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1
Content available remote On the mass discretization approach to elastodynamics of periodically stratified composites
Szlachetka O., Wągrowska M., Witkowska-Dobrev J., Woźniak C.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2012
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Vol. 11, nr 4
143-150
EN
The object of analysis are two component periodically stratified linear elastic multilayered composites. The aim of contribution is elastodynamics of these composites subjected to the mass discretization on the interfaces between adjacent homogeneous layers. Two specific cases of the mass discretizations are taken into account. In the first case the mass is assigned uniformly to every interface. It is shown that this kind of mass discretization leads to physically completely wrong results. In the second case, the mass is discretized uniformly but on the every second interface. In this case it is shown that the obtained elastodynamics equations have a physical sense provided that the wave are sufficiently long.
2
Content available remote On the certain asymptotic approach to the modelling of microheterogeneous media
Borowska J., Rychlewska J., Woźniak C.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2009
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Vol. 8, nr 1
5-12
EN
The object of analysis is mathematical modelling of thermomechanical problems of microheterogeneous media. The aim of this contribution is to propose a certain asymptotic modeling technique. The proposed approach is realized both in consistent and semiconsistent form.
3
Content available remote On the tolerance overaging for differential operators with periodic coefficients
Borowska J., Łaciński Ł., Rychlewska J., Woźniak C.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2008
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Vol. 7, nr 1
17-21
EN
The aim of this contribution is to propose the tolerance averaging for differential operators with periodic coefficients. The averaging technique presented in this paper is based on proper limit passages with tolerance parameter to zero. This approach is a certain generalization of that presented in [1].
4
Content available remote On the modelling of a certain quasi-linear heat conduction problem in a two-phased laminated medium
Siedlecka U., Woźniak C.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2008
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Vol. 7, nr 1
181-184
EN
The aim of the contribution is to obtain a macroscopic model equation for the quasi-linear heat conduction in a two phased-laminated medium. The analysis will be based on the tolerance averaging technique.
5
Remarks on the notion of tolerance
Woźniak C.
Zeszyty Naukowe Politechniki Świętokrzyskiej. Nauki Techniczne
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2007
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Z. 6
205-218
EN
The objective of this contribution is twofold. First, we recall the notion of a tolerance from the purely formal point of view. Second, we explain and discuss various applications of this notion and underline its role in the mathematical modelling of problems involving objects which can be treated as „indistinguishable”.
PL
Przedmiot pracy jest dwojaki. Najpierw omówiono pojęcie tolerancji z formalnego punktu widzenia. Następnie wytłumaczono i przedyskutowano różne zastosowania tego pojęcia oraz podkreślono jego rolę w modelowaniu matematycznym pewnych zagadnień natury technicznej.
6
Content available remote On a certain extension of the principle of stationary action and its applications
Łaciński Ł., Rychlewska J., Szymczyk J., Woźniak C.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2007
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Vol. 6, nr 1
141-145
EN
The aim of this contribution is to propose a certain extension of the principle of stationary action which can be applied to derive the hyperbolic and elliptic PDEs with quasi-linear operators. The proposed generalized form of the above principle will be used to formations of mathematical models for solids and structures.
7
Content available remote A contribution to the modeling of nonstationary processes in functionally graded laminates
Łaciński Ł., Rychlewska J., Szymczyk J., Woźniak C.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2006
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Vol. 5, nr 1
83-94
EN
The considerations are concerned with mathematical modeling of nonstationary thermomechanical processes in functionally graded laminates (FGL). The proposed modeling procedure is an extension of that based on the tolerance averaging technique [13].
8
Możliwości i bariery w modelowaniu kompozytów
Woźniak C.
Zeszyty Naukowe. Mechanika / Politechnika Opolska
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2005
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z. 87
209-216
PL
Są trzy cele wykładu. Po pierwsze, zawiera on omówienie różnych znaczeń terminu "kompozyt" oraz opisuje wzajemne zależności pomiędzy składnikami kompozytu w skali mikro i makro. Po drugie, rozwinięto tu ogólną koncepcję homogenizacji odniesionej do mechaniki kompozytów. Po trzecie, przedstawiono uzasadnienie modelowania poza granicami homogenizacji.
EN
The aim of the lecture is threefold. First, different meanings of the term "composite" are discussed and the interrelation between descriptions of the composite element on the micro- and macro- levels is specified. Second, the general idea of the homogenization approach to composite mechanics is developed. Third, some motivation of the modeling outside the limits of homogenization are shown.
9
Materiały gradientowe: koncepcja, motywacja, realizacja
Woźniak C.
Zeszyty Naukowe. Mechanika / Politechnika Opolska
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2005
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z. 87
203-208
PL
Idea materiałów funkcjonalnie stopniowanych (FGM) odgrywa ważną rolę i stanowi nowy kierunek w projektowaniu i wykonywaniu elementów konstrukcyjnych. Są to elementy, które na poziomie mikroskopowym są wykonane z co najmniej dwóch składników, a więc na poziomie makroskopowym ich charakterystyki powoli zmieniają się w pewnym zamierzonym kierunku. Celem wykładu jest zarysowanie tej idei, omówienie argumentów uzasadniających stosowanie tych materiałów i zwrócenie uwagi na pewne różnice pomiędzy mechaniką kompozytów a mechaniką omawianych materiałów.
EN
The concept of functionally graded materials (FGM) plays an important role and constitutes a new trend in the design and realization of some structural elements. They are elements which on the microscopic level are made of two or more components so that on the macroscopic level their effective characteristics are slowly varying in a certain preferred direction. The aim of the lecture is to outline this concept, to discuss some motivations for using FGM and to underline some differences between composite mechanics and mechanics of FGM.
10
Content available remote On the modelling of functionally graded laminated structures
Rychlewska J., Szymczyk J., Woźniak C.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2005
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Vol. 4, nr 1
230-238
EN
The object of analysis is a functionally graded material (FGM). The aim of this paper is threefold. Firstly, we outline and recall basic technological motivations and physical foundations of FGM concept. Secondly, we propose a certain special kind of FGM, which on the microstructural level are made of very thin laminae (a functionally graded laminate-FGL). Thirdly, a new approach to the formulation of averaged models for the analysis of dynamic problems in FGL is proposed. Example of applications of the proposed models will be discussed separately.
11
Content available remote A contribution to the heat conduction problem in a laminated medium
Łaciński Ł., Woźniak C.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2005
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Vol. 4, nr 1
123-128
EN
In this contribution we are to show that on the boundaries of a laminated medium, which are perpendicular to the laminae interfaces, some near-boundary phenomena related to boundary conditions take place. The aim of this note is to describe and discuss those phenomena. The analysis is carried out in the framework of the tolerance averaging technique, [1]. The obtained model is confronted with the homogenized model. General considerations are illustrated by a certain special problem.
12
Content available remote On the Modelling of Material Systems with a Periodic Structure
Woźniak C.
Vibrations in Physical Systems
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2004
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Vol. 21
55--58
13
Content available remote On the modelling of dynamic behaviour in a laminated medium with a space-varying structure
Rychlewska J., Woźniak C.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2004
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Vol. 3, nr 1
189--193
EN
In this contribution we propose an approach to the modelling of dynamic problems in a laminated solids with a space-varying structure. This approach is a certain generalization of the modelling procedure formulated in [3] for periodic structures, based on the simplicial subdivision of the unit cell and resulted in the finite difference form of the governing equations. Passage from the finite difference model to the discrete-continuum one is shown.
14
Content available remote On the certain approach to the hyperbolic heat propagation in a periodically laminated medium
Szymczyk J., Woźniak C.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2004
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Vol. 3, nr 1
209--215
EN
The object of our investigations constitutes hyperbolic heat propagation problem in an unbounded periodic laminated medium. We consider solid which has periodically heterogeneous structure in a certain direction and is homogeneous in any perpendicular direction. The main aim of this paper is formulation of a discrete and a discrete-continuum model for the hyperbolic heat transfer problems in the medium under consideration.
15
Simplified models for the vibration analysis of micro-periodic elastic media
Rychlewska J., Szymczyk J., Woźniak C.
Journal of Technical Physics
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2004
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Vol. 45, no 2
91-104
EN
The aim of this paper is to propose and apply a new approach to the formation of simplified models for the vibration analysis of a micro-periodic linear-elastic composite medium. First, we propose a discrete model which can be used to investigations of both long and short waves. The main feature of the obtained discrete model is the finite-difference form of governing equations. The continuum models are derived directly from the discrete one under the assumption that the macroscopic wavelength is large when compared to the length dimension of a periodicity cell. The proposed models describe both the low-frequency and high-frequency vibration problems and can be formulated on different levels of accuracy. The reliability of the procedure leading from discrete to continuum models is discussed on the illustrative example.
16
Content available remote Simplicial modelling of dynamic problems in a micro-periodic composite material
Rychlewska J., Woźniak C.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2003
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Vol. 2, nr 1
159--168
EN
The aim of this paper is to propose a certain new approach to the formulation of both discrete and continuum models for the analysis of dynamic problems in elastic composite solids with a periodic microstructure. The proposed approach is based on a periodic simplicial division of the unit cell and on the assumption of a uniform strain in every simplex. The main feature of the obtained discrete model is the finite-difference form of the governing equations. By applying smoothing operation the continuum models are derived directly from the discrete ones.
17
Content available remote On the modelling of hyperbolic heat conduction problems in periodic lattice structures
Szymczyk J., Woźniak C.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2003
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Vol. 2, nr 1
183--189
EN
A new modelling approach to the hyperbolic heat conduction problems in periodic lattice structures of an arbitrary form is discussed. Taking into account the results obtained in [5] we introduce a special description of the periodic lattice geometry which leads to the heat conduction model governed by the system of finite difference equations. The continuum models are derived from the finite difference equations by using the principle of stationary action.
18
Content available On elastodynamics of biperiodic composite media
Woźniak M., Woźniak C.
Journal of Theoretical and Applied Mechanics
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2003
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Vol. 41 nr 2
289-304
EN
The aim of this paper is twofold. First, we formulate a mathematical model for the analysis of waves propagating in a linear-elastic composite, which in every plane normal to a certain straight line has an identical periodic structure. Secong, we apply the derived model equations to the investigations of waves propagating across a laminated medium with periodically folded laminae. Lower and higher propagation speeds for the longtudinal and transversal waves are calculated and for the long waves represented in the form of simple asymptotic formulas.
PL
W artykule przedstawiono dwa problemy. Po pierwsze, sformułowano matematyczny model umożliwiający badanie propagacji fal w liniowo-sprężystych kompozytach, dla których każda płaszczyzna prostopadła do pewnej prostej ma taką samą dwuwymiarową strukturę periodyczną. Po drugie, otrzymany model zastosowano do analizy propagacji fal w laminacie o periodycznie pofałdowanych warstwach. Dla przypadku tego wyznaczono niższą i wyższą prędkość fazową propagacji, które w przypadku fal długich dają się wyrazić za pomocą prostych formuł asymptotycznych.
19
Content available On continuum modelling of dynamic problems in composite solids with periodic microstructure
Rychlewska J., Woźniak C.
Journal of Theoretical and Applied Mechanics
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2003
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Vol. 41 nr 4
735-753
EN
In this contribution we propose an approach to the macroscopic modelling of periodic composites which is based on the periodic simplicial subdivision of the unit cell. This approach makes it possible to derive a hierarchy of continuum models which describe dynamic behaviour of periodic composites on different levels of accuracy. The obtained results are compared and applied to the analysis of a certain wave propagation problem.
PL
W pracy zaproponowano nowe podejście do modelowania zagadnień dynamiki w liniowo-sprężystych mikroperiodycznych ośrodkach ciągłych, które za punkt wyjścia przyjmuje periodyczny podział symplicjalny elementu reprezentatywnego struktury. Podejście to umożliwia wyprowadzenie pewnej hierarchii modeli ciągłych, które opisują zagadnienia dynamiki z różną dokładnością. Otrzymane wyniki zastosowano do analizy propagacji fali w nieograniczonym ośrodku o budowie mikroperiodycznej.
20
Content available remote On vibrations of biperiodic composites
Jędrysiak J., Michalak B., Woźniak C.
Vibrations in Physical Systems
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2002
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Vol. 20
172--173
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