Optimization of uniformly stressed structures of cylindrical tanks in CAD - Saveleva, Oksana; Khomyak, Yurii; Stanovska, Iraida; Toropenko, Alla; Naumenko, Evgeniya (Eastern-European Journal of Enterprise Technologies, 2016)
It was established that in the housings of apparatuses that work under pressure, a flat bottom is the weakest element, because of which it is necessary to increase its thickness by 3–5 times in comparison with the wall thickness. This is connected with the fact that under conditions of loading of the bottoms of vessels, mechanical stresses in them are distributed extremely unevenly. Therefore, we set the purpose to decrease metal intensity of apparatuses at the stage of their automated designing by creating uniformly stressed structural elements with the retention of indices of their reliability through rational redistribution of the used materials inside the element, which ensures equal stress and minimally permissible mass of the finished product. We attempted to solve this problem through varying one of the main design characteristics – thickness of the flat bottom of a tank, loaded with internal pressure. To achieve this aim, a method for the optimization of shape of a round plate with variable thickness was developed. It implies transition from the fixed thickness of the plate in its center to its fixed volume. Within the method of optimization, we proposed a model of bend of a round plate with variable thickness in the form of exponential Gauss function, with regard to dependence of thickness in the center of a plate on its volume. In the method for solving the equation of plate bending, degenerate hyper-geometric functions of Kummer and Whittaker are used. The method was tested in the process of real automated design of the tank for storing caustic liquids.