Doubly periodic contact problems for an elastic layer

Александров, В. М.

doi:10.1016/s0021-8928(02)00036-9

Cited by 23 publications

(27 citation statements)

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“…They use integral transforms, and the solutions are generally very convoluted, difficult for numerical implementation and for estimation of the solution accuracy. The most recent publications can be quoted (Wozniak et al, 2002;Jaffar, 2002, Aleksandrov, 2002, where reader can find numerous other references.…”

Section: Introductionmentioning

confidence: 99%

Elementary solution of contact problems for a transversely isotropic elastic layer bonded to a rigid foundation

Fabrikant¹

2006

Z. angew. Math. Phys.

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The contact problem for an arbitrary punch acting on a transversely isotropic elastic layer bonded to a rigid foundation is solved by the generalized images method developed by the author earlier. The problem is reduced to that of an electrostatic problem of infinite row of coaxial charged disks in the shape of the domain of contact. The solution can be obtained by the method of iteration, collocations or any other standard procedure for solving integral equations. Exact inversion can be obtained in the case of a circular domain of contact. The mean value theorem can be used for estimation of the resultant force and tilting moment acting on a punch of arbitrary shape and circular domain of contact. A limiting case of general solution gives the solution for an isotropic layer.

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Section: Introductionmentioning

confidence: 99%

Elementary solution of contact problems for a transversely isotropic elastic layer bonded to a rigid foundation

Fabrikant¹

2006

Z. angew. Math. Phys.

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“…1 , γ (1) 1 , γ (1) 2 , etc. The material of the half-space is characterized by the constants H (2) , m (2) 1 , γ (2) 1 , γ (2) 2 , etc.…”

Section: Formulation Of the Contact Problem And Its Solutionmentioning

confidence: 99%

“…An arbitrary punch is pressed against the layer by a normal force P, so that the domain of contact is S and is located in the plane z =0. The mathematical formulation of the boundary conditions can be presented as follows: w = w (ρ, ϕ) , (ρ, ϕ) ⊆ S, σ z = 0, (ρ, ϕ) / ∈ S, z = 0; τ z = 0, ρ < ∞, z = 0 (8) w (1) = w (2) , τ (1) z = 0, τ (2) z = 0 for ρ < ∞, z = c (9) σ (1) …”

Section: Formulation Of the Contact Problem And Its Solutionmentioning

confidence: 99%

Application of generalized images method to contact problems for a transversely isotropic elastic layer on a smooth half-space

Fabrikant¹

2010

Arch Appl Mech

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The idea, first used by the author for the case of crack problems, is applied here to solve a contact problem for a transversely isotropic elastic layer resting on a smooth elastic half-space, made of a different transversely isotropic material. A rigid punch of arbitrary shape is pressed against the layer's free surface. The governing integral equation is derived; it is mathematically equivalent to that of an electrostatic problem of an infinite row of coaxial charged disks in the shape of the domain of contact. The case of circular domain of contact is considered in detail. As a comparison, the method of integral transforms is also used to solve the problem. The main difference of our integral transform approach with the existing ones is in separating of our half-space solution from the integral transform terms. It is shown that both methods lead to the same results, thus giving a new interpretation to the integral transform as a sum of an infinite series of generalized images.

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“…The monograph presents a vast material developed in numerous publications. There are also many studies in this field, which were published in recent years (Ulitko & Kochalovskaya, 1995;Pozharskii & Chebakov, 1998;, 2004Alexandrov et al, 2000;Osrtrik & Ulitko, 2000;Alexandrov & Klindukhov, 2000Pozharskii, 2000Pozharskii, , 2004Aleksandrov, 2002Aleksandrov, , 2006Alexandrov & Kalyakin, 2005).…”

Section: Introductionmentioning

confidence: 99%

Strength of a Polycrystalline Material

Galptshyan¹

2012

Polycrystalline Materials - Theoretical and Practical Aspects

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Doubly periodic contact problems for an elastic layer

Cited by 23 publications

References 0 publications

Elementary solution of contact problems for a transversely isotropic elastic layer bonded to a rigid foundation

Elementary solution of contact problems for a transversely isotropic elastic layer bonded to a rigid foundation

Application of generalized images method to contact problems for a transversely isotropic elastic layer on a smooth half-space

Strength of a Polycrystalline Material

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