SOME BASIC RELATIONS OF ASYMMETRIC DISTRIBUTIONS ALGEBRA IN THE TASKS OF INHOMOGENEOUS HEAT CONDUCTION AND THERMOELASTICITY

The method of presenting thermophysical and physical and mechanical properties of piecewise homogeneous production nodes and mechanisms of food facilities using asymmetric distributions has been suggested. These nodes, consisting of separate parts with different and nonconstant physical and mechanical characteristics within each of them, can be written for a piecewise homogeneous solid as a whole using asymmetric unit functions and full Dirac delta function. It is shown that the use of the apparatus of generalized functions stud-tion for the thermal state of heterogeneous elements of the design is one of the effective solution of problems theories thermomechanics bodies heterogeneous structure at the present stage of its investigation. This theory termomehanitsi bodies heterogeneous structure led to a new direction - the use of distributions in termomehanitsi heterogeneous body structure: multilayer reinforced bodies, the bodies of the cross and not cross inclusions coated with temperature-dependent thermophysical characteristics of continuous heterogeneity. With piecewise constant coefficients of heat transfer, multi-plates, shells, walls. In the proposed paper shows that the relevant heterogeneous characteristics may consist not only of different values of constant changing abruptly at the boundaries of interface, but with different pieces of continuous functions defined in the definition of each component inhomogeneous body as a whole. For this received the differentiation rules of discontinuous functions and functions that are represented as the product of two discontinuous functions and the rules of determination of the generalized derivative of piecewise continuous function have been obtained. It is shown that close task solving problem can be obtained by limiting transition in precise upshot. In particular example it was investigated limit of the admissibility of the application of the approximate upshot. Some basic relations of asymmetric distributions algebra in the tasks of inhomogeneous heat conduction and thermoelasticity.