Stress Concentrators in Continuous Deformable Bodies

Hakobyan, Vahram N.

doi:10.1007/978-3-031-16023-3

Cited by 12 publications

(6 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Introducing new variables t = x − 2ml, τ = s − 2kl in ( 6) and ( 7), taking into account the periodicity of the function P (x) and formula [4] ∞ k=−∞…”

Section: Statement Of Problems and Derivation Of Governing Equationsmentioning

confidence: 99%

“…Contact and mixed boundary value problems of the theory of elasticity, one of the developing directions of a deformable solid, which has great theoretical and practical significance. Many fundamental results in this direction are given in monographs [1][2][3][4]. Along with the classical models of contact of two bodies with static friction, L.A. Galin proposed a new, non-classical contact model in 1945 [1,5].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On two contact problems for a half-plane with static friction

Hakobyan,

Dashtoyan

2024

J. Phys.: Conf. Ser.

View full text Add to dashboard Cite

Exact solutions of two contact problems are constructed for a half-plane, when a finite number of absolutely rigid flat punches with friction are pressed into the half-plane under the influence of different concentrated loads, and when a periodic system of absolutely rigid flat punches with friction is pressed into the half-plane. It is assumed that friction in contact zones is associated with normal contact pressure by the generalized law of dry friction, in which the coefficient of friction depends on the coordinates of the contacting points of the contacting bodies and is directly proportional to the difference between the coordinates of these points and the coordinates of the middle points of the contact zones. The governing equations of the posed problems were obtained in the form of singular integral equations with variable coefficients relative to the contact pressure and their closed solutions were constructed.

show abstract

“…Introducing new variables t = x − 2ml, τ = s − 2kl in ( 6) and ( 7), taking into account the periodicity of the function P (x) and formula [4] ∞ k=−∞…”

Section: Statement Of Problems and Derivation Of Governing Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On two contact problems for a half-plane with static friction

Hakobyan,

Dashtoyan

2024

J. Phys.: Conf. Ser.

View full text Add to dashboard Cite

show abstract

“…, 0 0; , 0 0; 0 , 0 ; , 0 ; The solution to the boundary value problem (1) will be constructed using discontinuous solutions for a compound space with a circular disk-shaped crack obtained in [8,10].…”

Section: Statement Of the Problem And Derivation Of Governing Equationsmentioning

confidence: 99%

“…Most of the researches in this direction is devoted to the study of plane and axisymmetric contact and mixed problems for homogeneous and piecewise homogeneous massive bodies with stress concentrators such as punches, cracks, and absolutely rigid inclusions fully or partially coupled with the matrix. The exact and efficient solutions were represented in monographs [5][6][7][8]. We especially note the works in which axisymmetric problems are considered for a homogeneous and piecewisehomogeneous space with a disk-shaped crack, on the banks of which mixed conditions are given.…”

Section: Introductionmentioning

confidence: 99%

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

Hakobyan,

Sahakyan,

Dashtoyan

2023

Preprint

View full text Add to dashboard Cite

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.

show abstract

“…Based on the mathematical methods of Hankel transformations, pair integral equations, rotation operators, singular integral equations, and the Wiener-Hopf method, closed and effective solutions were obtained for a number of practically important contact and mixed boundary value problems. Many fundamental results are given in monographs [1][2][3][4][5][6], as well as in the collection of selected works by Popov [7]. Among the problems of contact interaction of an absolutely rigid cylindrical punch with an elastic half-space, we turn to the work [8], where the exact solution of the problem of indentation of a circular cylindrical punch into an inhomogeneous elastic half-space with adhesion is constructed.…”

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

View full text Add to dashboard Cite

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.

show abstract

Stress Concentrators in Continuous Deformable Bodies

Cited by 12 publications

References 0 publications

On two contact problems for a half-plane with static friction

On two contact problems for a half-plane with static friction

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

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

Contact Info

Product

Resources

About