Axisymmetrically loaded thin circular plate in adhesive contact with an elastic half-space

1988 ◽  
Vol 3 (4) ◽  
pp. 283-298 ◽  
Author(s):  
E. N. Mastrojannis ◽  
L. M. Keer ◽  
T. Mura
Keyword(s):  
Circular Plate ◽  
Half Space ◽  
Adhesive Contact ◽  
Elastic Half Space ◽  
Thin Circular Plate

Frequencies of a Flexible Circular Plate Attached to the Surface of a Light Elastic Half-Space

1959 ◽  
Vol 26 (1) ◽  
pp. 13-17
Author(s):  
G. N. Bycroft
Keyword(s):  
Free Vibration ◽  
Circular Plate ◽  
Half Space ◽  
Fundamental Frequency ◽  
Elastic Half Space ◽  
Flexible Circular Plate

Abstract The frequencies of free vibration of a thin, flexible, circular plate stuck to the surface of a massless elastic half-space are solved by an application of the Rayleigh-Ritz principle. The approximate fundamental frequency is considered in detail when the plate is clamped, free, or hinged at its periphery. The method of obtaining the higher frequencies, such as those involving nodal diameters, is indicated.

A Unified Treatment of Axisymmetric Adhesive Contact on a Power-Law Graded Elastic Half-Space

2013 ◽  
Vol 80 (6) ◽  
Author(s):  
Fan Jin ◽  
Xu Guo ◽  
Wei Zhang
Keyword(s):  
Half Space ◽  
Power Law ◽  
Contact Region ◽  
Adhesive Contact ◽  
Elastic Half Space ◽  
Hertzian Contact ◽  
Contact Radius ◽  
Abel Transformation ◽  
Numerical Solution Methods ◽  
Special Cases

In the present paper, axisymmetric frictionless adhesive contact between a rigid punch and a power-law graded elastic half-space is analytically investigated with use of Betti's reciprocity theorem and the generalized Abel transformation, a set of general closed-form solutions are derived to the Hertzian contact and Johnson–Kendall–Roberts (JKR)-type adhesive contact problems for an arbitrary punch profile within a circular contact region. These solutions provide analytical expressions of the surface stress, deformation fields, and equilibrium relations among the applied load, indentation depth, and contact radius. Based on these results, we then examine the combined effects of material inhomogeneities and punch surface morphologies on the adhesion behaviors of the considered contact system. The analytical results obtained in this paper include the corresponding solutions for homogeneous isotropic materials and the Gibson soil as special cases and, therefore, can also serve as the benchmarks for checking the validity of the numerical solution methods.

scholarly journals Variational Formulation of Interaction between Elastic Plate and Elastic Medium under the Influence of Surface Energy

2018 ◽  
Vol 206 ◽  
pp. 01012
Author(s):  
S. Tirapat ◽  
T. Senjuntichai ◽  
J. Rungamornrat ◽  
R. K. N. D. Rajapakse
Keyword(s):  
Surface Energy ◽  
Circular Plate ◽  
Half Space ◽  
Variational Formulation ◽  
Surface Elasticity ◽  
Elastic Half Space ◽  
Radial Coordinate ◽  
Vertical Loading ◽  
Elastic Circular Plate ◽  
Present Solution

A variational formulation of interaction problem is presented in this paper for the analysis of an elastic circular plate under axisymmetric vertical loading resting on an isotropic elastic half-space under the influence of surface energy. The Gurtin-Murdoch surface elasticity theory is adopted to take into account the surface energy effects. The contact surface between the plate and the half-space is assumed to be smooth, and the deflected shape of the plate is represented by a power series of the radial coordinate. The undetermined coefficients in the series are determined through the minimization of the total potential energy functional of the plate-half-space system. The accuracy of the present solution is verified by comparing with existing solutions, and selected numerical results are presented to portray the influence of surface energy effects on interaction between an elastic circular plate and an elastic half-space.

scholarly journals Discussion: Rigid circular plate resting on a non-homogenous elastic half-space

Géotechnique ◽  
1973 ◽  
Vol 23 (4) ◽  
pp. 596-600
Author(s):  
W. D. Carrier ◽  
J. T. Christian
Keyword(s):  
Circular Plate ◽  
Half Space ◽  
Elastic Half Space
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