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1
Modelowanie kompozytów o budowie periodycznej. Homogenizacja a modele nieasymptotyczne
100%
Woźniak C.
Zeszyty Naukowe. Budownictwo / Politechnika Śląska
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1999
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tom z. 86
231-238
PL
Celem pracy jest krytyczne spojrzenie na fizyczną poprawność rezultatów znanej w literaturze metody homogenizacji asymptotycznej, por. [2, 3], zwrócenie uwagi na jej usterki i ograniczenia, a następnie propozycja usunięcia tych niedomagań poprzez osłabienie fizycznych założeń homogenizacji. Wykazano, że proponowane podejście prowadzi do pewnych uśrednionych modeli nieasymptotycznych, które w szczególnych przypadkach są zgodne z rezultatami uzyskanymi metodą homogenizacji. Rozważania przeprowadzono na przykładzie równania przewodnictwa cieplnego.
EN
The aim of contribution is to discuss certain aspects of the known asymptotic homogenization method cf. [2, 3] related mainle to the physical reliability of its results and to propose a new modelling approach by related mainly to the physical reriability of its results and to propose a new modelling approach by retaining some terms neglected in the homogenization procedure. It will be shown that the proposed approach leads to an averaged but nonasymptotic model wich only for special problems coincides with the homogenized one. The analysis is ca
2
Content available remote Continuum modelling of laminates with a slowly graded microstructure
63%
Szymczyk J. , Woźniak C.
Archives of Mechanics
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2006
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tom Vol. 58, nr 4-5
445-458
EN
The considerations are concerned with modelling and analysis of the dynamic response for micro-laminated two-phased solids. The main attention is focussed on modelling of the laminates which have a slowly graded microstructure in the direction normal to the layering (slowly graded laminates, SGL). Periodic and functionally graded laminates can be treated as special cases of SGL. A new mathematical model which couples micro- and macro-response of the linear elastic SGL is proposed. It is shown that for laminates with a weak transversal inhomogeneity, the derived model equations can be decomposed into asymptotic equations which describe the behavior of a laminate independently on the macro- and micro-level. This decomposition is estimated on the example of a specific vibration problem.
3
Content available remote Boundary layer phenomena in elastodynamics of functionally graded laminates
63%
Rychlewska J. , Woźniak C.
Archives of Mechanics
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2006
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tom Vol. 58, nr 4-5
431-444
EN
The object of considerations are micro-laminated two-phase solids having macroscopic properties continuously varying in the direction normal to the layering (functionally graded laminates, FGL). The main question posed in this contribution is how to investigate both micro- and macro- dynamic response of the linear-elastic FGL. To answer this question, a new approximate mathematical model of FGL is proposed. This model is represented by a certain refined homogenized equation of motion for averaged displacements and a boundary-layer equation for intrinsic displacement fluctuations. Main attention is given to the investigations of near-initial and near-boundary dynamic phenomena in FGL, which are related to the specific form of initial and boundary conditions. For a periodically laminated medium the obtained results reduce to those derived in [7].
4
Content available remote On the macroscopic modelling of elastic/viscoplastic composites
63%
Woźniak C. , Wierzbicki E.
Archives of Mechanics
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2002
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tom Vol. 54, nr 5-6
737-750
EN
The aim of this contribution is to formulate a macroscopic model for the analysis of dynamic problems in micro-periodic composites made of elastic/viscoplastic and/or linear viscoelastic materials. The proposed modelling approach is based on the concept of tolerance averaging which so far was applied to the linear elastodynamics and heat transfer in periodic materials and structures. The obtained model equations, in contrast to homogenized equations, describe the effect of microstructure size on the overall behaviour of a composite solid.
5
Content available remote Vibrations of thin plates with multiperiodic structure
63%
Woźniak C. , Jędrysiak J.
Vibrations in Physical Systems
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2004
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tom Vol. 21
423--426
6
Internal variables in marcodynamics of two-dimensional periodic cellular media
51%
Cielecka I. , Woźniak C. , Woźniak M.
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tom z. 7
59-64
EN
A new continuum model for study elastodynamics of a cellular medium having a plane periodic structure is derived . The model is base don the concept of macro-internal variables , [3] , being able to describe structures of an arbitrary complex lay-out . The resulting equations constitute a certain generalization of the plane Cosserat continuum equations. The physical correctness of the model proposed is shown by comparing obtained solutions to the exact ones.
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