|Journal||Journal of Mechanical Engineering|
|Publisher||A. Podgorny Institute for Mechanical Engineering Problems
National Academy of Science of Ukraine
|ISSN||0131-2928 (Print), 2411-0779 (Online)|
|Issue||Vol. 23, no. 1, 2020 (March)|
|Cited by||J. of Mech. Eng., 2020, vol. 23, no. 1, pp. 58-64|
This paper considers the application of the random search method for the optimal design of both axially-compressed smooth cylindrical ideal thin-walled shells and a shell with initial imperfections. In stating a mathematical programming problem, the objective function is the minimum weight of the shell. As constraints imposed on the region of permissible solutions, the following constraints are adopted: on the critical load of local buckling, on the critical load of buckling of the shell axis; strength condition, and condition for constraining the dimensions of a shell (radius and wall thickness of a shell). With the optimal design of a shell with initial imperfections, the statement of the mathematical programming problem remains the same as for an ideal shell, with only local buckling constraint changing. The aim of this paper is both to study the zone of influence of the optimum shell weight on the value of compressive force and to determine the range of the external compressive loads at which the general and local buckling shell constraints are decisive. A numerical experiment was carried out. Dependences of the weight, wall thickness, radius of the middle surface, and the ratio of the middle surface radius to the wall thickness on the magnitude of the compressive load both for an ideal shell and a shell with initial imperfections were investigated. As a result of the numerical experiment, it was established that the presence of initial imperfections in an axially-compressed smooth cylindrical shell leads to an increase in its weight compared to that of an ideal shell. The weight does not increase over the entire range of compressive loads, but only with the loads at which both local and general buckling constraints are decisive. If the optimal solution pertains to the strength constraint, which is typical for large compressive loads, there is no influence of initial imperfections on the optimal design. The weight of an ideal shell and that of a shell with initial imperfections in the optimal design turn out to be the same.
Keywords: thin-walled cylindrical shell, initial imperfections, optimal design, random search.
Full text: Download in PDF
- Rastrigin, D. A. (1968). Statisticheskiye metody poiska [Statistical search methods]. Moscow: Nauka, 376 p. (in Russian).
- Volynskiy, E. I. & Pochtman, Yu. M. (1974). Ob odnom algoritme sluchaynogo poiska dlya resheniya mnogoekstremalnykh zadach [On a random search algorithm for solving multiextremal problems]. Izv. AN SSSR. Tekhn. kibernetika – Proceedings of the USSR Academy of Sciences. Technical cybernetics, no. 1, pp. 55–60 (in Russian).
- Filatov, G. V. (2003). Dva sposoba adaptatsii algoritma sluchaynogo poiska pri optimalnom proyektirovanii tsi-lindricheskikh obolochek [Two ways to adapt the random search algorithm for the optimal design of cylindrical shells]. Str-vo, materialovedeniye, mashinostroyeniye. Ser. Starodubovskiye chteniya – Construction, materials science, mechanical engineering. Series: Starodubov Readings, iss. 22, part 3, pp. 312–315 (in Russian).
- Ginzburg, I. N. & Kan, S. N. (1969). Ob odnom metode vybora optimalnykh parametrov tonkostennoy konstruktsii [On a method for choosing the optimal parameters of a thin-walled structure]. Proceedings of the VII All-Union Conference on the Theory of Shells and Plates, Dnepropetrovsk, pp. 271–273 (in Russian).
- Aleksandrov, A. Ya. & Naumova, M. P. (1965). Optimalnyye parametry trekhsloynykh plastin i pologikh obolochek s zapolnitelem iz nearmirovannogo i armirovannogo penoplasta pri szhatii [Optimal parameters of three-layer plates and shallow shells with aggregate of unreinforced and reinforced foam during compression]. Raschety elementov aviatsionnykh konstruktsiy – Calculations of elements of aviation structures, iss. 3, pp. 91–99 (in Russian).
- Alumyae, N. A. (1956). O predstavlenii osnovnykh sootnosheniy nelineynoy teorii obolochek [On the representation of the basic relations of the nonlinear theory of shells]. Prikl. matematika i mekhanika – Applied Mathematics and Mechanics, vol. 20, no. 1, pp. 136–139 (in Russian).
- Mushtari, Kh. M. & Galimov, K. Z. (1957). Nelineynaya teoriya uprugikh obolochek [Non-linear theory of elastic shells]. Kazan: Tatknigoizdat, 421 p. (in Russian).
- Volmir, A. S. (1967). Ustoychivost deformiruyemykh sistem [Stability of deformable systems]. Moscow: Nauka, 984 p. (in Russian).
- Gavrilenko, G. D. (1999). Ustoychivost rebristykh obolochek nesovershennoy formy [Stability of ribbed shells of imperfect shape]. Kiyev: In-t mekhaniki NAN Ukrainy, 190 p. (in Russian).
- Kan, S. N. (1966). Stroitelnaya mekhanika obolochek [Construction mechanics of shells]. Moscow: Mashinostroyeniye, 507 p. (in Russian).
- Filatov, G. V. (2016). The global method of random search with controlled boundaries of the interval parameters to be optimized. Intern. J. Emerging Techn. & Advanced Eng., vol. 6, iss. 9, pp. 231–247.
Received 25 November 2019
Published 30 March 2020