Asymptotic methods in contact mechanics

Alexandrov, V. M.

doi:10.1016/s0895-7177(98)00106-x

Cited by 10 publications

(8 citation statements)

References 2 publications

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“…При цьому при вирішенні таких задач вдається уникнути необхідності урахування сингулярностей в розрахункових алгоритмах шляхом відповідного підбору схем навантаження [9].…”

Section: літературний огляд та постановка проблемиunclassified

“…Важливого значення набуває також побудова мо-делей для оцінки зміни НДС дорожнього покриття з урахуванням особливостей реального стану покрит-тя (зміна геометричної конфігурації дорожнього по-криття, особливості експлуатації, тип транспортних засобів тощо) з використанням класичних підходів [8][9][10].…”

Section: літературний огляд та постановка проблемиunclassified

“…Умова (9) дозволяє зробити вис-новок про те, що максимальні зна-чення напружень досягається на певній глибині, яку можна визна-чити за формулою (9). Аналогічно можна встановити, що максималь-ні за модулем значення для σ 13 та σ 23 досягаються в точках:…”

Section: математична модель процесу деформування дорожнього покриттяunclassified

See 2 more Smart Citations

Mathematical model of the process estimation of the deformation of the road surface

Олійник¹,

Незамай²,

Пулик³

2014

EEJET

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Section: літературний огляд та постановка проблемиunclassified

Section: математична модель процесу деформування дорожнього покриттяunclassified

See 1 more Smart Citation

Mathematical model of the process estimation of the deformation of the road surface

Олійник¹,

Незамай²,

Пулик³

2014

EEJET

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“…In that case, a numerical resolution must be implemented: this is done in "contact", for example, but leads to prohibitive CPU time when a large number of simulation have to be done. Other authors [9][10][11], for example, solve the contact problem with various numerical methods but all resolutions give important CPU time. Our choice is to solve an approach but accurate problem proposed by Kalker [7].…”

Section: Steady State Rolling Contact Problemmentioning

confidence: 99%

Probabilistic model for random uncertainties in steady state rolling contact

Chevalier¹,

Cloupet

Soize³

2005

Wear

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Wear phenomena involve a large number of physical and mechanical parameters which are not always well known or controlled during relative movement between two bodies. Numerous industrial applications necessitate an evaluation of technological component life time and wear modelling often fails to give accurate estimation.We use the classical Archard's wear model where wear is related to dissipated power. It appears that great dispersion can occur in the estimation of dissipated power related to a lack of knowledge of certain parameters.We present here a probabilistic approach of the contact problem resolution. We consider the specific contact problem in the case of steady state rolling. A wear apparatus has been used to test different materials and we use the simplified model Fastsim to evaluate slip and tangential traction in the contact zone. For each parameter of the simulation, we construct a probabilistic density function with the only information available.A Monte-Carlo method is implemented and the resolution of numerous cases allows the dissipated energy to be evaluated as a mean value and a confidence region for 95% viability.

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“…Asymptotic solutions of the linear contact problem with a fixed circular contact area have been constracted in a number of papers [8][9][10][11] under the assumption that the relative thickness of the elastic layer is sufficiently large, that is, for large values of the ratio D h=a. In the non-axisymmetric case of an elliptical indenter, the 'method of large ' was applied by Aleksandrov and Vorovich [12] and later was further developed by Aleksandrov [13][14][15]. The so-called large method was used in a number of papers to solve two-dimensional [14,[16][17][18] and three-dimensional [19][20][21][22] contact problems.…”

Section: Introductionmentioning

confidence: 99%

An effective asymptotic method in the axisymmetric frictionless contact problem for an elastic layer of finite thickness

Argatov

2015

Math Methods in App Sciences

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A brief review of asymptotic methods to deal with frictionless unilateral contact problems for an elastic layer of finite thickness is presented. Under the assumption that the contact radius is small with respect to the layer thickness, an effective asymptotic method is suggested for solving the unilateral contact problem with a priori unknown contact radius. A specific feature of the method is that the construction of an asymptotic approximation is reduced to a linear algebraic system with respect to integral characteristics (polymoments) of the contact pressure. As an example, the sixth-order asymptotic model has been written out.

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Asymptotic methods in contact mechanics

Cited by 10 publications

References 2 publications

Mathematical model of the process estimation of the deformation of the road surface

Mathematical model of the process estimation of the deformation of the road surface

Probabilistic model for random uncertainties in steady state rolling contact

An effective asymptotic method in the axisymmetric frictionless contact problem for an elastic layer of finite thickness

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