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Kaminskii, A. A.; Zatula, N. I.; Dyakon, V. N.

doi:10.1023/a:1016079000224

Cited by 5 publications

(2 citation statements)

References 3 publications

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“…The detailed derivation of expressions (34) and (35) can be found in [Stehfest 1970;Kumar 2000]. The number of terms N St in the series is relatively small and usually varies in the range 2 ≤ N St ≤ 20 that makes the calculation procedure fast in comparison with some other methods; see the charts in [Davies and Martin 1979].…”

Section: Basic Equationsmentioning

confidence: 99%

Viscoelastic state of a semi-infinite medium with multiple circular elastic inhomogeneities

Pyatigorets

Mogilevskaya

2009

J. Mech. Mater. Struct.

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This paper is concerned with the problem of an isotropic, linear viscoelastic half-plane containing multiple, isotropic, circular elastic inhomogeneities. Three types of loading conditions are allowed at the boundary of the half-plane: a point force, a force uniformly distributed over a segment, and a force uniformly distributed over the whole boundary of the half-plane. The half-plane is subjected to farfield stress that acts parallel to its boundary. The inhomogeneities are perfectly bonded to the material matrix. An inhomogeneity with zero elastic properties is treated as a hole; its boundary can be either traction free or subjected to uniform pressure. The analysis is based on the use of the elastic-viscoelastic correspondence principle. The problem in the Laplace space is reduced to the complementary problems for the bulk material of the perforated half-plane and the bulk material of each circular disc. Each problem is described by the transformed complex Somigliana's traction identity. The transformed complex boundary parameters at each circular boundary are approximated by a truncated complex Fourier series. Numerical inversion of the Laplace transform is used to obtain the time domain solutions everywhere in the half-plane and inside the inhomogeneities. The method allows one to adopt a variety of viscoelastic models. A number of numerical examples demonstrate the accuracy and efficiency of the method.

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Section: Basic Equationsmentioning

confidence: 99%

Viscoelastic state of a semi-infinite medium with multiple circular elastic inhomogeneities

Pyatigorets

Mogilevskaya

2009

J. Mech. Mater. Struct.

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“…In accordance with [2,8], unknown densities of potentials for n-th boundary element of the p-th inclusion were approximated using the function f ( x…”

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confidence: 99%

Mathematical modeling of the stressed state of a viscoelastic half-plane with inclusions

Zatula

2022

BKNUPhM

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The application of the method of boundary integral equations is considered for studying the stress state of flat viscoelastic bodies with inclusions. The method is based on the use of complex potentials and the apparatus of generalized functions. An analytical solution of the problem is obtained for a half-plane with inclusions of arbitrary shape. For a numerical study of the change in the stress state depending on the time and geometry of the inclusions, a discrete analogue of the system of boundary-time integral equations has been developed.

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A time domain direct boundary integral method for a viscoelastic plane with circular holes and elastic inclusions

Huang

Crouch

Mogilevskaya

2005

Engineering Analysis with Boundary Elements

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Cited by 5 publications

References 3 publications

Viscoelastic state of a semi-infinite medium with multiple circular elastic inhomogeneities

Viscoelastic state of a semi-infinite medium with multiple circular elastic inhomogeneities

Mathematical modeling of the stressed state of a viscoelastic half-plane with inclusions

A time domain direct boundary integral method for a viscoelastic plane with circular holes and elastic inclusions

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