Rheologic of a polymer pipe from cyclic temperature and internal pressure in one-dimensional and two-dimensional formulations is considered. The resulting equations of the finite element method allow one to calculate both single-layer and multilayer thick-walled pipes taking into account creep. In the calculation, the temperature dependences of the elastic and rheological parameters of polymer pipes were used. The effect of variable thermal conditions on the VAT of a PVC pipe is investigated. It has been established that under unsteady thermal conditions, stresses can occur significantly higher than in a stationary temperature field. This is explained by the fact that polymers have a component of deformation that is lagging in phase from stresses (highly elastic deformation).
The article is a message containing systematized information on resource-saving technologies as the basic for involving metal-containing secondary raw materials in the economic turnover. The set of independent technologies arranged in a certain sequence that solve the problems of resource saving allows us to compare the specific features and effectiveness of the use of each of them, the details and features of the processes. It is shown that the following can be the main sources of rare metals and REE: phosphogypsum (REE, Sr); ash and slag waste from TPPs, ash and slag waste (REE, Ti, Sc); metallurgical slags (Ge, Be, Se, Te, V); sulfuric acid dust (Se, Te); alumina production waste - red mud (Sc, REE); liquid waste from sulphate production of titanium dioxide (Sc, Ti); refinery dust bins (Se, Te); wastes from production of permanent magnets (Nd, Sm). It is noted that the technology uses beneficiation methods, acid leaching and ion-exchange concentration, biotechnology, electrolysis, heat treatment, a combination of different methods. To assess the quality of man-made raw materials and their suitability for complex processing and utilization, the article uses the methodology of analytical research of a set of patented technological solutions (technological samples were taken from real man-made deposits).
In conclusion, one should say that, to determine the approximate stress state in the body, it is quite enough to consider the problem in a linearized problem setting. When determining the deformed state, it is necessary to consider the problem exclusively in a nonlinear setting.
We propose an improved version of the energy method in calculating rectangular beams for the stability of a flat bending shape. The essence of this variant of the method is to use the principle of the minimum total energy instead of the condition for the equality of the potential strain energy and the work of external forces. This version of the method makes it easy to obtain a numerical-analytical solution for any number of members of series. The solution of the problem for a pivotally supported beam is presented taking into account the vertical displacement of the load relative to the center of gravity.
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