Numerical Inversion of the Laplace Transform by Use of Jacobi Polynomials

Miller, Max K.; Guy, W. T.

doi:10.1137/0703055

Cited by 276 publications

(114 citation statements)

References 3 publications

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“…This method not only has reasonable accuracy for a fairly wide range of Laplace transforms [24], but also is very easy and simple, as compared to other numerical inversions such as Miller and Guy [25]. In (97), only one parameter L is involved, which is suggested by Stehfest [23] to be taken as lower integers, while more than two parameters are involved to other methods for an inversion of the Laplace transform.…”

Section: Resultsmentioning

confidence: 99%

The transient analysis of a conducting crack in magneto-electro-elastic half-space under anti-plane mechanical and in-plane electric and magnetic impacts

Rogowski

2014

Arch Appl Mech

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This paper investigated the fracture behavior of a magneto-electro-elastic material subjected to transient electrical, magnetic and mechanical loads. The "smart" medium contains a straight-line crack, which is parallel to its poling direction and free boundary surface. The Fourier and Laplace transform techniques are used to reduce the problem to the solution of one Fredholm integral equation in Laplace domain and second equation in real domain. The Laplace inversion yields the result in the time domain. The equation in real domain is solved exactly. The semipermeable crack-face magneto-electric boundary conditions are utilized. Field intensity factors of stress, electric displacement, magnetic induction, crack displacement, electric and magnetic potentials and the energy release rate are determined. The electric displacement and magnetic induction of crack interior are discussed. Strong coupling between stress and electric and magnetic field near crack tips has been found. Numerical results are presented, and some conclusions are drawn.

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Section: Resultsmentioning

confidence: 99%

The transient analysis of a conducting crack in magneto-electro-elastic half-space under anti-plane mechanical and in-plane electric and magnetic impacts

Rogowski

2014

Arch Appl Mech

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“…The analytical-numerical methods used in [20,21] are essentially followed in this work. Globally speaking, the Laplace and the Fourier transform techniques are used in resolving the problem [22].…”

Section: Temperature Fieldmentioning

confidence: 99%

Non-Fourier effect and inertia effect analysis of a strip with an induced crack under thermal shock loading

Song

et al. 2016

Engineering Fracture Mechanics

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a b s t r a c tIn this paper, the transient temperature fields and the dynamic stress intensity factors of a thermo-elastic strip containing an inner crack parallel to the heated surface under thermal shock are studied. The Biot number of the crack gap, hyperbolic heat conduction theory and equation of motion are considered to investigate the behavior of the temperature fields around the crack and the stress intensity factors. Fourier transform and Laplace transform are used to reduce this mixed boundary value problem. Numerical methods are used to solved the singular integrate equations. Finally, the numerical results are presented illustrating the influence of Biot number, non-Fourier effect and inertia effect on temperature field and stress intensity factors. It is found that the Biot number strongly affect the uniformity of the temperature field and the magnitude of the stress intensity factors. The stress intensity factors have higher amplitude and an oscillating feature comparing to those obtained under conventional Fourier thermal conduction condition and quasi-static hypothesis, which can help to better understand the crack behaviors of advanced materials under thermal impact loading.

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“…The analyticalnumerical methods used in [30,31] are essentially followed in this work. Globally speaking, the Laplace and the Fourier transform techniques are used in resolving the problem [19,20,32].…”

Section: Resolution Of the Governing Equationsmentioning

confidence: 99%

Inertia effect analysis of a half‐plane with an induced crack under thermal loading using hyperbolic heat conduction

Abdelmoula

et al. 2015

Z Angew Math Mech

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This paper considers the crack problem for a semi-infinite plate subjected to a thermal shock by using hyperbolic heat conduction equations and equations of motion. The Laplace transform and Fourier transform are used to reduce the problem to a system of singular integral equations which are solved numerically. Numerical results are presented illustrating the influence of non-Fourier effect and inertia effect on the stress intensity factor and normalized crack opening displacements. The results show that the stress intensity factors have higher amplitude and an oscillating feature comparing to those obtained under the conventional Fourier thermal conduction condition and quasi-static hypothesis. These results can help understand the crack behaviors of advanced materials under thermal impact loading.

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Numerical Inversion of the Laplace Transform by Use of Jacobi Polynomials

Cited by 276 publications

References 3 publications

The transient analysis of a conducting crack in magneto-electro-elastic half-space under anti-plane mechanical and in-plane electric and magnetic impacts

The transient analysis of a conducting crack in magneto-electro-elastic half-space under anti-plane mechanical and in-plane electric and magnetic impacts

Non-Fourier effect and inertia effect analysis of a strip with an induced crack under thermal shock loading

Inertia effect analysis of a half‐plane with an induced crack under thermal loading using hyperbolic heat conduction

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