In this paper, the state-of-the-art investigations of optimization problems with respect to the stress state of technological heating regimes for piecewise-homogeneous glass shell elements have been analysed, which are important for development of different types of production processes during production of elements of modern devices for specific target application, in particular, vacuum and power equipment. The directions of development of this class of problems of optimization and corresponding approaches to their formulation and solving are identified.
- Bartenev G. M. Mechanical properties and heat treatment of glass. Moscow, Stroyizdat (1960).
- Rowse B. Glass in electronics. Moscow, Sov. radio (1969).
- Espe B. Technology of electrovacuum devices. Moscow, Energia. 2. (1968).
- Banichuk N. V. Introduction into optimization of construction. Moscow, Nauka (1986).
- Dzyuba A. P., Vasilenko O. G., Dzyuba O. A. About one approach for solution of optimizational problems structural elements considering joint action power loads and aggressive environments. Methods of solving applied problems of mechanics of deformable solid. 8, 55–66 (2007).
- Krysko V. A., Pavlov V. A. Shape optimization of thermoelastic solids. Saratov, Sarat. state. University Press (2000).
- Majid K. I. Optimal design of structures. Moscow, Higher school (1979).
- Nemirovsky Y. V., Mishchenko A. V., Vokhmyanin I.T. Rational and optimal design of layered bar systems. Novosibirsk NGASU (2004).
- Savula Y. G., Fleishman N. P., Shcherbaty M. V. Shape optimization of elastic shells of rotetion. Math. methods and physical and mechanical fields. 19. 74–78 (1984).
- Sarkisyan V. S., Geghamyan B. N. Some problems of optimal design of anisotropic and inhomogeneous plates and shells. Problems of optimization in engineering. Kharkiv. P.82 (1982).
- Troitsky V. A., Petukhov L. V. Shape optimization of elastic bodies. Moscow, Nauka (1982).
- Drobenko B. D. Optimal design of T-joints. Physic.-Chemical Mechanics of Materials. 6, 89 (1984).
- Mangeron D., Poterasu V. F., Vulpe A. Teoria optimizacii structurilor cu aplicatii. Iasi: Junimea, 1980.
- Kruzelecki J. A review of optimal structural design of shells. 3rd Conference thinwalled vessels-Karlow 2004. 39 p.
- Grigolyuk E.I., Burak Y.I., Podstrihach Ya.S. On an extremal problem of thermoelasticity for an infinite cylindrical shell. Report of Academy of Sciences of USSR. 174, n.3, 534–537 (1967).
- Besedina L. P., Budz S. F., Zozulyak Y. D. On the construction of optimal thermal stress fields applying to the conditions of the heat treatment of plates and shells. Mat. Methods and Physics and Mechanics Fields. 7, 11–16 (1978).
- Besedina L. P., Burak Y. I., Podstrigach Ya. S. On the optimal heating of irregular shells of rotation. Mechanics of Solids. 6, 110–116 (1973).
- Burak Y. I., Zozulyak Y. D. Extreme temperature field and the stresses at local heating of a spherical shell. Applied mechanics. 6, n.12, 74–81 (1970).
- Burak Y. I., Zozulyak Y. D., Hera B. V. Optimization of transient processes in thermoelastic shells. Kiev, Naukova Dumka (1984).
- Zozulyak Y. D., Damanskii P. P. Application of extreme changes in temperature and force load to improve the efficiency of local heat treatment of shells of rotation. Mat. Methods and Physics and Mechanics Fields. 7, 111–115 (1978).
- Grigolyuk E. I., Podstrigach Ya. S., Burak Y. I. Optimization of heating shells and plates. Kiev, Naukova Dumka (1979).
- Podstrigach Ya. S., Burak Y. I., Shelepets V. I. et al. Optimization and control in electrical vacuum production. Kiev, Naukova Dumka (1980).
- Budz S. F. Optimal with respect to thermal stresses thermal regimes of zone annealing cylindrical shell. Phys. Chemical Mechanics of Materials. 4, 116–118 (1974).
- Budz S. F., Gachkevich N. G. Optimizing heat treatment of piecewise homogeneous shells EBL considering temperature dependence of the characteristics of the material, Phys. Chemical Mechanics of Materials. 5, 111–113 (1987).
- Budz S. F., Gachkevich N. G., Rodichev Y. M., Zolotarev P. F., Yakubishin A. T. Optimization of thermal treatment for the formation of compounds on the basis of glass-ceramic sealant in glass shells, Problems of strength. 2, 52–58 (1993).
- Budz S., Irza Ye., Kaspersky Z. Optimal by control speed cooling of glass solids of rotation under constraints on residual stresses. Visnyk of Donetsk university. Ser. A, Natural Sciences. 1, 59–62 (2008).
- Burak Y. I., Budz S. F. Determination of optimal modes of heating a thin spherical shell. Applied Mechanics. 10, n.2, 14–20 (1974).
- Burak Y. I., Budz S. F., Irza E. M. Optimization of heating a spherical shell with a heat transfer coefficient variable with time. Mat. Methods and Physics Mech. Fields. 8, 58–60 (1978).
- Gachkevich O. R., Gachkevich M. G., Sosnovyy Yu. R., Terletskyi R. F. Optimization of heat treatment of electrovacuum devices using electromagnetic radiation. Proceedings of Ukrainian Vacuum Society. 1, Kiev, P.317–319 (1995).
- Gachkevich A. R., Gachkevich N. G. Optimal heating by environment of piecewise uniform shells of rotation with internal heat sources. Journal of Applied Mechanics. 31, n.11, 51–57 (1995).
- Gachkevich A., Gachkevich N., Ghazaryan K., Kaspersky Z. Optimal technological heating by environment and heat sources of glass piecewise homogeneous cylindrical sell conjugated with a conical one. Proceedings of the National Academy of Sciences, Armenian Mechanics. 55, n.1, 40–54 (2002).
- Gachkevich M., Kaspersky Z., Trisch B.M., Chornyy B.I. Problems of thermoelasticity of piecewise homogeneous shell rotation at optimization of heating and force load. Visnyk of Donetsk university Ser. A. Natural Sciences. 2, 80–84 (2002).
- Gachkevich A., Gachkevich N., Irza E., Kaspersky Z. Simulation of processes of local heat treatment at optimization of the conjugating of glass bodies. Proektowanie i automatyzacja procesow produkcyjnych. Ksiazka pod red. A. Swic. – Lublin: W-wa Uczelniane Politechniki Lubelskiej. 2005. P.115–121 (172 p.).
- Gachkevich A. R., Gachkevich M. G., Shimura S. R. Optimal thermal modes of glass-ceramic sealant joint of shell structures with regards of thermosensitivity of allowable stresses. Visnyk of Donetsk university Series A. Natural Sciences. 1, 150–156 (2008).
- Gachkevich A. R., Gachkevich N. G., Irza E. M., Trisch B. M. Mathematical model of optimization of low-temperature heating piecewise homogeneous solids of rotation. Theoretical and Applied Mechanics. 43, 35–39 (2008).
- Gachkevich A., Gachkevich N., Irza E., Kaspersky Z., Trisch B. Method of numerical optimization of annealing glass bodies of rotation. Mashynoznavstvo. 4(142), 26–28 (2009).
- Lokhov V. A., Nyashyn Yu. I., Kuchumov A. G., Gachkevich A. R., Onyshko A. E. Stress control in living systems using the shape memory effect. Visnyk of Perm State Technical University. Applied Mathematics and Mechanics. 34–40 (2008).
- Vihak V. M. Optimal control of non-stationary temperature conditions. Kiyev, Nauk. Dumka (1979).
- Vihak V. M. Control of thermal tension and movement. Kiyev, Nauk. dumka (1988).
- Modeling and optimization in thermomechanics of electroconductive heterogeneous bodies / Ya. J. Burak, R. M. Kushnir. V.5. Optimization and identification in termomehanics of heterogeneous bodies / R. M. Kushnir, V. S. Popovych, A. V. Yasinskyy. Lviv, SPOLOM (2011).
- Burak Ya. I., Gachkevich A. R. Optimal by tension regimes of induction heating of a thin plate. Math. methods and phys.-mech. fields. 2, 93–98 (1975).
- Podstrigach Ya. S., Burak Ya. I., Gachkevich A. R., Chernyavskaya L. V. Thermoelasticity of conductive bodies. Kiyev, Nauk. dumka (1977).
- Nyashin Yu. I. About the control of material processing in order to reduce residual tension. Applied mathematics and mechanics. 45, n.2, 371–375 (1981).
- Nyashin Yu. Y., Pozdeev A. A., Trusov P. V. Large elastoplastic deformation: theory, algorithms, applications. Moscow, Nauka (1986).
- Podstrigach Ya. S., Burak Ya. Y., Besedina L. P. Optimal heating of an irregular cylindrical shell. Phys.-chemical mechanics of materials. 2, 67–74 (1971).
- Baranovsky V. I., Gusev V.N., Ivanov V. N. et al. Production of color kinescopes / Ed. V. I. Baranovsky. Moscow, Energia (1978).
- Podstrigach Ya. S., Kosarchin V. I., Margolin A. M., Chernuha Yu. A. Analysis of thermal tensions in the elements of electronic devices in the vicinity of metal inclusions. Mat. methods and phys.-mech. fields. 28, p.15 (1988).
- Butkovskiy A. G. Methods of control of systems with distributed parameters. Moscow, Nauka (1975).
- Mikhlin S. G. Numerical realization of variational methods. Moscow, Nauka (1966).
- Polak E. Numerical methods of optimization. Moscow, Mir (1974).
- Himmelblau D. Application of nonlinear programming. Moscow, Mir (1975).
- Chernousko F. M., Banichuk N. V. Variational problems in mechanics and control. Moscow, Nauka (1973).
- Grigorenko Ya. M., Budak V. D., Grigorenko O. Ya. Solving problems of theory of shells based on discrete-continuous methods. Nikolaev, Ilion (2010).
- Goodal I. W., Whituwan C. M. On optimizing thermal stresses in cylindrical shells. Intern. I. Mech. Shi. 15(1), 99–107 (1973).
- Gachkevich A.,Irza E., Kaspersky Z. Thermomechanical models of quantitative description of the mechanical behavior of glass bodies of rotation with the thermal load. Visnyk of Lviv National University. Ser. Mech.-math. 73, 37–44 (2010).
- Gachkevich A. R., Budz S. F., Irza E. M., Kaspersky Z. I. Optimization of stress-deformed state of the glass shells of rotation with a local high-temperature heating. Theoretical and applied mechanics. 40, 146–150 (2005).
- Ritz W.Über eine neue Methode zur Lösung gewisser Variationsprobleme der mathematischen Physik. Journal für die reine und angewandte Mathematik. 135, 1–61 (1908).
- Pontryagin P. S., Boltiansky V. G., Gamkrelidze R. V., Mishchenko E. F. The mathematical theory of optimal processes. Moscow, Fizmatgiz (1961).
- Yevtushenko Yu. G. Methods of solving extreme problems and their application in systems of optimization. Moscow, Nauka (1982).
- Burak Ya. I., Besedina L. P. Variable thickness local temperature fields for removal of residual intensity in the nonuniform cylindrical shells. Phys.-chemical. mechanics of materials. 2, 71–75 (1973).
- Gachkevich N. G. Optimal for heavy duty heating glass piecewise-uniform shell of rotation consisting of elements of different geometric shapes. Mat. Methods and Phys.-Mech. Fields. 38, 142–147 (1995).
- Gachkevich O., Gachkevich M., Vorobets B., Trisch B., Gayevska L.: Methods of optimization of heating glass piecewise-uniform shells of revolving considering heat sensitivity of allowable intensity. Mashynoznavstvo. 12(126), 17–23 (2007).