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1

Tolerance modelling of nonstationary problems of microheterogeneous media and structures

Jędrysiak J., Domagalski Ł., Marczak J., Pazera E.

Vibrations in Physical Systems

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2018

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Vol. 29

art. no. 2018001

EN

In this note a certain review of applications of a non-asymptotic modelling approach, called the tolerance modelling, is presented. Some objects and thermomechanical problems are shown, with a general outline of this method and an example of application for nonlinear vibrations of periodic beams.

2

Effect of temperature on vibrations of laminated layer

Pazera E., Jędrysiak J.

Vibrations in Physical Systems

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2018

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Vol. 29

art. no. 2018032

EN

In this note the influence of temperature on vibrations of laminated layer made of two different materials is presented. The macroscopic properties of this layer are changing continuously along one direction x1, perpendicular to the laminas. To obtain the equations describing this problem, the tolerance averaging technique is used [1]. In this work, three models are proposed: the tolerance and the asymptotic-tolerance model, taking into account the effect of the microstructure size on the overall behaviour of this type of structures, and the asymptotic model, which equations omit this effect. To solve the equations of these three models the finite difference method is used.

3

On thermoelasticity in FGL - tolerance averaging technique

Pazera E., Ostrowski P., Jędrysiak J.

Mechanics and Mechanical Engineering

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2018

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Vol. 22, nr 3

703--717

EN

In this paper the problem of linear thermoelasticity in a laminate with functional gradation of properties is considered. In micro level this laminate is made of two different materials, microlaminas, distributed non-periodically but also not randomly along one of directions, what in macro level results in aforementioned functionally gradation of laminate properties. In order to describe behavior of such structure, equations of two models are here presented - the tolerance and the tolerance-asymptotic model. Both are obtained by the tolerance averaging technique. The basic aim of this work is to analyse the influence of some terms from these averaged equations on the distribution and the values of the displacements and the temperature functions. To solve the equations of two proposed models the finite difference method is used.

4

Niestacjonarne zjawisko termosprężystości w nieperiodycznym laminacie

Jędrysiak J., Pazera E

Modelowanie Inżynierskie

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2017

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T. 32, nr 63

65--71

PL

W niniejszej pracy rozpatrywany jest efekt termosprężystości w zagadnieniu niestacjonarnym w laminacie nieperiodycznym. Własności takiego laminatu na poziomie makro zmieniają się w sposób ciągły wzdłuż osi prostopadłej do lamin, natomiast na poziomie mikro są opisane funkcjami tolerancyjnie-periodycznymi, nieciągłymi. W celu otrzymania równań o ciągłych współczynnikach funkcyjnych zastosowano metodę tolerancyjnego modelowania, czyli tzw. tolerancyjne modelowanie, oraz modelowanie asymptotyczne. Pierwsze z tych podejść pozwala uwzględnić w wyprowadzonych równaniach wpływ wielkości mikrostruktury laminatu. Zastosowanie otrzymanych równań pokazano na przykładzie jednokierunkowego przepływu ciepła prostopadle do lamin.

EN

In this work the thermoelasticity effect in a non-stationary heat problem for non-periodic laminates is considered. On the macro-level properties of this laminate are continuously varied along a direction normal to laminas, but on the micro-level they are described by tolerance-periodic, non-continuous functions. In order to obtain equations with continuous coefficients the tolerance method is applied, the tolerance modelling and the asymptotic modelling. The first of these approaches allows to take into account the effect of the microstructure size of the laminate in derived equations. An application of these model equations is shown on an example of one-directional problem along a direction perpendicular to laminas.

5

Vibrations of non-periodic thermoelastic laminates

Jędrysiak J., Pazera E.

Vibrations in Physical Systems

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2016

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Vol. 27

175--180

EN

Vibrations of non-periodic thermoelastic laminates, which can be treated as made of functionally graded material with macroscopic properties changing continuously along direction, x1, perpendicular to the laminas on the macrolevel are considered. Three models of these laminates are presented: the tolerance, the asymptotic-tolerance and the asymptotic. Governing equations of two first of them involve terms dependent of the microstructure size. Hence, these models (the tolerance, the asymptotic-tolerance) describe the effect of the microstructure. Averaged governing equations of these laminates can be obtained using the tolerance modelling technique, cf. Jędrysiak [1]. Because the model equations have functional, but slowly-varying coefficients calculations for examples can be made numerically or by using approximated methods.

6

Free vibrations of thin microstructured plates

Jędrysiak J., Pazera E.

Vibrations in Physical Systems

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2014

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Vol. 26

93--98

EN

In this paper it is presented a problem of free vibrations of thin microstructured plates, which can be treated as made of functionally graded material on the macrolevel. The size of the microstructure of the plates is of an order of the plate thickness. In order to obtain averaged governing equations of these plates the tolerance modelling technique is applied, cf. [14, 15, 7]. The derived tolerance model equations have the terms dependent of the microstructure size. Hence, the tolerance model describes the effect of the microstructure size. In order to evaluate results, the asymptotic model is introduced. Obtained results can be compared to those calculated by using the finite element method.