Axisymmetric mixed boundary problem for a composite space with a circular disc-shaped crack

Hakobyan, Vahram N.; Amirjanyan, H.A.

doi:10.33018/74.3.1

Cited by 3 publications

(5 citation statements)

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“…In ref [19], an algorithm is presented that can be used to obtain a numerical inversion of rotation operators even in cases where the reduced unknown functions have an exponential singularity with oscillation. Using this algorithm, a numerical calculation was made and the reduced normal pressure was determined…”

Section: Numerical Calculationsmentioning

confidence: 99%

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On an indentation of a circular cylindrical punch into an elastic half‐space under friction

Hakobyan,

Dashtoyan,

Amirjanyan

2024

Z Angew Math Mech

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The paper discusses an axisymmetric contact problem of indentation of a circular cylindrical punch with a flat base into a homogeneous elastic half‐space with friction. It is assumed that the shear contact stresses are related to the normal contact pressure by the law of dry friction, in which the coefficient of friction depends on the radial coordinates of the points of the surfaces in contact and is directly proportional to them. With the help of rotation operators, the solution of the stated problem is reduced to the solution of a singular integral equation of the second kind with variable coefficients, and its closed solution in quadratures is constructed. The numerical calculations display the patterns of change in contact stresses and rigid displacement of the punch depending on the maximum value of the friction coefficient.

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Section: Numerical Calculationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On an indentation of a circular cylindrical punch into an elastic half‐space under friction

Hakobyan,

Dashtoyan,

Amirjanyan

2024

Z Angew Math Mech

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“…It is easy to check that the function ( ) * wx  is odd, hence the second of conditions ( 7) is satisfied automatically. Therefore, to determine the rigid displacement of the stamp and the constant * c , we must use the last condition (7) and condition (12). We expand the functions ( ) ( )…”

Section: Solution Of the System Of Governing Equationsmentioning

confidence: 99%

“…Thus, we must consider the system of functional equations (10) under the last two conditions (7) and condition (12).…”

Section: ( )mentioning

confidence: 99%

“…Popov, for a piecewise-homogeneous space with an interfacial disc-shaped crack. In [11][12], exact solutions of two axisymmetric contact problems are constructed for a piecewise-homogeneous space with a crack under various classical contact conditions However, in addition to determining the local stress fields arising near stress concentrators of various types located in deformable homogeneous or piecewise homogeneous bodies and identifying the patterns of their mutual influence, from the point of view of contact and mixed problems of the theory of elasticity and fracture mechanics, it is also important to select the model of stress concentrators and conjugation conditions with a matrix, which makes it possible to more accurately identify the features of changes in stress fields around them and the mutual influence of various stress concentrators. The research study [13] is a good case in point, where L.A. Galin proposed a new model for the contact for an absolutely rigid punch with an elastic half-plane.…”

Section: Introductionmentioning

confidence: 99%

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Axisymmetric Contact Problem for a Homogeneous Space with a Circular Disk-Shaped Crack Under Static Friction

Hakobyan,

Sahakyan,

Dashtoyan

2023

Preprint

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The paper considers an axisymmetric stress state of a homogeneous elastic space with a circular disc-shaped crack, one of the edges of which is pressed into a cylindrical circular punch with static friction. It is assumed that the contact zone is considered under the generalized law of dry friction, i.e. tangential contact stresses are proportional to normal contact pressure, while the proportionality coefficient depends on the radial coordinates of the points of the contacting surfaces and is directly proportional to them. Considering the fact that in this case the Abel images of contact stresses are also related in a similar way, the solution of the problem, with the help of rotation operators and theory of analytical functions, is reduced to an inhomogeneous Riemann problem for two functions and the closed solution in quadratures is constructed. A numerical analysis was carried out and regularities of changes in both normal and shear real contact stresses, as well as rigid displacement of the punch depending on the physical and geometric parameters were revealed.

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Mixed Boundary Value Problem For Compound Space With Interphase Defects

Hakobyan

2022

Advanced Structured Materials

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Axisymmetric mixed boundary problem for a composite space with a circular disc-shaped crack

Cited by 3 publications

References 0 publications

On an indentation of a circular cylindrical punch into an elastic half‐space under friction

On an indentation of a circular cylindrical punch into an elastic half‐space under friction

Axisymmetric Contact Problem for a Homogeneous Space with a Circular Disk-Shaped Crack Under Static Friction

Mixed Boundary Value Problem For Compound Space With Interphase Defects

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