The dynamics of an elliptical crack in an elastic space: Solution using padé approximations

Kaptsov, Alexander V.; Shifrin, E. I.

doi:10.1016/0021-8928(91)90048-y

Cited by 4 publications

(4 citation statements)

References 10 publications

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“…In this table, three decimal places are given to compare with [41]. It should be also noted that due to different introduction of the Fourier transform, the real and imaginary parts of the eigenfrequencies calculated in this study and by Kaptsov and Shifrin [41] change places.…”

Section: Eigenfrequenciesmentioning

confidence: 92%

Section: Eigenfrequenciesmentioning

confidence: 99%

“…The eigenfrequencies of an open circular crack in the homogeneous space made of glass calculated by the present BIEM have been compared with [41], where the first three eigenfrequencies were computed using Padé approximations: the results of comparison are given in Table 3. In this table, three decimal places are given to compare with [41]. It should be also noted that due to different introduction of the Fourier transform, the real and imaginary parts of the eigenfrequencies calculated in this study and by Kaptsov and Shifrin [41] change places.…”

Section: Eigenfrequenciesmentioning

confidence: 99%

“…The BIEM is efficient for the solution of the scattering problem for strip-like [24][25][26], penny-shaped [24,[27][28][29][30][31][32][33][34][35], elliptic [36], rectangular [37,38] arbitrary shaped [39] cracks. In the 1990s, location of the resonance poles or eigenfrequencies in the complex frequency plane for an elastic space was investigated for circular crack [40], elliptical crack [41] as well as rectangular and L-shaped cracks [38]. Boundary integral equations derived for a crack in a homogeneous space can be uncoupled into two equations, which is not possible for interface cracks between two dissimilar media.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of Eigenfrequencies of a Circular Interface Delamination in Elastic Media Based on the Boundary Integral Equation Method

Golub

Doroshenko

2021

Mathematics

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The widespread of composite structures demands efficient numerical methods for the simulation dynamic behaviour of elastic laminates with interface delaminations with interacting faces. An advanced boundary integral equation method employing the Hankel transform of Green’s matrices is proposed for modelling wave scattering and analysis of the eigenfrequencies of interface circular partially closed delaminations between dissimilar media. A more general case of partially closed circular delamination is introduced using the spring boundary conditions with non-uniform spring stiffness distribution. The unknown crack opening displacement is expanded as Fourier series with respect to the angular coordinate and in terms of associated Legendre polynomials of the first kind via the radial coordinate. The problem is decomposed into a system of boundary integral equations and solved using the Bubnov-Galerkin method. The boundary integral equation method is compared with the meshless method and the published works for a homogeneous space with a circular open crack. The results of the numerical analysis showing the efficiency and the convergence of the method are demonstrated. The proposed method might be useful for damage identification employing the information on the eigenfrequencies estimated experimentally. Also, it can be extended for multi-layered composites with imperfect contact between sub-layers and multiple circular delaminations.

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Section: Eigenfrequenciesmentioning

confidence: 92%

Section: Eigenfrequenciesmentioning

confidence: 99%

Section: Eigenfrequenciesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Analysis of Eigenfrequencies of a Circular Interface Delamination in Elastic Media Based on the Boundary Integral Equation Method

Golub

Doroshenko

2021

Mathematics

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Padé approximants for the numerical solution of singular integral equations

Tsamasphyros

Theotokoglou

1999

Computational Mechanics

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A method for accelerating the convergence of the numerical solution of a singular integral equation, based on Pade Â Approximants, is given in this paper. At ®rst the general form of the Pade Â Table and of the``epsilon'' algorithm are presented. Taking into consideration the classical quadrature method, based on the GaussJacobi quadrature rule, an approximate formula is derived for the unknown density function of the Cauchy-type singular integral equation or of the equivalent Fredholm integral equation. In this formula applying the``epsilon'' algorithm to the solution for the stress intensity factors, the convergence is achieved after a few operations. The number of numerical operations required for the determination of stress intensity factors is considerable reduced, when compared to the number of operations required for a classical type of solution. Illustrative examples are given, indicating the ef®ciency of the method.

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