings with localised and extended defects

An extensive review of vibration modelling of rolling element bearings with localised and extended defects

Comparative study of numerical explicit schemes for impact problems

A time domain FEM approach based on implicit Green's functions for non‐linear dynamic analysis

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