Torsion of a cracked elastic body by an embedded semi-infinite rigid cylinder

Malits, P.

doi:10.1007/s00033-020-1255-3

Cited by 3 publications

(5 citation statements)

References 16 publications

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“…J ν (ξ ), Y ν (ξ ), and H (k) ν (ξ ) , k = 1, 2, are Bessel functions of the first, second, and third kind, respectively, satisfies the differential equation (5) and boundary conditions (1) and (2).…”

Section: (ξ ) Hmentioning

confidence: 99%

“…The study of the above-stated problem is helpful for various engineering applications, e.g., for analyzing mechanical behavior of systems with rigid cylindrical piles or cylindrical piers. The only somewhat similar problem was studied in Malits [1]. In the dimensionless cylindrical coordinates ρ = r/a, ζ = z/a, the boundary conditions are as follows:…”

Section: Introduction and Governing Equationsmentioning

confidence: 99%

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Debonding of an elastic layer with a cavity from a rigid substrate caused by rotation of a bonded rigid cylinder

Malits

2024

Mathematics and Mechanics of Solids

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Debonding of an elastic layer with a circular cylindrical cavity [Formula: see text], [Formula: see text], from a rigid substrate under action of a rigid cylinder is the object of this study. The annular debonding zone [Formula: see text] is caused by rotation of a cylinder bonded to the cavity surface. The problem is reformulated as dual integral equations with Weber integral transforms kernels. A Volterra operator transforming a Weber transforms kernel into a Bessel function of the first kind and Hankel integral transforms allow us to reduce dual equations to a Fredholm integral equation of the second kind and then, by some transformation, to another Fredholm integral equation which is more suitable for approximate methods. As [Formula: see text] and [Formula: see text], a highly accurate analytic approximate solution of the problem is suggested. The asymptotic solution of the problem is obtained as the width of debonding zone is very small while the thickness is not small. When the thickness is small, the Fredholm integral equations are computationally inefficient. A new method based on an operator transforming a Bessel function of the first kind into the kernel of Mehler–Fock integral transforms enabled us to convert one of the above-mentioned Fredholm equations into an equivalent Fredholm integral equation of the second kind that is effective for a small thickness. The asymptotic solution of the problem is obtained when both the layer thickness and the debonding zone width are small. Accurate mathematical methods, in particular investigations, and transformations of equations, developed in this study can be interesting to researchers employing dual integral equations technique in problems of mechanics and mathematical physics with mixed boundary conditions.

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Section: (ξ ) Hmentioning

confidence: 99%

Section: Introduction and Governing Equationsmentioning

confidence: 99%

Debonding of an elastic layer with a cavity from a rigid substrate caused by rotation of a bonded rigid cylinder

Malits

2024

Mathematics and Mechanics of Solids

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“…To find an approximate solution of the integral equation (28), we note that the operator R differs by a multiplier of 2 from the operator studied in Malits [14] and, therefore, (28) can be treated in the same way as in the abovementioned paper. In particular,…”

Section: External Solutionmentioning

confidence: 99%

“…and I + R is a bounded coercive self-adjoint operator because ‖ ω ‖ L 2 2 ≤ 〈 ( I + R ) ω , ω 〉 ≤ ( 1 + ρ R ) ‖ ω ‖ L 2 2 . Then, according to the papers Malits [15] and Malits [14], an approximate L 2 -solution ψ true~ ( x ) can be taken in the form…”

Section: External Solutionmentioning

confidence: 99%

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Contact stress induced by the rotation of a rigid bolt bonded to an elastic body

Malits

2022

Mathematics and Mechanics of Solids

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Torsional deformation of an elastic half-space containing a vertical cylindrical cavity caused by a rotation of a bonded rigid bolt with a long shank is studied in this article by employing Weber integral transforms and integral equations. In the limiting case of the infinite shank, we suggest two different techniques reducing the problem to the regular integral equations of the second kind, which permit efficient solutions in distinct ranges of geometric parameters and allow us to derive a highly accurate approximate analytic solution of the problem for any values of the parameters. Almost exact approximations are suggested for the stress concentration at the edge of the bolt head. In the case of a bolt with a long finite shank, relationships between the torque and the angle of twist of the bolt are derived by utilizing solutions obtained for the bolt with the infinite shank as asymptotic approximations. The effect of the geometric parameters is investigated providing insight into the behavior of the bolt and contact stress in dependence on the bolt head radius and the length of the shank.

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Torsion of an elastic half-space with a cylindrical cavity by a punch

Malits

2021

European Journal of Mechanics - A/Solids

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Torsion of a cracked elastic body by an embedded semi-infinite rigid cylinder

Cited by 3 publications

References 16 publications

Debonding of an elastic layer with a cavity from a rigid substrate caused by rotation of a bonded rigid cylinder

Debonding of an elastic layer with a cavity from a rigid substrate caused by rotation of a bonded rigid cylinder

Contact stress induced by the rotation of a rigid bolt bonded to an elastic body

Torsion of an elastic half-space with a cylindrical cavity by a punch

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