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Surface localized heat transfer in periodic composites

Kula Dorota, Wierzbicki Ewaryst

Acta Mechanica et Automatica

2019

Vol. 13, no. 2

124--129

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.

On Fourier implementation of tolerance modeling of linear elastodynamics of periodic composites

Kula D.

Journal of Applied Mathematics and Computational Mechanics

2014

Vol. 13, nr 4

73--80

The report presents a new model of linear elastodynamics of periodic composites. The study deals with a certain extension of the ideas yield tolerance modelling. In the proposed model the displacement field is determined by an infinite number of unknowns. This disappointment seems to be apparent in many cases of periodicity since the sequence of tolerance shape functions used in the modelling procedure is not unique and opens the possibility to control the model equations. It has been formulated and solved, within the framework of the resulting model, the problem of independence short-term and long-term perturbations by linearly elastic composite solid.

Shakedown- and limit analysis of periodic composites

Weichert D., Hachemi A.

Journal of Theoretical and Applied Mechanics

2002

Vol. 40 nr 1

273-289

A methodology for the assessment of periodic composites under variable repeat loads by means of the shakedown theory is presented and applied to metal-matrix-composites. The approach is based on the local shakedown analysis in a representative volume element of the composite and the use of averaging techniques to determine the domains of admissible stresses on the macro-level.

W pracy zaprezentowano metodologię oceny kompozytów o strukturze periodycznej przenoszących zmienne, powtarzalne obciążenia na podstawie teorii przystosowania w zastosowaniach do kompozytów z metalową osnową. Metodologię oparto na lokalnej analizie przystosowania dla reprezentatywnego elementu kompozytu i zastosowaniu technik uśredniających w celu określenia dopuszczalnych naprężeń na poziomie makroskali.