The object of analysis is a heat conduction problem within the framework of tolerance modelling in laminated media with a functional gradation of effective properties. In contrast to the known asymptotic models (based on the homogenization technique), the characteristic feature of the tolerance model equations is that they make it possible to analyze the effect of the microstructure size on the overall behavior of the laminate. The proposed model equations describe heat conduction in laminates by mean of partial differential equations with smooth and slowly varying functions. This paper describes a certain extension of the unified tolerance modelling procedure, which makes it possible to analyze specific problems of heat conduction in laminates with a transversal gradation of effective properties.
In this article the subject of multi-spot underground garages, as well as complex engineering problems arising in their design and implementation were taken up. In addition, the basic elements of the project and selected problems that manifest themselves in garages during their exploitation were analyses.
The present study aims to analyse a two-dimensional problem of displacements in theory of thermal stresses for multicomponent, multi-layered periodic composites. The model equations are obtained within the framework of the tolerance modelling procedure. These equations allow to determine the distribution of displacements caused by the temperature field in the theory of thermal stresses. The paper presents an example of a solution of a boundary value problem.
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