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1

Surface localized heat transfer in periodic composites

Kula Dorota, Wierzbicki Ewaryst

Acta Mechanica et Automatica

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2019

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Vol. 13, no. 2

124--129

EN

A characteristic feature of the description of physical phenomena formulated by an appropriate boundary or initial-boundary value problem and occurring in microstructured materials is the investigation of the unknown field in the form of decomposition referred to as micro-macro hypothesis. The first term of this decomposition is usually the integral average of the unknown physical field. The second term is a certain disturbance imposed on the first term and is represented in the form of a finite or infinite number of singleton fluctuations. Mentioned expansion is usually referred to as a two-scale expansion of the unknown physical field. In the paper, we purpose to apply two-scale expansion in the form of a certain Fourier series as a result of an applying Surface Localization of the unknown field. The considerations are illustrated by two examples, which results in analytical approximated solutions to the Effective Heat Conduction Problem for periodic composites, including the full dependence on the microstructure length parameter.

2

An interface anticrack in a periodic two-layer piezoelectric space under vertically uniform heat flow

Kaczyński A., Kaczyński B.

Mechanics and Mechanical Engineering

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2018

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Vol. 22, nr 3

667--681

EN

This paper aims to investigate 3D static thermoelectroelastic problem of a uniform heat flow in a bi-material periodically layered space disturbed by a thermally and electrically-insulated rigid sheet-like inclusion (so-called anticrack) situated at one of the interfaces. An approximate analysis of the considered laminated composite is given in the framework of the homogenized model with microlocal parameters. Accurate results are obtained by constructing suitable potential solutions and reducing to the corresponding homogeneous thermoelectromechanical (or thermomechanical) anticrack problems. The governing boundary integral equation for a planar interface anticrack of arbitrary shape is derived in terms of a normal stress discontinuity. As an illustration, a complete solution for a rigid circular inclusion is obtained in terms of elementary functions and interpreter from the failure perspective. Unlike existing solutions for defects at the interface of materials, the solution obtained displays no oscillatory behavior.

3

On axisymmetric heat conduction problem for multilayer graded coated half-space

Perkowski D. M., Kulchytsky-Zhyhailo R., Kołodziejczyk W.

Journal of Theoretical and Applied Mechanics

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2018

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Vol. 56 nr 1

147--156

EN

The technique of integral Hankel transform to find the solution of heat conduction in half-space coated by a multilayered package of homogenous laminae is applied. The half-space is heated by the given heat flux on the boundary surface. The temperature and heat flux distribution in the radial direction is analyzed for two types of coatings: 1) when the heat conductivity coefficient is described by a power or exponential function of the distance to the boundary surface; 2) multilayered coating has a periodic structure.

4

Singularity of stresses in a periodic laminated semi-space with a boundary normal to the layering

Matysiak S. J., Perkowski D. M.

Journal of Theoretical and Applied Mechanics

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2007

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Vol. 45 nr 2

325-335

EN

The paper deals with the pIane problem of stress distributions in a nonhomogeneous elastic semi-space caused by concentrated loadings acting on its boundary. The body is composed of periodically repeated two-constituent laminae, and its boundary is assumed to be normal to the layering. The solution to the problem is presented within the framework of the homogenized model with microlocal parameters (Woźniak, 1987; Matysiak and Woźniak, 1987). Analytical results for stresses are obtained and shown in figures.

PL

W pracy rozpatrzono płaskie zagadnienie dotyczące rozkładu naprężeń w niejednorodnej sprężystej półprzestrzeni wywołanych obciążeniami skupionymi działającymi na jej brzegu. Ośrodek jest złożony z periodycznie powtarzającymi się dwuskładnikowymi laminami, a jego brzeg jest prostopadły do uwarstwienia. Otrzymano rozwiązanie w ramach modelu homogenizowanego z parametrami mikrolokalnymi (Woźniak 1987; Matysiak i Woźniak, 1987). Zostały podane analityczne wyrażenia dla naprężeń i następnie przedstawione w postaci wykresów.

5

On the probabilistic analogy between homogenized and tolerance models of two-constituent microperiodic isotropic laminated composites

Łacińska L., Wierzbicki E.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

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2006

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Vol. 5, nr 1

71-82

EN

In the note an interrelation between tolerance and homogenized effective moduli for two-constituent elastic microperiodic composite are examined. It is shown that, in the case in which constituents are isotropic, effective modulae are identical. The proof is based on the probabilistic analogy formulated for both kinds of modulae.

6

On homogenized model of periodic stratified micropolar elastic composites

Matysiak S. J.

Journal of Theoretical and Applied Mechanics

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2005

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Vol. 43 nr 4

789--804

EN

The paper deals with modelling problems of periodic stratified composites with micropolar elastic components. By using the linear theory of micropolar elasticity and the homogenization method with microlocal parameters, a homogenized model accounting certain local effects of stresses and coupled stresses is derived. From the obtained model, systems of equations for the "first" and the "second" plane state of strain of the layered composites are presented.

PL

Praca dotyczy zagadnień modelowania periodycznych warstwowych kompozytów o składnikach mikropolarnych. Wykorzystując liniową teorię mikopolarnej sprężystości i metodę homogenizacji z parametrami mikrolokalnymi wyprowadzono model homogenizowany uwzględniający pewne efekty lokalne w naprężeniach i naprężeniach momentowych. Z otrzymanego modelu otrzymano układy równań dla" pierwszego" i "drugiego" płaskiego stanu odkształcenia dla periodycznie warstwowych kompozytów mikropolarnych.

7

Some Nonstationary Heat Conduction Problems of a Composite Layer on a Homogeneous Foundations

Matysiak S., Yevtushenko A.

Vibrations in Physical Systems

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2004

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Vol. 21

263--266

8

The 3D thermoelastic problem of uniform heat flow disturbed by an interface crack in a periodic two-layer composite

Kaczyński A., Matysiak S. J.

Journal of Theoretical and Applied Mechanics

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2004

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Vol. 42 nr 1

59-68

EN

This paper is concerned with the problem of an interface insulated plane crack obstructing a uniform heat flux in a two-layer microperiodic space. An approximate analysis is performed within the framework of linear stationary thermoelasticity with microlocal parameters. A general method of solving the resulting boundary-value problem is presented. It is based on the use of potential functions and an analogy between the thermal crack problem and the skew-symmetric mechanical loading problem. The thermal stress singularities are discussed.

PL

Problem stałego przepływu ciepła zakłóconego istnieniem izolowanej termicznie szczeliny międzywarstwowej w periodycznie dwuwarstwowej przestrzeni jest przedmiotem pracy. Przybliżoną analizę przeprowadzono w ramach liniowej stacjonarnej termosprężystości z parametrami mikrolokalnymi. Podano i zilustrowano metodę rozwiązania wynikającego zagadnienia brzegowego, polegającą na zastosowaniu potencjałów harmonicznych i ustaleniu analogii z odpowiadającym mechanicznym, niesymetrycznym problemem szczeliny. Zbadano osobliwości naprężeń cieplnych wokół szczeliny.