A high precision direct integration scheme for structures subjected to transient dynamic loading

Lin, J. H.; Shen, Wei; Williams, Frederick W.

doi:10.1016/0045-7949(94)00537-d

Cited by 89 publications

(42 citation statements)

References 2 publications

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“…For the systems with applied loading, Zhong [2] established the HPD-L algorithm, in which the loading is simulated by piecewise linear loading within a time-step. Lin et al [3] proposed HPD-F that is based on Fourier expansion and the theory of di erential equation:…”

Section: Introductionmentioning

confidence: 99%

Homogenized high precision direct integration scheme and its applications in engineering

Wang

Tian

Gang

2002

Commun. Numer. Meth. Engng.

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SUMMARYDynamics response of systems to impact or loading may be e ectively treated by direct integration. However, it is often di cult to select the time-step of integration properly, especially in the case where the system is badly sti . Zhong presented an explicit direct integration scheme, HPD, for the homogeneous systems. This paper extends HPD scheme to analyse systems with loading or impact, through Fourier expansion and homogenizing the initial system. Compared with other methods, the new scheme named homogenized high-precision direct integration (HHPD) has a higher precision and wider application and is less time-consuming, and several examples in this paper show HHPD's e ectiveness in engineering.

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Section: Introductionmentioning

confidence: 99%

Homogenized high precision direct integration scheme and its applications in engineering

Wang

Tian

Gang

2002

Commun. Numer. Meth. Engng.

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“…In the past decades, expanding dimension methods 8,[19][20][21][22] were widely used for the nonhomogeneous dynamic systems. The nonhomogeneous loading form could be classified into three types: the polynomial loading form, the sinusoidal loading form, and the arbitrary loading form.…”

Section: Time-varying Systems and Their Homogenized Formsmentioning

confidence: 99%

A modified homogenized highly precise direct integration method for time-varying nonhomogeneous systems

Zhu

Zhou

Liu

et al. 2017

Advances in Mechanical Engineering

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This article investigates a novel method for time-varying systems with an impact term; we call it a modified homogenized highly precise direct integration method. Modified homogenized highly precise direct integration method can deal with the time-varying nonhomogeneous systems effectively by direct integration with high precision. Even though it is often difficult to select the time step size of integration properly for stiff problems, modified homogenized highly precise direct integration method can effectively deal with the this problem with a large time step size. By introducing new variants twice, modified homogenized highly precise direct integration method can easily deal with the nonhomogeneous term by a novel way, inherit the advantages of highly precise direct integration method and avoid the calculation of inverse matrix. The convergency and efficiency analyses are given in this article. Several numerical simulations and an application example are presented to demonstrate the high accuracy, effectiveness and application for engineering problems of modified homogenized highly precise direct integration method.

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“…Meanwhile, Lin [3] HPD-F method, wh ich is based on Fourier expansion, is also proposed. However, HPD-L and HPD-F have to co mpute the inverse matrix.…”

Section: Introductionmentioning

confidence: 99%

A High Precision Direct Integration Scheme Based on Variational Principle and Its Applications

Zhu

Gang

Liu

et al. 2016

MATEC Web of Conferences

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Abstract. Dynamics response of systems to impact or loading may be effectively treated by direct integration. However, it is often difficult to select the time-step of integration properly, especially in the case wh ich the system is badly stiff. High Precision Direct integration based on variational principle is given (HP D-VP) for homogeneous systems and HHPD-VP method for the nonhomogeneous systems are given. This method not only takes the advantage of variational principle formula, which is m uch precise an d is stiff A-stable, but also can avoid the truncation error of the computer. For the large systems, especially, the systems with different frequency or the stiff systems, our methods are stable, accurate and efficient. Numerical experiments show the convergence order of the scheme derived from the variational principle, and is much precise and is effective in engineering.

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A high precision direct integration scheme for structures subjected to transient dynamic loading

Cited by 89 publications

References 2 publications

Homogenized high precision direct integration scheme and its applications in engineering

Homogenized high precision direct integration scheme and its applications in engineering

A modified homogenized highly precise direct integration method for time-varying nonhomogeneous systems

A High Precision Direct Integration Scheme Based on Variational Principle and Its Applications

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