Mixed boundary value problem of elasticity for a quarter space

Вайсфельд, Н. Д.; Popov, G. Ya.

doi:10.3103/s0025654409050082

Cited by 3 publications

(4 citation statements)

References 3 publications

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“…are zeros of the Chebyshov polynomials of the first kind. So, after substitution we get For the analysis of the reliability of the calculations, we perform a test based on the obtained formula (12) for the fulfillment of the boundary condition of the problem. To this end, we consider the temperature (12) in the corner point of the layer…”

Section: Appendix 1 Deriving the Formula (12) For The Temperature Fumentioning

confidence: 99%

“…By the method of integral transforms applied directly to the transformed equations of equilibrium and the boundary conditions of the initial stated problem, one reduces it to a one-dimensional vector boundary value problem, which is solved exactly. The problem of elasticity for a quarter space was solved with this method in [12]. The elastic layer, as an important and frequently used model object, has been studied by many authors.…”

Section: Introductionmentioning

confidence: 99%

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An uncoupled thermoelasticity problem for a semi-infinite layer with regard of its proper weight

Fesenko

Vaysfeld²

2019

Frattura Ed Integrità Strutturale

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The exact solution of the uncoupled thermoelasticity problem for a semi-infinite elastic layer with regard to its proper weight was constructed. The originality of the proposed paper is based on reducing Lame equations to two jointly and one separately, solvable equations. It allows the application of integral transformations directly to the transformed equations of equilibrium and makes it possible to reduce the initial problem to a one-dimensional vector boundary problem. A special technique is given to calculate multiple integrals containing oscillating functions that appear during the inversion of the transforms. The character of the temperature and proper weight influence on the value of normal stress on the lateral face of the semi-infinite layer, the zone of tensile stress depending on the shapes of the distributed load section and the temperature and Poisson's ratio is established. The parameters of dimensionless mechanical load and temperature, when the separation of the side wall of the semi-infinite layer can be eliminated, were established. A study of the influence of the layer's proper weight on the stress emerging on the layer's edge is conducted. The constructed exact solution can be used as a model for solving a similar class of problems by numerical methods.

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Section: Appendix 1 Deriving the Formula (12) For The Temperature Fumentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An uncoupled thermoelasticity problem for a semi-infinite layer with regard of its proper weight

Fesenko

Vaysfeld²

2019

Frattura Ed Integrità Strutturale

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“…Therefore, the task of this paper is to reduce the system of equations to a form a numerical solutionof which it is less costly. Unfortunately, because of the non-uniform mixed boundary conditions, the attempts to use the results of the solution of the elasticity problem for a quarter of space in [4,5] were unsuccessful.…”

Section: Introductionmentioning

confidence: 99%

“…Citation: Arakcheev AS and Arakcheev SA (2018) Solution to Force Problem of Linear Elasticity Theory for Quarter Space with Edge-uniform Forces. J Apl Theol 2(2): [5][6][7][8][9][10][11][12] Using expression (6.12) and taking the integral with respect to ξ , we have:…”

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confidence: 99%

Solution to Force Problem of Linear Elasticity Theory for Quarter Space with Edgeuniform Forces

Arakcheev¹

2018

J Apl Theol

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Citation: Arakcheev AS and Arakcheev SA (2018) Solution to Force Problem of Linear Elasticity Theory for Quarter Space with Edgeuniform Forces. J Apl Theol 2(2): 5-12. AbstractIn the paper, the force problem of the linear elasticity theory is solved for a quarter space with edge-uniform forces. It is demonstrated that it is possible find a Green function analog that corresponds to the derivative of the delta function in the boundary conditions. In this formulation of the problem, it is reduced to the Fredholm integral equation of the second kind with a solution in the form of a rapidly convergent series. The method applied can be used to solve the force problems of the linear elasticity theory for a space sector with a dihedral angle of arbitrary value.

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Mechanical response of a semi-infinite poroelastic cuboid to an external load

Zhuravlova

2023

Mat. Met. Fiz. Mekh. Polya

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Mixed boundary value problem of elasticity for a quarter space

Cited by 3 publications

References 3 publications

An uncoupled thermoelasticity problem for a semi-infinite layer with regard of its proper weight

An uncoupled thermoelasticity problem for a semi-infinite layer with regard of its proper weight

Solution to Force Problem of Linear Elasticity Theory for Quarter Space with Edgeuniform Forces

Mechanical response of a semi-infinite poroelastic cuboid to an external load

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