Plane contact problem on indentation of a flat punch into a transversely-isotropic half-plane with functionally graded transversely-isotropic coating

Vasiliev, Andrey S.; Volkov, S. S.; Aizikovich, S. M.; Mitrin, B. I.

doi:10.1007/s00033-016-0746-8

Cited by 24 publications

(15 citation statements)

References 54 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…is the relative thickness of the lower coating; µ=H 2 /H 1 is the ratio of the coating's thicknesses; functions are defined as solutions of two-point boundary value problems for a system of ordinary differential equation with variable coefficients, which can be obtained similar to (Vasiliev et al, 2017a).…”

Section: Solution Of the Problemmentioning

confidence: 99%

Plane contact of two elastic solids with functionally graded coatings joined by an imperfect interface

2018

Engineering Mechanics

View full text Add to dashboard Cite

Plane contact problem on normal interaction of two dissimilar elastic solids is considered. The solids consist of a homogeneous semi-infinite substrate and a functionally graded coating joined by an imperfect interface to the substrate. The problem is reduced to the solution of a dual integral equation which is solved by the bilateral asymptotic method. Numerical results illustrating the difference between the ideal and imperfect interface of the coating and the substrate are provided.

show abstract

Section: Solution Of the Problemmentioning

confidence: 99%

Plane contact of two elastic solids with functionally graded coatings joined by an imperfect interface

2018

Engineering Mechanics

View full text Add to dashboard Cite

show abstract

“…Coefficients D m (m=1,…,N) are calculated from the system of linear algebraic equations below (n=1,…,N): (4) was obtained earlier [17,23,24]:…”

Section: Solution Of Dual Integral Equationmentioning

confidence: 99%

“…The present paper addresses the solution of one class of dual integral equations arising in the solution of wide range of plane and antiplane contact problems, see for example [5,17,24,25]. Feature of the paper is that the right-hand side of the integral equation is represented by the full Fourier series that can be used to model nonsymmetric contact.…”

Section: Introductionmentioning

confidence: 99%

Solution of a dual integral equation arising in the contact problems of elasticity theory with the full Fourier series as the right-hand side

Vasiliev

Volkov

2017

MATEC Web Conf.

View full text Add to dashboard Cite

Abstract.A class of dual integral equations is analyzed which arises in solution of a wide range of plane and antiplane contact problems of elasticity theory for a half-plane with functionally graded coating. In particular, a similar equation arises in solution of the contact problem on indentation in the presence of tangential stresses on a surface. The solution of the dual integral equation is sought in the form of a sum of even and odd functions. It makes possible to reduce the problem to independent solution of two dual integral equations over odd and even functions. Kernel transform of these equations is approximated by a product of fractional quadratic functions. The solution of dual integral equations is constructed in approximated analytical form by the bilateral asymptotic method. The expressions obtained are asymptotically exact for small and large values of a characteristic geometrical parameter.

show abstract

“…In the papers by Aizikovich [21], Vasiliev et al [17]- [19] and Volkov et al [20] solution of axisymmetric and plane contact problems for elastic solids with a functionally graded coating were constructed using the bilateral asymptotic method. This approach has a few advantages.…”

Section: Introductionmentioning

confidence: 99%

Simplified Analytical Solution of the Contact Problem on Indentation of a Coated Half-Space by a Spherical Punch

Sadyrin

Vasiliev

Volkov

et al. 2018

WIT Transactions on Engineering Sciences

View full text Add to dashboard Cite

This paper is devoted to construction of a mathematical model combining simplicity for practical usage and high accuracy. It is based on the solution of an axisymmetric contact problem on penetration of a rigid indenter into an elastic half-space with a functionally graded or homogeneous coating. The problem is reduced to solution of a dual integral equation. Asymptotically exact expressions for indentation force, depth, contact stiffness and distribution of contact pressures are obtained in simplified analytical form using one-parameter approximation of the integral equation kernel transform. Numerical calculations are provided for a number of homogeneous and functionally graded coatings. Accuracy of the solution is analyzed against ratio of Young's moduli of coating and substrate and the value of relative coating thickness.

show abstract

Plane contact problem on indentation of a flat punch into a transversely-isotropic half-plane with functionally graded transversely-isotropic coating

Cited by 24 publications

References 54 publications

Plane contact of two elastic solids with functionally graded coatings joined by an imperfect interface

Plane contact of two elastic solids with functionally graded coatings joined by an imperfect interface

Solution of a dual integral equation arising in the contact problems of elasticity theory with the full Fourier series as the right-hand side

Simplified Analytical Solution of the Contact Problem on Indentation of a Coated Half-Space by a Spherical Punch

Contact Info

Product

Resources

About