Solution of Variational Inequalities in Mechanics

Hlaváček, Ivan; Haslinger, Jaroslav; Nečas, Jindřich; Lovíšek, Ján

doi:10.1007/978-1-4612-1048-1

Cited by 451 publications

(327 citation statements)

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“…On the other hand, by the definition of operator Λ, hypothesis (8), condition (17) and the Jensen inequality, one can verify that…”

Section: Page 9 Of 22 15mentioning

confidence: 94%

“…During the last four decades, the number of contributions to the area of variational and hemivariational inequalities was enormous, both in the theory and applications, cf. e.g., [9,10,17,20,27,30,36,39,41] and the references therein. A part of this progress was motivated by new models and their formulations arising in Contact Mechanics, cf.…”

Section: Introductionmentioning

confidence: 99%

“…A part of this progress was motivated by new models and their formulations arising in Contact Mechanics, cf. e.g., [16,17,35,40,41,45]. Hemivariational inequalities and their systems play nowadays a crucial role in a description of on dynamic contact with velocity dependent friction can be found in Kuttler and Shillor in [22,23].…”

Section: Introductionmentioning

confidence: 99%

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Dynamic history-dependent variational-hemivariational inequalities with applications to contact mechanics

Migórski

Ogorzaly

2016

Z. Angew. Math. Phys.

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Abstract. In the paper we deliver a new existence and uniqueness result for a class of abstract nonlinear variationalhemivariational inequalities which are governed by two operators depending on the history of the solution, and include two nondifferentiable functionals, a convex and a nonconvex one. Then, we consider an initial boundary value problem which describes a model of evolution of a viscoelastic body in contact with a foundation. The contact process is assumed to be dynamic, and the friction is described by subdifferential boundary conditions. Both the constitutive law and the contact condition involve memory operators. As an application of the abstract theory, we provide a result on the unique weak solvability of the contact problem.Mathematics Subject Classification. 35J87, 47J20, 47J22, 74M15, 74G25.

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“…On the other hand, by the definition of operator Λ, hypothesis (8), condition (17) and the Jensen inequality, one can verify that…”

Section: Page 9 Of 22 15mentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Dynamic history-dependent variational-hemivariational inequalities with applications to contact mechanics

Migórski

Ogorzaly

2016

Z. Angew. Math. Phys.

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“…In the existing literature we can find only approaches that concern the existence of solutions together with necessary optimality conditions see e.g. [2,5,14,15], and second order sufficient optimality conditions see e.g. [4,6,7,9].…”

Section: Introductionmentioning

confidence: 99%

“…In [14,15] the results concerning the existence, regularity and finite-dimensional approximation of solutions to the mentioned problem are given. Shape optimization of many problems are considered, among others, in [7-9, 14, 19] where necessary optimality conditions, results concerning convergence of the finite-dimensional approximation and numerical results are provided.…”

Section: Introductionmentioning

confidence: 99%

Dynamic programming approach to structural optimization problem - numerical algorithm

Fulmański¹,

Nowakowski²,

Pustelnik³

2014

OpMath

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Abstract. In this paper a new shape optimization algorithm is presented. As a model application we consider state problems related to fluid mechanics, namely the Navier-Stokes equations for viscous incompressible fluids. The general approach to the problem is described. Next, transformations to classical optimal control problems are presented. Then, the dynamic programming approach is used and sufficient conditions for the shape optimization problem are given. A new numerical method to find the approximate value function is developed.

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A new strategy for the solution of frictional contact problems

Refaat

Meguid

1998

Int. J. Numer. Meth. Engng.

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This article is devoted to the development of a new heuristic algorithm for the solution of the general variational inequality arising in frictional contact problems. The existing algorithms devised for the treatment of the variational inequality representing frictional contact rely on the decomposition of the physical problem into two sub-problems which are then solved iteratively. In addition, the penalty function method and=or the regularization techniques are typically used in the solution of these reduced sub-problems. These techniques introduce user-deÿned parameters which could in uence the convergence and accuracy of the solution. The new method presented in this article overcomes these di culties by providing a solution for the general variational inequality without decomposition into sub-problems. This is accomplished using a new heuristic algorithm which utilizes mathematical programming techniques, and thus avoids the use of penalty or regularization methods. The versatility and reliability of the developed algorithm were demonstrated through implementation to the case of frictional contact of an elastic hollow cylinder with a rigid foundation. ? 1998 John Wiley & Sons, Ltd.

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Solution of Variational Inequalities in Mechanics

Cited by 451 publications

References 0 publications

Dynamic history-dependent variational-hemivariational inequalities with applications to contact mechanics

Dynamic history-dependent variational-hemivariational inequalities with applications to contact mechanics

Dynamic programming approach to structural optimization problem - numerical algorithm

A new strategy for the solution of frictional contact problems

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