Аuthors

Tereshchenko T. S.

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

e-mail: tereschenkots@mai.ru

Abstract

When a solid body is exposed to laser radiation, the properties of its material change significantly. The peculiarities of heating with laser radiation are associated with high rates of temperature growth and decrease, as well as its large gradients. This leads to significant differences in the mechanisms of thermal processes compared to other types of heating. The problem of determining the stress-strain state of a metal-powder composition in the process of selective laser melting of a half-plane is solved. To solve this problem, an additional study is conducted to solve the auxiliary problem of nonstationary heating of an isotropic half-plane with a mobile surface heat source. For this purpose, a mathematical model is constructed for the generalized heat equation based on classical theory and Green-Naghdi type II. Mathematical formulations of problems of nonstationary thermal conductivity corresponding to models of classical thermal conductivity based on Fourier's law and the generalized Green-Naghdi type II model are presented. Using integral Fourier transforms in spatial coordinates and Laplace transforms in time, fundamental solutions of the equations of classical and generalized models of thermal conductivity, Green-Naghdi type II, are constructed. Graphical results are presented and analyzed. The differences between the considered models of thermal conductivity are shown and recommendations for their application in practical calculations are given. The solutions found correspond to the effect of a surface heat source concentrated in time and coordinates in the form of a delta function located in a thermally conductive half-plane.

Keywords:

Dynamic heating of a half-plane with a mobile laser radiation source considering heat transfer on the surface

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