Sudden Loading of an Elastoplastic Rod Interacting With the Environment

Begmatov, A.; Mamatova, Nigora

doi:10.1134/s0021894422010187

Cited by 2 publications

(2 citation statements)

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“…Let us find out the error value of the difference scheme ( 8)- (9). In [21], the approximation of a system of partial differential equations to finite-difference equations was studied in detail in solving non-stationary boundary value problems on the interaction of rigid bodies.…”

Section: Error Of the Difference Schemementioning

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%

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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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Section: Error Of the Difference Schemementioning

confidence: 99%

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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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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Sudden Loading of an Elastoplastic Rod Interacting With the Environment

Cited by 2 publications

References 0 publications

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

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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