Axisymmetric contact problem for an elastic half-space with a cylindrical hole

Parlas, Solon C.; Michalopoulos, C. D.

doi:10.1016/0020-7225(72)90064-x

Cited by 8 publications

(2 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In spite of this fact, the subject is barely investigated and very few accurate theoretical results basing on contact mechanics are known because of significant mathematical difficulties arising in study of mixed boundary problems of this geometry. The indentation of an elastic half-space containing a circular cylindrical hole by a frictionless rigid bolt with flat head and infinite shank was first studied by Parlas and Michalopoulos [1] who reduced the axisymmetric problem by using Weber–Orr integral transforms to a singular integral equation solved numerically though no proof was presented for the suggested numerical procedure. Latter, in the paper by Malits [2], the equivalent contact problem was solved by reducing to an integral equation of the second kind on the infinite interval with a compact Hankel integral operator and then to a regular infinite system of linear algebraic equations with a Hankel matrix.…”

Section: Introduction and Governing Equationsmentioning

confidence: 99%

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

Malits

2022

Mathematics and Mechanics of Solids

View full text Add to dashboard Cite

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.

show abstract

Section: Introduction and Governing Equationsmentioning

confidence: 99%

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

Malits

2022

Mathematics and Mechanics of Solids

View full text Add to dashboard Cite

show abstract

“…In this connection we think of the work of e.g. Bondareva on elastic spheres [ll]; of Pari as and Michalopoulos on the axisymmetric contact problem for a half-space with a cylindrical hole [73] ; of the work done on the Melan problem of a half-space on which elastic stiffeners are welded, by Arutiunian and Mkhitarian [6], whose paper contains numerous references.…”

Section: Other Problemsmentioning

confidence: 99%