scholarly journals Mathematical modeling of the contact problem for two elastic bodies with curvilinear boundaries on mismatched grids

2019 ◽  
pp. 1-27
Author(s):  
Pavel Sergeevich Aronov ◽  
Aleksandr Sergeevich Rodin
Keyword(s):  
Mathematical Modeling ◽  
Contact Problem ◽  
Elastic Bodies

scholarly journals On the contact problem of layered elastic bodies

1967 ◽  
Vol 25 (3) ◽  
pp. 233-242 ◽  
Author(s):  
Ting-Shu Wu ◽  
Y. P. Chiu
Keyword(s):  
Contact Problem ◽  
Elastic Bodies

Contact problem for wavy surfaces in the presence of an incompressible liquid and a gas in interface gaps

2018 ◽  
Vol 24 (11) ◽  
pp. 3381-3393 ◽  
Author(s):  
Oleh Kozachok ◽  
Rostyslav Martynyak
Keyword(s):  
Surface Tension ◽  
Contact Problem ◽  
Incompressible Liquid ◽  
Constant Pressure ◽  
Cauchy Kernel ◽  
Hilbert Kernel ◽  
Elastic Bodies ◽  
Laplace Formula ◽  
Interface Gaps ◽  
Wavy Surfaces

This paper presents a study on smooth elastic contact between two semi-infinite elastic bodies, one of which has a wavy surface, for the case when there are an incompressible liquid, not wetting the surfaces of the bodies, at the central region of each interface gap and a gas under constant pressure at the edges of each gap. Due to the surface tension of the liquid, a pressure drop occurs in the liquid and the gas, which is described by the Laplace formula. The formulated contact problem is reduced to a singular integral equation (SIE) with the Hilbert kernel, which is transformed into a SIE with the Cauchy kernel for a derivative of a height of the gaps. A system of transcendental equations for a width of each gap and a width of the gap region filled with the liquid is obtained from the condition of boundedness of the contact stresses at the gap ends and the condition of liquid amount conservation. It is solved numerically, and the dependences of the width and shape of the gaps, the width of the gap regions filled with the liquid and the contact approach of the bodies on the applied load and the surface tension of the liquid are analyzed.

The Contact Problem Studied by Pseudocaustics Formed at the Vicinity of the Contact Zone

1984 ◽  
Vol 106 (3) ◽  
pp. 211-215 ◽  
Author(s):  
P. S. Theocaris ◽  
C. A. Stassinakis
Keyword(s):  
Contact Problem ◽  
Contact Zone ◽  
Contact Area ◽  
The Other ◽  
Tangential Stresses ◽  
Elastic Bodies ◽  
First Case ◽  
Reflected Light ◽  
Spline Polynomial ◽  
Distribution Of Stresses

The method of caustics is applied to formulate the normal and tangential stresses developed in the contact zone of two elastic bodies, and also for one elastic and the other plastic. The stresses are represented by a cubic spline polynomial, its coefficients calculated by pseudocaustics from reflected light around the contact zone. The method is applied to determine the stresses along the boundary of a half-plane and the stresses along the contact area of two disks. The deviation of calculated stresses from the applied ones, in the first case was small, while in the second case it was found that the normal distribution of stresses was similar to a Hertzian distribution. This experimental method can be used to accurately obtain contact stresses.

scholarly journals MATHEMATICAL MODELING OF EXPERIMENT ON BERKOVICH NANOINDENTATION OF ZRN COATING ON STEEL SUBSTRATE

2020 ◽  
Vol 27 ◽  
pp. 18-21
Author(s):  
Evgeniy Sadyrin ◽  
Andrey Vasiliev ◽  
Sergei Volkov
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Analytical Solution ◽  
Contact Problem ◽  
Half Space ◽  
Steel Substrate ◽  
Elastic Half Space ◽  
Functionally Graded ◽  
Good Agreement

In the present paper the experiment on Berkovich nanoindentation of ZrN coating on steel substrate is modelled using the proposed effective mathematical model. The model is intended for describing the experiments on indentation of samples with coatings (layered or functionally graded). The model is based on approximated analytical solution of the contact problem on indentation of an elastic half-space with a coating by a punch. It is shown that the results of the model and the experiment are in good agreement.

scholarly journals Contact problem of two elastic bodies. III

1980 ◽  
Vol 25 (2) ◽  
pp. 137-146
Author(s):  
Vladimír Janovský ◽  
Petr Procházka
Keyword(s):  
Contact Problem ◽  
Elastic Bodies

Mathematical modeling of spinning elastic bodies for modal analysis.

AIAA Journal ◽  
1973 ◽  
Vol 11 (9) ◽  
pp. 1251-1258 ◽  
Author(s):  
PETER W. LIKINS ◽  
FRANK J. BARBERA ◽  
VICTOR BADDELEY
Keyword(s):  
Mathematical Modeling ◽  
Modal Analysis ◽  
Elastic Bodies
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