Quasistatic elastic-plastic loading and unloading of rods with coulomb dry friction

Mamatova, Nigora

doi:10.1051/e3sconf/202126401040

Cited by 3 publications

(4 citation statements)

References 7 publications

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“…6. Changes in the wave parameters in time and coordinate practically coincide with the results of problems with friction (4)- (5). Fig.…”

Section: The Case Of Friction Of the Kelvin-voigt Typesupporting

confidence: 77%

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Wave propagation in a cylindrical body in the presence of surface forces depending on the relative displacement

Rikhsieva,

Khusanov

2023

E3S Web of Conf.

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Studies of wave propagation in extended bodies with external friction have a wide range of applications and are significant for various engineering and scientific fields. They contribute to the development of new technologies, improve the design and construction of structures, and expand our understanding of the physical processes occurring in various materials and media. In this article, axisymmetric two-dimensional problems of the propagation of longitudinal waves in a cylindrical body are numerically solved in the presence of surface friction forces of the Winkler and Kelvin-Voigt types. For the numerical solution, the Wilkins scheme of the finite difference method was used. The influence of friction forces on the wave parameters is revealed. It is determined that the results of the considered problems are between solutions using slippery contact without friction and with friction according to the Coulomb law. A 5-7% deviation of the hypothesis of flat sections is shown, which makes it possible to reduce such a problem to a one-dimensional formulation.

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“…6. Changes in the wave parameters in time and coordinate practically coincide with the results of problems with friction (4)- (5). Fig.…”

Section: The Case Of Friction Of the Kelvin-voigt Typesupporting

confidence: 77%

“…the forces acting on the outer surface of an extended body are included in the equations of motion [1][2][3][4]. Many problems [5][6][7][8][9], applied in the field of seismic resistance of underground pipelines, were solved in this formulation, with various types of external frictions.…”

Section: Introductionmentioning

confidence: 99%

Wave propagation in a cylindrical body in the presence of surface forces depending on the relative displacement

Rikhsieva,

Khusanov

2023

E3S Web of Conf.

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“…Thus, the solution to the systems of equations ( 1)-( 4) is required with the corresponding initial (5) and boundary ( 6), (7) conditions. When solving by the difference method, it is convenient to take a finite difference scheme [20] using a quadrangular grid.…”

Section: Statement Of the Problemmentioning

confidence: 99%

“…There is only a limited range of problems solved analytically, that take into account the elasticplastic properties of soils. In some cases, this is achieved by setting specific boundary conditions [5][6][7], in other cases, by considering some idealized cases of deformation [8][9][10]. This does not detract from the merits of analytical methods of solution but focuses on the need to use a numerical method.…”

Section: Introductionmentioning

confidence: 99%

Accuracy and stability of a finite difference scheme for two-dimensional problems of soil dynamics

Rikhsieva,

Khusanov

2023

E3S Web Conf.

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Problems of numerical methods for calculating hyperbolic systems of equations with several variables are considered topical. At present, for most technical issues, the solution to one-dimensional non-stationary problems can be conducted with sufficient accuracy. It is too early to assert the mass solution of three-dimensional problems. Therefore, the present study is focused on the consideration of the accuracy and stability of the two-dimensional difference method for solving non-stationary dynamic problems. Unlike conventional difference schemes, the M. Wilkins difference scheme, based on the integral definition of partial derivatives, is considered here. The order of approximation error for arbitrary quadrangular cells is shown. Analytical methods are used to determine the accuracy and stability of the difference relations for the linear equations of the dynamics of a deformable rigid body, as applied to the problems of the interaction of rigid bodies with soil.

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Longitudinal wave propagation in an extended cylindrical body with external Coulomb friction

Khusanov¹,

Rikhsieva²,

Salikhova³

2023

E3S Web of Conf.

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The propagation of elastic longitudinal waves in an extended cylindrical body located inside an unstrained body and interacting according to the Coulomb law is considered in the article. The problem is studied in a two-dimensional statement; therefore, the friction force (i.e., the interaction conditions) is included in the system of equations as a boundary condition. The Coulomb friction force arises due to the deformation of a cylindrical body. The reliability of numerical calculations is substantiated by solving test cases and comparing the calculations with experimental results. The numerical results obtained are presented in the form of graphs and analyzed. It is shown that the parameters (stresses and strains) of waves propagating in an elastic cylindrical body with external Coulomb dry friction decay with distance. The mechanism for reducing the stress-strain state and wave parameters is explained by the consumption of elastic energy to overcome the friction force that occurs on the contact surface. The results of the two-dimensional problem are also compared with the results of a similar problem in the one-dimensional theory, where the friction force enters directly into the equations of motion. The deviations of the results of the one-dimensional theory are up to 8-15% depending on the accepted values of the friction coefficient, i.e. the violation of the plane section hypothesis taken in one-dimensional calculations amounts to 15%. With a decrease in the radius of a cylindrical body, these deviations are reduced.

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Quasistatic elastic-plastic loading and unloading of rods with coulomb dry friction

Cited by 3 publications

References 7 publications

Wave propagation in a cylindrical body in the presence of surface forces depending on the relative displacement

Wave propagation in a cylindrical body in the presence of surface forces depending on the relative displacement

Accuracy and stability of a finite difference scheme for two-dimensional problems of soil dynamics

Longitudinal wave propagation in an extended cylindrical body with external Coulomb friction

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