The variational method in contact problems. The present state of the problem and trends in its development

Кравчук, А. С.

doi:10.1016/j.jappmathmech.2009.07.004

Cited by 8 publications

(2 citation statements)

References 22 publications

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“…Constructively nonlinear problems have been popular since 1970s in works of Kravchuk, Bathe, Kikuchi, Glowinski [2][3][4][5][6]. Klarbring, Hlaváček and Cottle considered variational formulations [7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Algorithm for calculating the problem of unilateral frictional contact with an increscent external load parameter

Popov,

Lovtsov

2023

Struct. Mech. of Eng. Const. and Build

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The subject of the study is the contact interaction of deformable elements of linear complementarity problem (LCP). To solve the linear complementarity problem, the Lemke method with the introduction of an increasing parameter of external loading is used. The proposed approach solves the degenerated matrix in a finite number of steps, while the dimensionality of the problem is limited to the area of contact. To solve the problem, the initial table of the Lemke method is generated using the contact matrix of stiffness and the contact load vector. The unknowns in the problem are mutual displacements and interaction forces of contacting pairs of points of deformable solids. The proposed approach makes it possible to evaluate the change in working schemes as the parameter of external load increases. The features of the proposed formulation of the problem are shown, the criteria for stopping the stepwise process of solving such problems are considered. Model examples for the proposed algorithm are given. The algorithm has shown its efficiency in application, including for complex model problems. Recommendations on the use of the proposed approach are given.

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Section: Introductionmentioning

confidence: 99%

Algorithm for calculating the problem of unilateral frictional contact with an increscent external load parameter

Popov,

Lovtsov

2023

Struct. Mech. of Eng. Const. and Build

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“…[17]. A detailed review of investigations in the field of variational methods for the solution contact problems can be found in [5].…”

Section: Introductionmentioning

confidence: 99%

Contact Problems of Motion of Elastic Bodies Along Hard Surfaces

Kuz'menko

Mykhal’chuk

2014

J Math Sci

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We propose a mathematical model of motion of an elastic body along a hard surface in the absence of friction forces. The formulations of the problem in the form of a variational inequality and in the form of the extremum variational problem are obtained. For the discretization of the extremum variational problem, we use the finite-element method. As an example, we consider the motion of a body with rectangular cross section under the conditions of plane deformation. We investigate strains and stresses formed in the case of motion along the surfaces in the horizontal and vertical directions.

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A Method for the Solution of a Three-Dimensional Contact Problem of Interaction of Two Elastic Bodies in the Presence of Friction

Aleksandrov

2015

J Math Sci

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The variational method in contact problems. The present state of the problem and trends in its development

Cited by 8 publications

References 22 publications

Algorithm for calculating the problem of unilateral frictional contact with an increscent external load parameter

Algorithm for calculating the problem of unilateral frictional contact with an increscent external load parameter

Contact Problems of Motion of Elastic Bodies Along Hard Surfaces

A Method for the Solution of a Three-Dimensional Contact Problem of Interaction of Two Elastic Bodies in the Presence of Friction

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