Design and Optimization of Thick-Walled Cylinders with Load Localization Near the End Face
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DESIGN AND OPTIMIZATION OF THICK-WALLED CYLINDERS WITH LOAD LOCALIZATION NEAR THE END FACE V. L. Marchenko
UDC 621.73.043 621.777
The paper presents a procedure for determining the design parameters of multilayer thick-walled structures with a local load on the inner surface portion located near the end face. The design provides for the use of two layers, of which the outer layer can have a smaller height. The procedure involves obtaining numerical results of calculating the stress state of the inner cylinder, their approximation, the use of the Lame–Gadolin solution for shroud design. In the computational scheme for the first cylinder, the internal and external load intensities were taken to be constant. The result of the research is analytical relations relating the inner-to-outer radius ratios of the cylinder and shroud height to their strength characteristics. The use of these relations makes it possible to optimize the design. Numerical results obtained in the approximation and optimization of the design are presented. Keywords: multilayer cylinders, local shrouding, numerical methods, Lame–Gadolin solution, optimization. Thick-walled cylinders with significant load levels are fairly commonly used structural elements of tool and rig. They are, first of all, a tool in metal forming processes, booster jacks. Only a few analytical methods to design them are known. Among them, the Lame–Gadolin solution is certainly noteworthy, which has already become classical. However, the range of its applications is rather limited: they are infinite cylinders uniformly loaded on the entire inner or outer surface [1–3]. In this case, a two-dimensional stress state occurs, which makes it possible to obtain an analytical solution. The above loading conditions are implemented in practice rather rarely; the calculation accuracy decreases with any deviation from them. The results are affected even by the limitation in the length of cylinders. All the more essential is load localization. For the cases of load localization near the cylinder end face, there are also analytical solutions [4–6]. Calculations showed that such analytical solutions give fairly close results and differ slightly in laboriousness [7]. Of course, in the case of more complex geometry of the inner cylinder, the load diagram may differ greatly, and to design such structures, numerical methods must be employed. In this case, the problem is a contact one. However, when numerical methods are used, it is rather difficult to optimize the design. In this case, calculations must be made many times. Moreover, in the absence of analytical solutions, the effect of certain parameters on the stress-strain state of structural elements cannot be analyzed. There are no methods of designing multilayer structures in which loading is local. It is for these structures, i.e., the structures in which the height of the outer layers may differ from that of the inner cylinder, that the use of local shrouding will be expedient. The use of such structures was considered earlier [8, 9]. T
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