A simple numerical approach for solving the frictionless contact problem of elastic wavy surfaces

Meccanica ◽  
2015 ◽  
Vol 51 (2) ◽  
pp. 463-473 ◽  
Author(s):  
K. Houanoh ◽  
H.-P. Yin ◽  
Q.-C. He
Keyword(s):  
Contact Problem ◽  
Numerical Approach ◽  
Frictionless Contact ◽  
Wavy Surfaces

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.

A dynamic frictionless contact problem using signorini like compliance laws

1997 ◽  
Vol 35 (12-13) ◽  
pp. 1245-1260
Author(s):  
G. Bayada ◽  
M. Chambat ◽  
A. Lakhal ◽  
L. Rochet
Keyword(s):  
Contact Problem ◽  
Frictionless Contact

scholarly journals An analytical and numerical approach to a bilateral contact problem with nonmonotone friction

2013 ◽  
Vol 23 (2) ◽  
pp. 263-276 ◽  
Author(s):  
Mikaël Barboteu ◽  
Krzysztof Bartosz ◽  
Piotr Kalita
Keyword(s):  
Contact Problem ◽  
Frictional Contact ◽  
Numerical Approach ◽  
Bundle Method ◽  
Nonconvex Problem ◽  
Proximal Bundle Method ◽  
Loss Of Contact ◽  
The Galerkin Method ◽  
Bilateral Contact ◽  
Numerical Approaches

We consider a mathematical model which describes the contact between a linearly elastic body and an obstacle, the so-called foundation. The process is static and the contact is bilateral, i.e., there is no loss of contact. The friction is modeled with a nonmotonone law. The purpose of this work is to provide an error estimate for the Galerkin method as well as to present and compare two numerical methods for solving the resulting nonsmooth and nonconvex frictional contact problem. The first approach is based on the nonconvex proximal bundle method, whereas the second one deals with the approximation of a nonconvex problem by a sequence of nonsmooth convex programming problems. Some numerical experiments are realized to compare the two numerical approaches.

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