Stresses in an Infinite Circular Cylinder with Four Cylindrical Cavities

Nikolaev, O. G.; Tanchik, E. A.

doi:10.1007/s10958-016-2974-z

Cited by 6 publications

(6 citation statements)

References 2 publications

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“…In contrast to the works [24][25][26][27][28][29][30][31][32][33][34][35], which also use the generalized Fourier method with separate addition theorems, in this work a number of tools were applied simultaneously. These are transition functions in basic interchanges between cylindrical coordinate systems, transition functions between cylindrical (including shifted) and Cartesian coordinate systems for both layer boundaries.…”

Section: Discussion Of the Results Of Studying The Stress-strain Stat...mentioning

confidence: 99%

“…On the basis of the generalized Fourier method, a number of problems of the theory of elasticity for a cylinder with cylindrical cavities or inclusions are solved. Thus, in [24], the problem was solved for a cylindrical body with four cylindrical cavities. The problem for a cylinder with N cylindrical cavities is considered in [25].…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

“…The problem for a cylinder with cylindrical cavities forming a hexagonal structure is considered in [26] and a cylinder with 16 cylindrical inclusions in [27]. In these papers [24][25][26][27], addition theorems of the generalized Fourier method were applied for several cylindrical systems. But they do not take into account the addition formulas for solving the Lame equation between Cartesian and cylindrical coordinate systems.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

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Solution of the problem of the theory of elasticity and analysis of the stress state of a fibrous composite layer under the action of transverse compressive forces

Miroshnikov

Savin

Younis

et al. 2022

EEJET

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An analytical-numerical solution of the spatial problem of elasticity theory for a composite in the form of a layer with two longitudinal endless continuous cylindrical inclusions is proposed. Homogeneous, isotropic materials of the layer and inclusions differ from each other in the modulus of elasticity and Poisson's ratio. Normal stresses are set on the upper and lower boundaries of the layer. The object of study is the stress state of such a composite. The problem is the lack of a high-precision method for calculating multiply connected bodies of this type. The solution of the problem is based on the generalized Fourier method for the Lame equations in various coordinate systems. The problem is reduced to an infinite system of linear algebraic equations, which is solved by the reduction method. In a numerical study, the stress state was obtained inside the composite bodies, within their conjugations, and on the isthmus between inclusions. It has been established that extreme stresses sρ=–0.9306 MPa, sf=–0.5595 MPa, tρf=–0.315 MPa occur on the mating face. Analysis of the stress state indicates the need to take into account the normal stresses on the mating surface. This is due to the presence of a binder, which may differ in physical characteristics from the main components of the composite. The results have logical physical correctness and, in simplified versions, are fully consistent with the results of similar problems from other approved sources. In the work, the transition formulas in the basic solutions between different coordinate systems, the conjugation conditions for different bodies, and the strict fulfillment of the equilibrium conditions for given boundary functions are simultaneously applied. This made it possible to obtain a high-precision solution of a new problem in the theory of elasticity for a layer with cylindrical inclusions and given only stresses on the boundary surfaces. The proposed method of calculation can be applied in the design of structures made of fibrous composites in the aircraft industry and construction.

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Section: Discussion Of the Results Of Studying The Stress-strain Stat...mentioning

confidence: 99%

Section: Literature Review and Problem Statementmentioning

confidence: 99%

Section: Literature Review and Problem Statementmentioning

confidence: 99%

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Solution of the problem of the theory of elasticity and analysis of the stress state of a fibrous composite layer under the action of transverse compressive forces

Miroshnikov

Savin

Younis

et al. 2022

EEJET

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“…Thus, in [17], the problem for an infinite cylinder with four cylindrical cavities parallel to each other was solved using the generalized Fourier method. The problem for an elastic cylinder with N parallel cylindrical cavities was solved in [18].…”

Section: Introductionmentioning

confidence: 99%

“…The problem for a model where cylindrical cavities form a hexagonal structure in a cylinder was solved in [19], and for a model where 16 cylindrical inclusions are in an elastic cylinder in [20]. Works [17][18][19][20] use formulas for the transition of basic solutions only between different cylindrical coordinate systems. This approach does not allow solving problems for a layer where the Cartesian system is used.…”

Section: Introductionmentioning

confidence: 99%

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

Miroshnikov

2022

Lecture Notes in Mechanical Engineering

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Stresses in an Infinite Circular Cylinder with Four Cylindrical Cavities

Cited by 6 publications

References 2 publications

Solution of the problem of the theory of elasticity and analysis of the stress state of a fibrous composite layer under the action of transverse compressive forces

Solution of the problem of the theory of elasticity and analysis of the stress state of a fibrous composite layer under the action of transverse compressive forces

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

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

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