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1

Application of computational mechanics approaches for increasing of tribosystem operational parameters by using plasma hardening method

Kopylov Viacheslav, Kuzin Oleg, Kuzin Nickolai

Journal of Applied Mathematics and Computational Mechanics

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2021

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Vol. 20, nr 1

61--70

EN

On the basis of the mathematical model of the continual description of functionalgradient metal systems, taking into account their structure, a computational computer scheme has been developed that makes it possible to assess the stress-strain state of local volumes of parts taking into account their spatial inhomogeneity. With the use of modern software components of computational mechanics - FEniCS finite element analysis package and its implementation in Python, the optimal structural characteristics of wheelsets of railway locomotive tires after plasma treatment have been established. It is shown that, depending on the value of the load, hardening of products must be carried out to a depth of 4.5 mm; with a further increase in thickness, the parameters of operational strength do not change.

2

On elastic contact problems of micro-periodic slant layered composite pressed by a rigid punch with a parabolic or rectangular shape

Sebastianiuk Piotr, Perkowski Dariusz M., Kulchytsky-Zhyhailo Roman

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2021

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Vol. 69, nr 6

art. no. e138091

EN

The paper presents an analysis of the influence of the shape of the rigid body pressed into the micro-periodic composite half-space on the examples of two punch shapes – parabolic and rectangular. The presented material is a layered body that consists of infinitely many thin alternately arranged homogenous layers. Layers of the presented composite are oblique to the boundary surface. Two cases of punch tip shape are examined – parabolic and rectangular. The presented problem has been formulated within the framework of a homogenized model with microlocal parameters and solved using the elastic potentials method and averaged boundary condition. Fourier integral transform method has been used to obtain the solution and the inverse integrals have been calculated numerically. Solutions in terms of contact pressure and maximum pressure characteristics were shown in the form of graphs.

3

Dwustronna więź kontaktowa Hertz’a w numerycznej analizie drgań sprzężonego układu pociąg-tor

Bryja Danuta, Chojnacki Wojciech

Przegląd Komunikacyjny

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2019

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R. 74, nr 11

2--7

PL

W pracy przedstawiono i porównano dwie metody symulacji drgań układu pociąg-tor, różniące się modelem kontaktu koło-szyna. W pierwszej metodzie zastosowano dwustronną, odkształcalną więź kontaktową typu Hertz’a, w drugiej – więź nieodkształcalną. W obu metodach przyjęto płaski model obliczeniowy, złożony z belki Eulera spoczywającej na podłożu sprężysto-tłumiącym typu Winklera i zestawu pojazdów szynowych modelowanych układami dynamicznymi o dziesięciu stopniach swobody. Przedstawiono wyniki analiz numerycznych, których celem było określenie wpływu podatności dwustronnych więzi kontaktowych na wyniki symulacji drgań rozważanego układu. Stwierdzono, że zastąpienie sztywnych więzi kontaktowych przez dwustronne więzi sprężyste Hertz’a nie ma istotnego wpływu na symulacje drgań toru i ma niewielki wpływ na symulacje drgań nadwozia pojazdu i wózka jezdnego. Zaproponowana metoda symulacji będzie mogła być wykorzystana do badań numerycznych zjawiska chwilowego odrywania kół od szyn, po niewielkich modyfikacjach w celu wprowadzenia jednostronnych więzi Hertz’a (nie przenoszących sił rozciągających), które są dokładniejszym modelem kontaktu.

EN

The paper presents and compares two methods for simulation the train-track system vibrations, differing in the wheel-rail contact model used. In the first method, two-way Hertzian spring is used, in the second – a non-deformable constraint. In both methods, a flat computational model is assumed, consisting of an Euler-Bernoulli beam resting on a Winkler-type elastic foundation with damping and a set of rail vehicles modeled by dynamic systems with ten degrees of freedom. The results of numerical analysis are presented, in order to determine an influence of the contact constraints’ deformability on the vibration simulations. It is found that the replacement of non-deformable contact constraints by two-way Hertzian springs has no significant effect on track vibration simulations and has a little effect on vibration simulations of vehicle body and bogie. The developed simulation method can be used for numerical studies of the phenomenon of instantaneous detachments of wheels from rails, after minor modifi cations directed to introduce one-way Hertzian springs (i.e. not carrying tensile forces) being a more accurate contact model.

4

An axisymmetric contact problem of an elastic layer on a rigid circular base

Kebli B., Berkane S., Guerrache F.

Mechanics and Mechanical Engineering

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2018

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Vol. 22, nr 1

221--237

EN

An analytical solution is presented to a doubly mixed boundary value problem of an elastic layer partially resting on a rigid smooth base. A circular rigid punch is applied to the upper surface of the medium where the contact is supposed to be smooth. The case of the layer with a cylindrical hole was considered by Toshiaki and all [5]. The studied problem is reduced to a system of dual integral equations using the Boussinesq stress functions and the Hankel integral transforms. With the help of the Gegenbauer formula we get an infinite algebraic system of simultaneous equations for calculating the unknown function of the problem. The truncation method is used for getting the system coefficients. A closed form solution is given for the displacements, stresses and the stress singularity factors. The stresses and displacements are then obtained as Bessel function series. For the numerical application we give some conclusions on the effects of the radius of the punch with the rigid base and the layer thickness on the displacements, stresses, the load and the stress singularity factors are discussed.

5

Frictionless contact between a rigid indentor and a transversely isotropic functionally graded layer

Patra R., Barik S. P., Chaudhuri P. K.

International Journal of Applied Mechanics and Engineering

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2018

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Vol. 23, no. 3

655--671

EN

This article is concerned with the study of frictionless contact between a rigid punch and a transversely isotropic functionally graded layer. The rigid punch is assumed to be axially symmetric and is supposed to be pressing the layer by an applied concentrated load. The layer is resting on a rigid base and is assumed to be sufficiently thick in comparison with the amount of indentation by the rigid punch. The graded layer is modeled as a non-homogeneous medium. The relationship between the applied load P and the contact area is obtained by solving the mathematically formulated problem through using the Hankel transform of different order. Numerical results have been presented to assess the effects of functional grading of the medium and the applied load on the stress distribution in the layer as well as on the relationship between the applied load and the area of contact.

6

Symmetrized semi-smooth Newton method for solving 3D contact problems

Kucera R., Haslinger J., Motycková K., Markopoulos A.

Systemy Wspomagania w Inżynierii Produkcji

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2017

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Vol. 6, iss. 4

286--293

EN

The semi-smooth Newton method for solving discretized contact problems with Tresca friction in three space dimensions is analyzed. The slanting function is approximated to get symmetric inner linear systems. The primal-dual algorithm is transformed into the dual one so that the conjugate gradient method can be used. The R-linear convergence rate is proved for an inexact globally convergent variant of the method. Numerical experiments conclude the paper. The contact problems are important in many practical applications, e.g., biological processes, design of machines, transportation systems, metal forming, or medicine (bone replacements).

CS

V práci je analyzována nehladká Newtonova metoda pro rešení diskretizovaných kontaktních úloh s Trescovým trením ve trech prostorových dimenzích. Slanting funkce je aproximována za úcelem získání symetrických vnitrních lineárních úloh. Pro použití metody sdružených gradientu je primárne-duální algoritmus preveden na duální. R-lineární rychlost konvergence je dokázána pro nepresnou globálne konvergentní variantu metody. Záverem jsou uvedeny numerické experimenty. Kontaktní úlohy mají radu významných aplikací, napr. biologické procesy, design stroju a prepravních systému, tvárení kovu nebo medicína (modelování kostních náhrad).

7

Continuous contact problem of a functionally graded layer resting on an elastic half‐plane

Öner E., Adiyaman G., Birinci A.

Archives of Mechanics

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2017

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Vol. 69, nr 1

53--73

EN

In this study, the continuous contact problem of a functionally graded layer resting on an elastic half-plane and loaded by a rigid rectangular stamp is examined. The problem is solved assuming that the functionally graded (FG) layer is isotropic and the shear modulus and mass density vary exponentially throughout the layer’s thickness. However, the body force of the elastic half-plane is neglected. In addition, it is assumed that all surfaces are frictionless and only compressive stress is transferred along the contact surfaces. The mathematical problem is reduced to a singular integral equation in which the contact stress under the rigid stamp is unknown using the Fourier integral transform and boundary conditions related to the problem. This singular integral equation is solved numerically using the Gauss–Chebyshev integration formula. The dimensionless contact stress under the rigid stamp, the initial separation loads and the initial separation distances between the FG layer and the elastic half-plane are obtained for various dimensionless quantities.

8

Contact problem of conducting and heated punch on a multifield foundation

Rogowski B.

International Journal of Applied Mechanics and Engineering

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2015

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Vol. 20, no. 3

531--564

EN

The solution for a multifield material subjected to temperature loading in a circular region is presented in an explicit analytical form. The study concerns the steady – state thermal loading infinite region (heated embedded inclusion), half – space region and two – constituent magneto – electro – thermo – elastic material region. The new mono – harmonic potential functions, obtained by the author, are used in the analysis of punch problem. The more interested case in which the contact region is annular is analyzed. By using the methods of triple integraf equations and series solution technique the solution for an indentured multifield substrate over an annular contact region is given. The sensitivity analysis of obtained indentation parameters shows some interesting points. In particular, it shows that the increasing of the applied electric and magnetic potentials reduces the indentation depth in multifield materials.

9

Friction effect in a plane problem of punch acting on a half-space weakened by cracks

Tomczyk A.

Acta Mechanica et Automatica

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2014

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Vol. 8, no. 2

107--114

EN

This work makes use of singular integral equations method to solve plane contact problem for a half-space containing cracks. This method is based on complex variables. Relationships are presented which help find the contact pressure under the punch and the value of stress intensity factors at the crack tips. A detailed solution is presented for the problem of a punch pressed to the surface of a half-space weakened by a single straight crack. It includes both a situation where the punch has a flat and parabolic base. The influence of friction and the position of the crack on the distribution of the values of stress intensity factors KI i KII in the functions of crack length and distance from the contact zone was analyzed in detail.

10

Modelowanie procesów kruszenia za pomocą MES – propozycja metody identyfikacji danych materiałowych oraz właściwości zadania kontaktowego

Mańkowski J., Ciężkowski P.

Zeszyty Naukowe Instytutu Pojazdów / Politechnika Warszawska

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2013

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z. 4/95

125--135

PL

Ośrodki kruche należą do grupy materiałów o bardzo złożonej strukturze. Jako ośrodki niejednorodne i anizotropowe, mają losowo rozłożone nieciągłości struktury, tzn. rysy, spękania, pory. Jednym z istotnych problemów, który bardzo często pojawia się podczas analiz, jest identyfikacja właściwości zarówno danych materiałowych, jak i charakterystyk oddziaływania narzędzia na ośrodek kruchy. W niniejszej pracy przedstawiono propozycję metody identyfikacji parametrów materiałowych oraz propozycję metody modelowania zagadnienia kontaktowego na przykładzie wapienia "Morawica". Badania i analizy zostały przeprowadzone dla próby ściskania walca. Uzyskano bardzo dobrą zbieżność wyników analiz z wynikami z eksperymentu wykonanego na obiekcie rzeczywistym.

EN

Brittle materials belong to the group of brittle materials with a very complex structure. As heterogeneous and anisotropic materials, are randomly distributed discontinuity structures such as scratches, cracks, pores. One of the problems, which often occurs during the analysis is to identify the properties of materials data and identify the characteristics of the impact of the tool on a brittle material. This paper presents a method of identification of material parameters and a method of modeling the contact problems for limestone “Morawica”. Tests and analyzes were performed for a roller compression test. Very good convergence of the results of analysis and of the results of an experiment performed on a real object was obtained.

11

Symulacje numeryczne fragmentu łańcucha kinematycznego pontonów mostu pływającego

Krasoń W., Derewońko A., Chłus K., Popławski A., Golczak K.

Przegląd Mechaniczny

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2013

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nr 1

15--19

PL

W pracy przedstawiono jeden z etapów numerycznych analiz fragmentu łańcucha kinematycznego pontonów mostu pływającego. Omówiono modele pojedynczego pontonu oraz dwóch pontonów z uwzględnieniem zespołu zamków mechanicznych stanowiących kompletny sprzęg łączący pontony na wodzie. Przedstawiono wybrane wyniki numerycznej symulacji współpracy podzespołów, stanowiących fragment takiego łańcucha kinematycznego pontonów mostu pływającego.

EN

The paper presents a numerical analysis of stages of a kinematic chain fragment of floating bridge pontoons. There were discussed models of a single pontoon and two inflatable pontoons including a set of mechanical locks con-stituting a complete coupling connecting pontoons on the water. Selected results of numerical simulation of collaboration components, forming a part of such a kinematic chain fragment of floating bridge pontoons, were presented.

12

Comparison of contact stress distribution for foam seat and seat of auxetic spring skeleton

Janus-Michalska M., Jasińska D., Smardzewski J.

International Journal of Applied Mechanics and Engineering

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2013

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Vol. 18, no. 1

55--72

EN

The objective of this paper is to present and compare the results of numerical solutions of contact problem for two types of seats subjected to typical sitting loadings. The first seat is made of a typical hyperelastic foam, the other is designed with an auxetic polyamid spring skeleton. Computer simulations of the seat structure under a typical static loading exerted by a human body are performed by means of ABAQUS FEA. The model provides an insight into deformation modes and stress field in relation to geometric and material parameters of the seat structure.The other type of seat, due to the fact of global auxecity and progressive springs characteristics reduces contact stress concentrations, giving an advantegous distribution of pressure and provides the sensation of physical comfort. The proper seat skeleton shape leads to an improvement of ergonomic quality.

13

Relationship in between compression of the rollers and contact area width and the clamp force

Jurkiewicz A., Pyryev Y.

Challenges of Modern Technology

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2013

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Vol. 4, no. 2

31--36

EN

In an offset printing machine the rollers (ink unit) and the cylinders (printing unit) are in contact in a lot of places. The contact surfaces comprise a metal surface and a rubber surface. As appears from findings based on the professional literature and experience of people working in printing houses the issue of contact between ink rollers and printing cylinders in an offset printing machine is of great importance. It has impact on the quality of printouts (generation of printouts errors), consumption of energy, time of making the printing machine ready for operation, wear of the machine’s components and related consumables like ink, dampening solution, paper, ink rollers, plate. During the theoretical studies, the equations were derived to show how the rollers compression depends on the contact area width and clamping force. The equations involve Young’s modulus and Poisson’s ratio of rollers’ materials. The difference between these equations and the so far existing equations has resulted from changing the place of applying the clamping force and involving Poisson’s ratio. The paper includes the comparison of the aforesaid new equations and those known from the literature. Moreover, the relationship in between the contact area width and the compression of metal roller and rubber-covered roller was subject to experimental attempts aimed at verification of the equation presented. In order to measure the rollers compression a clock sensor was used, and for measurement of the contact area width – a device called Roller Nip Control. The results of these measurements are presented in this paper and are compared with the results obtained from the equation derived in the course of theoretical studies using the analytical method.

14

Printouts' Quality Depending on Too Small Pressure of a Blanket Cylinder Against an Impression Cylinder and a Plate Cylinder in Offset Machine

Jurkiewicz A., Pyryev Y., Kowalczyk J.

Challenges of Modern Technology

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2013

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Vol. 4, no. 4

12--17

EN

It has been written in many books that correct setting of clamp in a printing offset machine has impact on wear of consumables and machine elements, and quality of printouts. However there has been no clear recipe to do that. In our article we present research on effect of too small pressure between a blanket cylinder against a plate cylinder and an impression cylinder. The challenge was to find method for gaining results of printing with different clamp but with the same printing conditions. During printing, especially when the printing machine stops and starts, a balance between ink and dampening solution is changing. To obtain the same printing conditions with different clamp on the blanket cylinder under blanket, there were fixed underlay sheets with the same thickness and width but different length. To reduce influence of variable thickness of glue the underlay sheets was glued to each other only on the one edge. We printed on two kind of papers: coated and uncoated. The amount of ink transported on paper was adjusted by changing rotation of the ink fountain roller. The spectrophotometer was used to measure optical density. The tone value increase was computed with Murray-Davies equation. While the tone value increase and optical density are very important printoutÂ parameters, our research shows how change of pressure changes printing quality. Our results also help to understand behavior of ink under pressure. Depending on paper and clamp ink could penetrate into the paper or spreads on the paper surface.

15

Receding contact problem for a coated layer and a half-plane loaded by a rigid cylindrical stamp

Adibelli H., Comez I., Erdol R.

Archives of Mechanics

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2013

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Vol. 65, nr 3

219--236

EN

In this study, the frictionless contact problem between a coated layer and a half-plane is considered when they are pressed by a rigid cylindrical stamp. Upon loading, two unknown contact widths and contact pressures occur on the contact areas the advanced contact area between the stamp and the coating; and the receding contact area between the layer and the half-plane. This problem is reduced to two singular integral equations by using the Fourier transform and applying the boundary conditions of the problem. The numerical solution of the system of singular integral equations is obtained by applying the Gauss–Chebyshev integration formulas.

16

Contact Problem of Disk on Shaft Fixed by Induction Shrink Fit

Ulrych B., Kotlan V, Doležel I.

Przegląd Elektrotechniczny

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2012

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R. 88, nr 12b

32-34

EN

The problem of shrink fit between the disk and shaft is solved. The shrink fit realized by induction heating must transfer the prescribed torque and power. Both disk and shaft are considered elastic. The first step of the task is to find appropriate dimensions of the disk and interference. The second step is to suggest the parameters of its induction heating. The methodology is illustrated by a typical example.

PL

W artykule rozwiązano problem pasowania kurczowego między tarczą a wałem. Pasowanie kurczowe zrealizowane zostało metodą indukcyjną – musi ono przenieść założone moment i moc. Zarówno tarcza jak i wał zostały potraktowane jako elastyczne. Pierwszym krokiem w rozwiązaniu zadania jest znalezienie dogodnych rozmiarów tarczy. Drugim krokiem jest zasugerowanie parametrów jej nagrzewania indukcyjnego. Ta metodyka została zilustrowana typowym przykładem. (Problem kontaktu tarczy na wale poprzez zastosowania pasowania kurczowego)

17

A study on the design of auxetic structure of seat skeleton

Jasińska D., Janus-MIchalska M., Smardzewski J.

Mechanics and Control

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2012

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Vol. 31, no. 2

72-76

EN

This paper presents numerical study of deformation and stresses in seat skeleton elements subject to static and dynamic pressure loads. Elastic skeleton made of polyamide or elastomer is taken as an example of a seat material. Auxetic type of seat structure ensures the reduction of real contact stresses between human body and seat, making it more comfortable than typical. FEM analysis is performed using ABAQUS system. Numerical calculations are carried out to determine the nonlinear stiffness characteristics of seat springs. The study makes possible the selection of material and structural topology fulfilling design constraints and additional recommendations concerning structural flexibility, stability and optimal reduction of contact stresses. This paper presents an application of the theoretical prediction to solve the practical problem.

PL

Artykuł przedstawia studium obliczeniowe elementów szkieletu siedziska wykonanych z elastomeru lub poliamidu poddanych typowym obciążeniom statycznym i dynamicznym od siedzenia. Auksetyczne własności struktury szkieletu siedziska powodują redukcją naprężeń kontaktowych między ciałem człowieka i siedziskiem, czyniąc je bardziej komfortowym w użytkowaniu. Obliczenia przeprowadzono programem ABAQUS metodą elementów skończonych. W wyniku otrzymano nieliniowe charakterystyki sprężyn siedziska. Studium obliczeniowe pozwala na wybór materiału i kształtu sprężyn spełniających warunki projektowe dotyczące wytrzymałości, podatności stabilności oraz optymalnej redukcji naprężeń kontaktowych. Praca prezentuje zastosowanie teoretycznych rezultatów do rozwiązań stosowanych w praktyce

18

Analysis of pressure force between two cylinders

Jurkiewicz A., Pyryev Y.

Challenges of Modern Technology

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2012

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Vol. 3, no. 1

10--14

EN

Cylinders are very important elements in an offset printing machine because after being supplied with ink they transfer a printing image on paper. A type of setting as regards the stress between cylinders affects quality of printouts as well as rate of wear and tear of operating materials and machine’s elements. It is of great importance to provide for accurate calculation of stress force between two cylinders because this allows for setting an adequate contact zone width and cylinders indentation. In the printing unit of the offset machine there occurs contact between a metal cylinder and cylinder with fixed rubber blanket. The said blanket is composed of some layers, where one of them is a compressible layer. Therefore, the problem is not of trivial nature, as the blanket is made of a non-linear material.

19

A sign preserving mixed finite element approximation for contact problems

Hild P.

International Journal of Applied Mathematics and Computer Science

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2011

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Vol. 21, no 3

487-498

EN

This paper is concerned with the frictionless unilateral contact problem (i.e., a Signorini problem with the elasticity operator). We consider a mixed finite element method in which the unknowns are the displacement field and the contact pressure. The particularity of the method is that it furnishes a normal displacement field and a contact pressure satisfying the sign conditions of the continuous problem. The a priori error analysis of the method is closely linked with the study of a specific positivity preserving operator of averaging type which differs from the one of Chen and Nochetto. We show that this method is convergent and satisfies the same a priori error estimates as the standard approach in which the approximated contact pressure satisfies only a weak sign condition. Finally we perform some computations to illustrate and compare the sign preserving method with the standard approach.

20

Problems regarding stress between offset printing rollers

Jurkiewicz A., Pyryev Y.

Challenges of Modern Technology

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2011

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Vol. 2, no. 2

27--30

EN

At present, companies show particular care about quality and profit which are inherent with costs. An in adequately set stress between the printing rollers may significantly worsen the quality and increase costs of printing. Until now, a contact between rollers used to be set by a printer, where it was based on his experience. A width of the surface contact was measured or a distance between the form plate or the rubber to the bearer rings (rings made of hardened metal) was calculated. This paper includes a presentation regarding an attempt to solve the contact-related problems by way of mathematical methods.