Frictional Hertzian contact between a laterally graded elastic medium and a rigid circular stamp

Date

2013-08-01

Author

Dağ, Serkan
YILDIRIM, BORA
Ozatag, A. Cihan

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

206
views

0
downloads

This study investigates the problem of sliding frictional contact between a laterally graded elastic medium and a rigid circular stamp. Analytical and computational methods are developed to evaluate the contact stresses. In the analytical formulation, spatial variation in the shear modulus of the graded medium is represented by an exponential function, and Poisson's ratio is taken as a constant. Coulomb's dry friction law is assumed to hold within the contact area. The two-dimensional plane elasticity problem is formulated utilizing Fourier transforms, and the resulting Cauchy-type singular integral equation of the second type is solved by applying an expansion-collocation technique. The finite element method is used in the computational analysis of the contact problem. In the finite element model, continuous variation of the shear modulus is taken into account by specifying this property at the centroid of each finite element. The finite element-based solution procedure is verified by making comparisons to the results obtained through the analytical method. Numerical results generated for the laterally graded medium with an exponential variation in the shear modulus illustrate the influences of lateral gradation and coefficient of friction upon the contact stress distributions. The capability of the proposed finite element method is further demonstrated by providing numerical results for a laterally graded medium whose shear modulus is represented by a power function.

Subject Keywords

Mechanical Engineering, Computational Mechanics

URI

https://hdl.handle.net/11511/36084

Journal

ACTA MECHANICA

DOI

https://doi.org/10.1007/s00707-013-0844-z

Collections

Department of Mechanical Engineering, Article

Suggestions

OpenMETU
Core

Analytical solution to the bending of a nonlinearly hardening wide curved bar Arslan, Eray; Eraslan, Ahmet Nedim (Springer Science and Business Media LLC, 2010-02-01) An analytical solution to the partially plastic deformation of a nonlinearly hardening wide curved bar is derived. The bar considered has a narrow rectangular cross-section and is under pure bending. The analytical treatment is based on Tresca's yield criterion, its associated flow rule and a Swift-type nonlinear hardening law. Taking numerical limits, the complete solution is verified in comparison to the linear hardening solution available in the literature.
Exact solution of rotating FGM shaft problem in the elastoplastic state of stress Akis, Tolga; Eraslan, Ahmet Nedim (Springer Science and Business Media LLC, 2007-10-01) Plane strain analytical solutions to estimate purely elastic, partially plastic and fully plastic deformation behavior of rotating functionally graded (FGM) hollow shafts are presented. The modulus of elasticity of the shaft material is assumed to vary nonlinearly in the radial direction. Tresca's yield criterion and its associated flow rule are used to formulate three different plastic regions for an ideal plastic material. By considerina different material compositions as well as a wide range of bore radi...
On the plane strain and plane stress solutions of functionally graded rotating solid shaft and solid disk problems Eraslan, Ahmet Nedim (Springer Science and Business Media LLC, 2006-01-01) Closed form solutions to functionally graded rotating solid shaft and rotating solid disk problems are obtained under generalized plane strain and plane stress assumptions, respectively. The nonhomogeneity in the material arises from the fact that the modulus of elasticity of the material varies radially according to two different continuously nonlinear forms: exponential and parabolic. Both forms contain two material parameters and lead to finite values of the modulus of elasticity at the center. Analytica...
Frictionless double contact problem for an axisymmetric elastic layer between an elastic stamp and a flat support with a circular hole Mert, Oya; Geçit, M. Ruşen; Department of Engineering Sciences (2011) This study considers the elastostatic contact problem of a semi-infinite cylinder. The cylinder is compressed against a layer lying on a rigid foundation. There is a sharp-edged circular hole in the middle of the foundation. It is assumed that all the contacting surfaces are frictionless and only compressive normal tractions can be transmitted through the interfaces. The contact along interfaces of the elastic layer and the rigid foundation forms a circular area of which outer diameter is unknown. The probl...
Propagation of waves from a spherical cavity with and without a shell embedment Akkas, N; Zakout, U; Tupholme, GE (Springer Science and Business Media LLC, 2000-01-01) A spherical cavity in an infinite, elastic medium with and without a shell embedment is subjected to axisymmetric, non-torsional surface loads in the radial and meridional directions. The so-called Residual Variable Method (RVM) is used to obtain exact, closed-form solutions of the wave propagation problems. Some representative numerical results are presented graphically for the stresses created in two realistic loading situations.

Citation Formats

S. Dağ, B. YILDIRIM, and A. C. Ozatag, “Frictional Hertzian contact between a laterally graded elastic medium and a rigid circular stamp,” ACTA MECHANICA, pp. 1773–1789, 2013, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/36084.