HEAT-CODUCTION OF THIN ORTHOTROPIC SHALLOW SHELLS UNDER THE EFFECT OF A MOVING PULSED LOCAL HEAT SOURCE
Abstract
The problem of heat-conduction of thin shallow orthotropic shells of non-negative Gaussian curvature under the effect of a local pulsed heat source moving over the shell surface is analyzed. A normally-circular source having the form of a normal distribution curve is taken as a source of external energy. Such modeling makes it possible to analyze the effect of a heat flow from a welding arc or a gas burner. A linear temperature distribution through the thickness of the shell and convective heat-exchange from its surfaces according to Newton's law are assumed. The ambient temperature and the temperature of the shell at an initial time are taken to be zero. Using integral Fourier and Laplace transforms, an analytical form of the solution has been obtained. The effect of the heating character of the shell, of the rate of motion of the heat source, of the thermal-mechanical properties of the material, as well as the value and character of the heat-exchange with the ambient medium on the distribution of the temperature field of the shell has been studied. Based on the numerical analysis for a case of a heat source moving along the generatrix at a constant velocity, diagrams of distribution of the average temperature and a temperature moment for a spherical and a cylindrical shell made of orthotropic and isotropic materials have been constructed. The results of the analyses make it possible to conclude that, in determining a temperature field in orthotropic shells under the effect of a local heat source, it is necessary to take into account the rate of motion and the form of the heat source, the character of the pulsed effect (duration of the pulse, duration of the pause and the number of pauses), the orthotropic properties of the material of the shell and the value of the heat-exchange with the ambient medium.
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