Rotation of the Layer with the Cylindrical Pipe Around the Rigid Cylinder

Miroshnikov, Vitaly

doi:10.1007/978-3-031-18487-1_32

Cited by 5 publications

(9 citation statements)

References 18 publications

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“…This approach does not allow solving problems for a layer where the Cartesian system is used. This relationship is applied in [21][22][23][24][25][26][27], where the generalized Fourier method is also used. For example, the problem for an elastic half-space with a longitudinal cylindrical cavity was solved in an actually flat formulation in [21] and in a spatial formulation in [16].…”

Section: Introductionmentioning

confidence: 99%

“…However, problems for half-space do not take into account the lower surface of the layer. The lower bound has been considered in the problems for a layer with a single circular cylindrical cavity or a single elastic cylindrical inclusion in [22][23][24][25][26]. Thus, the third basic problem of elasticity theory is considered in [22].…”

Section: Introductionmentioning

confidence: 99%

“…Paper [24] solved the problem of an infinite elastic layer with an elastic solid cylindrical inclusion and given displacements on the layer surface. In [25], stresses are set on the layer surfaces, and zero displacements are set on the inner surface of an embedded cylindrical pipe. In [26], a calculation methodology is proposed, and a numerical analysis of the stressed state is performed for a bilayer structure with a cylindrical void between parallel flat surfaces.…”

Section: Introductionmentioning

confidence: 99%

“…In [26], a calculation methodology is proposed, and a numerical analysis of the stressed state is performed for a bilayer structure with a cylindrical void between parallel flat surfaces. However, papers [22][23][24][25][26] do not take into account the formulas for the transition between basic solutions from one cylindrical coordinate system to another, which does not allow solving problems with more than one cylindrical stress concentrator. The formulas for two cylindrical stress concentrators are considered in [27], where a method for solving the problem for a fiber composite (in the form of a layer with two cylindrical solid inclusions) is proposed.…”

Section: Introductionmentioning

confidence: 99%

“…From this point of view, the closest to the present work are publications [25,27], where displacements are set on the inner cylindrical surface of the pipe, or a rigid cylindrical inclusion is placed in the layer (under the condition of load balancing). This makes it possible to compare some of the results obtained in order to assess their reliability.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Solving the Problem of Elasticity for a Layer with N Cylindrical Embedded Supports

Miroshnikov,

Savin,

Sobol

et al. 2023

Computation

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The main goal of deformable solid mechanics is to determine the stress–strain state of parts, structural elements, and their connections. The most accurate results of calculations of this state allow us to optimize design objects. However, not all models can be solved using exact methods. One such model is the problem of a layer with cylindrical embedded supports that are parallel to each other and the layer boundaries. In this work, the supports are represented by cylindrical cavities with zero displacements set on them. The layer is considered in Cartesian coordinates, and the cavities are in cylindrical coordinates. To solve the problem, the Lamé equation is used, where the basic solutions between different coordinate systems are linked using the generalized Fourier method. By satisfying the boundary conditions and linking different coordinate systems, a system of infinite linear algebraic equations is created. For numerical realization, the method of reduction is used to find the unknowns. The numerical analysis has shown that the boundary conditions are fulfilled with high accuracy, and the physical pattern of the stress distribution and the comparison with results of similar studies indicate the accuracy of the obtained results. The proposed method for calculating the stress–strain state can be applied to the calculation of structures whose model is a layer with cylindrical embedded supports. The numerical results of the work make it possible to predetermine the geometric parameters of the model to be designed.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Solving the Problem of Elasticity for a Layer with N Cylindrical Embedded Supports

Miroshnikov,

Savin,

Sobol

et al. 2023

Computation

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Analysis of the Stress State for a Layer with Two Incut Cylindrical Supports

Miroshnikov¹,

Savin²,

Hrebennikov³

et al. 2023

J. of Mech. Eng.

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The stress state of a homogeneous isotropic layer under the action of a spatial static external load is studied. Two circular cylindrical supports are cut into the body of the layer parallel to its borders. The supports and body of the layer are rigidly coupled. The spatial problem theory of elasticity is solved using the analytical-numerical generalized Fourier method. The layer is considered in the Cartesian coordinate system, the supports are considered in the local cylindrical coordinates. Stresses are set on the upper and lower surfaces of the layer. The supports are considered as cylindrical cavities in a layer with zero displacements set on their surfaces. Satisfying the boundary conditions on the upper and lower surfaces of the layer, as well as on the cylindrical surfaces of the cavities, a system of infinite integro-algebraic equations, which are further reduced to linear algebraic ones, is obtained. An infinite system is solved by the reduction method. In the numerical studies, the parameters of integration oscillatory functions are analyzed, problems at different distances between supports are solved. A unit load in the form of a rapidly decreasing function is applied to the upper boundary between the supports. For these cases, an analysis of the stress state was performed on the surfaces of the layer between the supports and on the cylindrical surfaces in contact with the supports. The numerical analysis showed that when the distance between the supports increases, the stresses σx on the lower and upper surfaces of the layer and the stresses τρφ on the surfaces of the cavities increase. The use of the analytical-numerical method made it possible to obtain a result with an accuracy of 10-4 for stress values from 0 to 1 at the order of the system of equations m=6. As the order of the system increases, the accuracy of fulfilling the boundary conditions will increase. The presented analytical-numerical solution can be used for high-precision determination of the stress-strain state of the presented problems type, as well a reference for problems based on numerical methods

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Analysis of the Stress State of a Layer with Two Cylindrical Swivel Joints and a Cylindrical Cavity

Miroshnikov,

Pelykh,

Denshchykov

2024

J. of Mech. Eng.

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In practice, connections in the form of cylindrical swivel joints are often encountered. However, exact methods for calculating such models are absent. Therefore, the development of algorithms to solve such problems is relevant. In this study, a spatial elasticity problem is solved for an infinite layer with two cylindrical swivel joints and a cylindrical cavity positioned parallel to each other and parallel to the layer surfaces. The embedded cylindrical swivel joints are represented as cavity with given contact-type conditions (normal displacements and tangential stresses). Stresses are specified on the layer surfaces and the cavity surface. The layer is considered in a Cartesian coordinate system, while the cylindrical cavities are considered in local cylindrical coordinates. The spatial elasticity problem is solved using the generalized Fourier method applied to the Lamé equations. Satisfying the boundary conditions results in a system of infinite linear algebraic equations, which undergo reduction methods. In the numerical study, the accuracy of boundary condition fulfillment reached 10-3 for stress values ranging from 0 to 1, with the equation system (Fourier series members) order of m=4. As the order of the system equations increases, the accuracy of calculations increases. Stress state analysis was conducted at varying distances between supports. The obtained results indicate that with an increased distance between supports, stresses on the supporting cylindrical surfaces of the layer and the cylindrical cavity surface decrease. These stresses are redistributed to the upper and lower surfaces of the layer, where the stresses increase and exceed the specified ones. The numerical outcomes can be applied to predict geometric parameters during design processes.

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Rotation of the Layer with the Cylindrical Pipe Around the Rigid Cylinder

Cited by 5 publications

References 18 publications

Solving the Problem of Elasticity for a Layer with N Cylindrical Embedded Supports

Solving the Problem of Elasticity for a Layer with N Cylindrical Embedded Supports

Analysis of the Stress State for a Layer with Two Incut Cylindrical Supports

Analysis of the Stress State of a Layer with Two Cylindrical Swivel Joints and a Cylindrical Cavity

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