Wyniki wyszukiwania - Biblioteka Nauki

1

On Janmann-Zaremba time derivative

100%

Piskorek A.

Matematyka Stosowana : matematyka dla społeczeństwa

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1995

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tom Nr 38

51--80

EN

This is an extended discussion of the introduction and role played by the so-called co-rotational derivative (also called the Jaumann derivative in Germany and, rightfully, the Zaremba derivative in Poland) and other "objective'' time derivatives of geometrical objects as they appear in continuum physics. This is achieved in a somewhat abstract formalism starting with clearly defined "spatial" and "material" notions, the differentiable-manifold definition of deformation tensors, and the notions of parallel transport and Lie derivative. The notion of "objectivity'' (as common in continuum mechanics since the pioneering work of W. Noll) and Piola transformations follow next. The paper ends with a reminder on local balance equations and objective constitutive equations such as those of the time-rate type. It seems that the author does not know the famous book of J. E. Marsden and T. J. R. Hughes [Mathematical foundations of elasticity, corrected reprint of the 1983 original, Dover, New York, 1994; MR1262126], where most of the given material can be found.

2

Non-isothermal constitutive relations and heat transfer equations of a two-phase medium

80%

Uciechowska-Grakowicz A. , Strzelecki T.

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tom Vol. 39, nr 3

67--78

EN

In the case of a two-phase medium – such as the soil, which consists of an elastic skeleton and is filled with pore fluids – stress and strain within the medium are dependent on both phases. Similarly, in the case of heat transfer, heat is conducted through the two phases at different rates, with an additional heat transfer between the phases. In the classical approach to modelling a porous medium, it is assumed that the fluid filling the pore space is water, which is incompressible. In the case of gas, the volume of which is strongly dependent on temperature and pressure, one should take this behavior into account in the constitutive relations for the medium. This work defines the physical relations of a two-phase medium and provides heat transfer equations, constructed for a porous, elastic skeleton with fluid-filled pores, which may be: liquid, gas, or mixture of liquid and a gas in non-isothermal conditions. The paper will present constitutive relations derived from the laws of irreversible thermodynamics, assuming that pores are filled with either a liquid or a gas. These relations, in the opinion of the authors, may be used as the basis for the construction of a model of the medium filled partly with a liquid and partly with a gas. It includes the possibility of independent heat transfer through any given two-phase medium phase, with the transfer of heat between the phases.

3

Static electromechanical characteristics of piezoelectric converters with various thickness and length of piezoelectric layers

80%

Mieczkowski G.

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2019

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tom Vol. 13, no. 1

30--36

EN

The paper presents the analysis of electromechanical characteristics of piezoelectric converters subjected to an electric field and mechanical load. The analyses were performed based on a method consisting implementation of special segments responsible for electrical boundary conditions to a homogeneous beam. Constitutive equations were developed, allowing one to obtain static electromechanical characteristics for piezoelectric actuators with freely defined boundary conditions and geometry. Moreover, based on constitutive equations obtained, a particular solution for cantilever transducer subjected to concentrated force has been developed. The resulting analytical solution was compared with the data available in the literature, and the developed FEM solution. Furthermore, the influence of factors such as relative length, thickness and location of particular piezoelectric layers on electromechanical characteristics of the transducer was defined.

4

Dilation and Modelling of Sands in the Light of Experimental Data

80%

Sawicki A.

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2014

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tom Vol. 61, nr 1-2

3--15

EN

The problem of dilation is discussed in the context of classical Cam-Clay model, which was developed on the basis of a specific assumption regarding the plastic work. This assumption leads to a special form of the dilation function, from which a shape of yield function is derived. The above mentioned assumption is compared with the results of the triaxial tests, performed on the model “Skarpa” sand. It is shown that the Cam-Clay approach is not realistic, as it is based on the assumption which is not consistent with experimental data. Some general considerations and discussion of this problem are also presented.

5

Równania konstytutywne materiału z przemianą martenzytyczną typu atermicznego

80%

Ziętek G.

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2001

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tom Z. 24

483--490

PL

W pracy przedstawiono opis materiału, w którym zachodzi przemiana martenzytyczna typu atermicznego, poddanego jednoosiowemu, cyklicznemu rozciąganiu i ściskaniu. Narastająca faza martenzytyczna ma wpływ na związki między odkształceniem i naprężeniem, co uwzględniono poprzez wprowadzenie skalarnego parametru wewnętrznego opisującego objętościowy udział martenzytu w austenicie. Parametr ten wprowadzony do równań konstytutywnych ciała sprężysto-plastycznego ze wzmocnieniem kinematycznym odpowiednio je modyfikuje. Identyfikację modelu przeprowadzono na podstawie prób cyklicznego ściskania i rozciągania cylindrycznych próbek wykonanych ze stali AISI 304L.

EN

The paper presents the description of material with athermal martensitic transformation under uniaxial tension and compresion. The growing martensitic phase changes stress-strain dependence what was taken into accaunt with the help of scalar internal parameter - the value ratio of martensite in austenite. This parameter modifies constitutive equations of elasto-plastic material with kinematic hardening. Identification of the model has been performed for cyclic tension and compression of specimens made up from AISI 304 steel.

6

The constituent equations of piezoelectric cantilevered three-layer actuators with various external loads and geometry

80%

Mieczkowski G.

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tom Vol. 55 nr 1

69--86

EN

This paper presents test results for deformation conditions of three-layer, piezoelectric cantilever converters subjected to various electrical and mechanical boundary conditions. A general solution has been developed based on implementation of piezoelectric triple segments (PTS) to the beam. A working mechanism and conditions for strain of the PTS segment have been determined. Basing on the general solution, for the cantilever actuator subjected to an external force (of single and dual PTS segments) and a uniform load (of single PTS segment), particular solutions have also been developed. Moreover, dimensionless frequencies of the oscillating motion for the analyzed converters have been determined. In the next step, the influence of such factors as length, quantity and position of PTS segments, their relative stiffness and unit weight on values of the obtained frequencies of vibration have been defined. The resulting analytical solutions have been compared with the developed FEM solution.

7

The Correlation between Solidification Rates, Microstructure Integrity and Tensile Plastic Behaviour in 4.2 wt.% Silicon Strengthened Ductile Iron

70%

Angella G. , Taloni M. , Donnini R. , Zanardi F.

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tom Vol. 6, no. 1

1--7

EN

High Silicon Strengthened Ductile Iron (HSiSDI) with 4.2 wt.% of silicon was produced in Y-blocks with different thicknesses to investigate the effects of the solidification rate on microstructure integrity and tensile mechanical properties. With decreasing solidification rates, the graphite degeneracy with the appearance of chunky graphite became more significant at the highest silicon contents, so chemical ordering and graphite degeneracy seemed to be qualitative explanations of tensile property degradation. However, a deeper analysis of the relationship between solidification rate, microstructure and tensile properties was realized through an innovative approach based on the Matrix Assessment Diagram (MAD), where the parameters of Voce equation resulting from best-fitting the experimental tensile flow curves of a significant number of HSiSDI samples, were plotted. For 3.5 wt.% silicon content, the MAD analysis indicated that the microstructure was sound for any solidification rate, while for 4.5 wt.% the microstructure was sound only for the fastest solidification rates. For 4.2 wt.% silicon content the MAD analysis pointed out that the tensile plastic behaviour and the microstructure integrity was in between the 3.5 and 4.5 wt.% silicon contents, representing a composition threshold where the reliable microstructures were only found with the fastest solidification rates, while considerable variability was found for the slowest ones. Support to the MAD analysis results was given from microstructure observations.

8

Teoria dyfuzji wieloskładnikowej w ośrodkach płynnych. Cz. 2, Zastosowanie konstytutywnych równań dyfuzji wieloskładnikowej

60%

Burghardt A.

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tom nr 21

15--32

PL

Konstytutywne równania dyfuzji wieloskładnikowej wyprowadzone w części pierwszej opracowania [1] w oparciu o mechaniczną teorię dyfuzji mogą być stosowane do dowolnych mieszanin izotropowych, takich jak gazy pod niskim i wysokim ciśnieniem, ciecze, roztwory elektrolitów i polimerów oraz plazma. Dlatego w tej części (drugiej) opracowania przedstawiono przykłady zastosowań zależności teoretycznych wyprowadzonych w części pierwszej do izotropowych układów płynnych wymienionych powyżej.

EN

The constitutive equations of multicomponent diffusion derived in the first part of the study [1] basing of the mechanical theory of diffusion are applicable to any isotropic fluid mixture like gases under low and high pressure, liquids, electrolyte and polymeric solutions as well as plasma. Therefore in this (second) part of the study examples of application of the theoretical expressions derived in the first part are presented with respect to the fluid systems mentioned above.

9

Generalization of Linear Rosenstark Method of Feedback Amplifier Analysis to Nonlinear One

60%

Borys A. , Zakrzewski Z.

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tom Vol. 60, No. 1

48-60

EN

Generalization of Linear Rosenstark Method of Feedback Amplifier Analysis to Nonlinear One This paper deals with an extension of the Rosenstark’s linear model of an amplifier to a nonlinear one for the purpose of performing nonlinear distortion analysis. Contrary to an approach using phasors, our method uses the Volterra series. Relying upon the linear model mentioned above, we define first a set of the so-called amplifier’s constitutive equations in an operator form. Then, we expand operators using the Volterra series truncated to the first three components. This leads to getting two representations in the time domain, called in-network and input-output type descriptions of an amplifier. Afterwards, both of these representations are transferred into the multi-frequency domains. Their usefulness in calculations of any nonlinear distortion measure as, for example, harmonic, intermodulation, and/or cross-modulation distortion is demonstrated. Moreover, we show that they allow a simple calculation of the so-called nonlinear transfer functions in any topology as, for example, of cascade and feedback structures and their combinations occurring in single-, two-, nd three-stage amplifiers. Examples of such calculations are given. Finally in this paper, we comment on usage of such notions as nonlinear signals, intermodulation nonlinearity, and on identification of transfer function poles and zeros lying on the frequency axis with related real-valued frequencies.

10

Modyfikacja liniowej teorii laminowania

51%

Wilczyński A. P.

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tom R. 4, nr 10

184-188

PL

Przedstawiany tekst jest nieco skróconą wersją wykładu wygłoszonego przez Autora w czasie IV Szkoły Kompozytów, Wisła 8-10 grudnia 2003 r. Teoria laminowania, czasami zwana mesomechaniką kompozytów, zajmuje się zazwyczaj przewidywaniem właściwości kompozytu warstwowego, na ogół z warstwami ułożonymi pod różnymi kierunkami, w celu dostosowania tych właściwości do aktualnych wymagań. W przypadku, mających najczęstsze zastosowanie, polimerowych kompozytów włóknistych budowa tej teorii opiera się na liniowej teorii płyt anizotropowych, co znajduje uzasadnienie w fakcie, że konstrukcje kompozytowe wykonuje się przeważnie jako cienkościenne elementy powłokowe. W zależności od dokładności stosowanej teorii płyt można mówić o teorii liniowej [1] lub nieliniowej [2]. Niedawno, na skutek pewnej inspiracji wynikami pracy [3], udało się stworzyć teorie laminowania, która w oparciu o pewne dodatkowe założenia daje dokładniejszy obraz rzeczywistości, pozostając nadal liniową i nie tracąc wiele ze swojej prostoty. Poniżej przedstawiono skrótowo tworzenie takiej teorii, ze szczególnym zwróceniem uwagi na różnice w porównaniu z rozwiązaniem klasycznym.

EN

This is an improved and shortened version of the Authors lecture at the IV School of Composites, held at Wisła on 8-10 December, 2003. The theory of lamination, known sometimes as meso-mechanics of composites is dealing with prediction of properties of multi-layered composites, providing means for their practical applications. In the case of fibrous, polymeric laminates for this purpose usually the classical, linear theory of plates is employed, basing on the fact, that composite structures in general are constructed as thin-walled plates and shells. In such a case the results are greatly simplified in comparison with non-linear theories, while introduced in this way discrepancies are mostly of no significance. The final effect of application of the theory of lamination is providing global constitutive equations for the laminate and means for calculations of local stresses in particular layers. Some time ago the paper [3] gave an inspiration for forming a new, linear theory of lamination, based not on response to curvatures of the layers but their mean angle of deflection, taking into account values resulting from inter-laminar shear. The derivation of the theory, presented in this paper allows for calculation and inclusion of shear stresses into strength and safety factor calculations, better understanding of the problems of lamination and a tool for more accurate determination of laminate deflections.

11

Studies on constitutive equation that models bone tissue

51%

Pawlikowski M. , Klasztorny M. , Skalski K.

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tom Vol. 10, nr 4

39-47

EN

A method for identifying viscoelastic constitutive equations for bone is developed. In the method, anisotropy, non-homogeneity and bone remodelling are taken into consideration. The equations correspond to monotropic rheological model of bone. In order to calculate the material parameters of elasticity and viscosity, a new algorithm is developed, in which the results of creep compression and shear tests are used. The way of determining the material constants of elasticity and viscoelasticity for bone in the areas that are crucial in strain and stress analysis is shown a well. The strength experiments (tests) and creep tests were performed on bone samples extracted from the femur of calf. The method of bone modelling in terms of rheology is the following: bone samples are properly prepared from biological material. For given bone samples, which have more or less the same density, three independent short-term creep tests are carried out. The results of the creep tests permit us to determine five elastic constants and viscoelastic constants of a monotropic material [1]. In order to describe rheological processes in terms of structural models, fractional exponential functions and normal exponential functions are used. The constitutive equations are formulated in the compliance form. The computer program that executes the algorithm of elastic and viscoelastic constant determination is used.

12

Structure-controlled bifurcation in mathematical modelling of fibre spinning

41%

Ziabicki A. , Jarecki L.

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tom Vol. 58, nr 4-5

459-475

EN

In the mathematical model of melt spinning of fibres from crystallizing polymers the set of conservation equations is completed with structure-controlled constitutive equations and structure evolution equations describing kinetics of stress-induced crystallization. In a definite range of conditions, bifurcation of solutions is observed. Maximum filament velocity is limited and the same boundary conditions yield different steady-state dynamic and structure profiles. Bifurcation is observed when stress-induced crystallization leads to rapid solidification of the material. Critical conditions for bifurcation in melt spinning are analyzed and physical mechanism of such a behaviour is discussed.

13

Some remarks on the concept of stream tubes for numerical simulations of complex fluid flows - applications

41%

Clermont J. , Normandin M. , Radu D.

Control and Cybernetics

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2000

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tom Vol. 29, no 2

535-553

EN

This paper presents new theoretical elements for numerical simulation of two- and three-dimensional flows, based on the concept of streamlines and domain decomposition. The so-called "stream-tube method", considered previously particularly for flows inolving open streamlines, is extended to general streamline comfigurations. It is shown how local transformation functions may be defined in order to simulate flows of complex fluids, notably those requiring evaluation of particle time history. The specific features (for example : mass conservation, simplicity in handling time-dependent constitutive equations) of the stream-tube methods previously investigated numerically are still preserved in the new formulation. An example of calculations is given in the case of the two-dimensional flow of a Newtonian fluid between two eccentric cylinders where results are found to be consistent with literature data.