Stress State of an Elastic Layer with a Cylindrical Cavity on a Rigid Foundation

Miroshnikov, Vitaly

doi:10.1007/s10778-020-01021-x

Cited by 10 publications

(16 citation statements)

References 11 publications

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“…This limit is taken into account in [30], where the problem is solved for a layer with one cylindrical cavity in displacements. A similar stress problem is considered in [31] and of a mixed type in [32]. A two-layer composite with a cylindrical stress cavity is considered in [33].…”

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: Literature Review and Problem Statementmentioning

confidence: 99%

“…A two-layer composite with a cylindrical stress cavity is considered in [33]. However, the methods proposed in [28][29][30][31][32][33] do not allow one to take into account longitudinal inclusions.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

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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“…The authors of work [19] solved a boundary problem for the half-space with two cylindrical cavities, on the boundary surfaces of which the contact type conditions are assigned. The stress-strain of the layer with a cylindrical cavity on a hard base is investigated in [20]. he addition theorems of the solutions to the Lamé equation for the half-space and cylinder were also used to solve the problems in [19,20].…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

“…The stress-strain of the layer with a cylindrical cavity on a hard base is investigated in [20]. he addition theorems of the solutions to the Lamé equation for the half-space and cylinder were also used to solve the problems in [19,20].…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

“…Hence, it follows that different methods have solved the boundary problems related to the theory of elasticity for unlimited elastic bodies with cavities of finite size. Works [16][17][18][19][20] report solving boundary problems for the half-space and layer with an infinite cylindrical cavity or cavities in different statements. However, the mixed problem in elasticity theory for half-space with an infinite cylindrical cavity in the case where displacements are assigned at the boundary of the half-space, and stresses on the surface of the cylinder, is not solved.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

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Solving a one mixed problem in elasticity theory for half-space with a cylindrical cavity by the generalized Fourier method

Ukrayinets¹,

Murahovska²,

Prokhorova³

2021

EEJET

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Designing and constructing underground structures for various purposes, such as tunnels, mines, mine workings, necessitate the development of procedures for calculating their strength and reliability. The physical model of such objects worth considering is a homogeneous isotropic half-space that contains an infinitely long hollow cylinder, located parallel to its border. One can explore problems related to the mechanics of deformable solids for such a multiply connected body. This paper reports the proofs of addition theorems for the basic solutions to the Lamé equation regarding the half-space and cylinder recorded, respectively, in the Cartesian and cylindrical coordinate systems. This result is important from a theoretical point of view in order to substantiate a numerical-analytical method ‒ the generalized Fourier method. This method makes it possible to solve spatial boundary problems from the theory of elasticity and thermo-elasticity for isotropic and transversal-isotropic multiply connected bodies. Similar to the classical Fourier method, the general solutions to equilibrium equations have been used here but in several coordinate systems rather than one. From a practical point of view, this method has made it possible to investigate the combined problem of elasticity theory regarding the multiply-connected body described above. The analysis of the stressed-strained state of this elastic body has made it possible to draw conclusions on determining those regions that are most vulnerable to destruction. The highest values are accepted by normal stresses in the region between the boundaries of the half-space and the cylinder. Changing the σy component along the Ox axis corresponds to the displacements assigned on the half-space. The τxy component contributes less to the distribution of stresses than σx and σy. The applied aspect of using the reported results is the possibility to apply them when designing underground structures

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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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Stress State of an Elastic Layer with a Cylindrical Cavity on a Rigid Foundation

Cited by 10 publications

References 11 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 a one mixed problem in elasticity theory for half-space with a cylindrical cavity by the generalized Fourier method

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

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