On the theory of contact problems taking account of friction on the contact surface

Кравчук, А. С.

doi:10.1016/0021-8928(80)90178-1

Cited by 18 publications

(6 citation statements)

References 4 publications

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“…Each researcher will have to decide which method will be used to solve the problem. For example, in [83] and [84] an algorithm with a finite element method in the first part has been used. We will use here the BIEs and its numerical realization of the boundary element method (BEM) as the first part of the algorithm.…”

Section: \\K T Q N \*N T \Dnm\mentioning

confidence: 99%

Fracture Dynamics with Allowance for Crack Edge Contact Interaction

Guz¹,

Zozulya²

2001

International Journal of Nonlinear Sciences and Numerical Simulation

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In this review article general results are presented concerning problems in the fracture dynamics of elastic bodies with allowance for unilateral crack edge contact interaction with friction.. A formulation has been made of the elastodynamic contact problem with unilateral restrictions for bodies with cracks under arbitrary dynamic loading . A specific case of liarmonic loading important to these applications has also been considered. The mathematical aspects of the elastodynamics problem for bodies with cracks and with unilateral restrictions in the form of inequalities on the crack edges have been considered in brief. A variational formulation of the problem has been given. Boundary variational inequalities and boundary functionals have been derived. The boundary integral equations (BIE) method in a Laplace transform domain has been used as a solution for the elastodynamic problem for bodies with cracks. Singularities of the kernels in these integral equations have been studied. Two regularization methods of the potentials with "strongly" singular kernels have been considered. The first is based on its transformation into integro-differentional equations. The second consists of the utilization of the BIE with hypersingular integrals, which are considered in the sense of a finite part, according to Hadamard. An algorithm for the solution of the elastodynamic unilateral contact problem for bodies with cracks has been elaborated. The algorithm is based on finding a saddle point of a sub-differentional boundary functional. It has been shown that the algorithm may be considered as a compressive operator, which acts in corresponding functional spaces. This means that the algorithm is convergent. Numerical methods have been elaborated for the solution to elastodynamic contact problems with unilateral restrictions and friction for bodies with cracks. The problem has been solved, for plane liarmonic tension-compression wave propagation in a plane with one and two colinear finite length cracks and with allowance for unilateral contact interaction of the crack edges. Dependence of the solution accuracy on the approximation of coordinates and time, and also of numbers of terms in the expansion of the stress-strain state components into Fourier series, has been investigated. Numerical results have also been presented. Quantitative and qualitative effects caused by contact interaction of the crack edges have been investigated. This review contains 170 references.

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Section: \\K T Q N \*N T \Dnm\mentioning

confidence: 99%

Fracture Dynamics with Allowance for Crack Edge Contact Interaction

Guz¹,

Zozulya²

2001

International Journal of Nonlinear Sciences and Numerical Simulation

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“…Problems PW t and PW are equivalent if dt is sufficiently small. Applying the iteration method 4,9 to Problem PW t , we obtain Problem PW (k) with "specified friction" (static, if u t f is removed): it is required to findũ (k+1) ∈K and t (4.8)…”

Section: Variational Formulation Of the Problemmentioning

confidence: 99%

The Signorini problem with Coulomb friction for a hyperelastic body under finite deformations

Kosushkin¹

2008

Journal of Applied Mathematics and Mechanics

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“…Numerical solutions of problems of the contact of deformable bodies with friction using velocities, including more complex loading processes, were given for the first time using the example of the axisymetric problem of the indentation of a sphere into a half-space, 4 in which the linearized impenetrability condition was used. Below we will present a comparison of the solutions of the problems for one and several steps of the parameter t (one step corresponds to the use of the displacements in the friction law).…”

Section: Examples Of Numerical Solutions and Their Analysis Descriptmentioning

confidence: 99%

“…The change to a variational formulation was first made in Ref 4,. subsequently reproduced in Ref 11.…”

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confidence: 99%

The solution of contact problems using boundary element method

Кравчук¹,

Neittaanmäki²

2007

Journal of Applied Mathematics and Mechanics

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On the theory of contact problems taking account of friction on the contact surface

Cited by 18 publications

References 4 publications

Fracture Dynamics with Allowance for Crack Edge Contact Interaction

Fracture Dynamics with Allowance for Crack Edge Contact Interaction

The Signorini problem with Coulomb friction for a hyperelastic body under finite deformations

The solution of contact problems using boundary element method

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