Özet:

In the bodies of cylindrical apparatuses that operate under pressure, one of the weak elements is a flat bottom whose thickness is increased by 4…5 times in comparison with the wall thickness. This is due to the fact that the bottom is exposed to a more unfavorable bending deformation compared to the wall that «works» on stretching. In order to reduce specific metal consumption for the bottom, we propose the optimization of the shape of a radial cross-section by a rational redistribution of the material: to increase thickness of the bottom in the region of its contact with the wall and to significantly reduce it in the central zone. To describe a variable thickness of the bottom, we applied the Gauss equation with an arbitrary parameter that determines the intensity of change in the thickness in radial direction. We have obtained a general solution to the differential equation of the problem on bending a bottom at a given law of change in its thickness, which is represented using the hypergeometric Kummer’s functions. A technique for concretizing the resulting solution was proposed and implemented, based on the application of conditions of contact between a cylindrical shell and a bottom. The solution derived was used to minimize the mass of the bottom. We have designed a zone of transition from the bottom to the wall whose strength was verified by the method of finite elements under actual conditions. Author Biographies Yuriy Khomyak, Odessa National Polytechnic University Shevchenka ave., 1, Odessa, Ukraine, 65044 PhD, Associate professor Department of Oilgas and chemical mechanical engineering

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