Mathematical model of optimization of annealing regimes by the stress state for heat-sensitive glass elements of structures

: 134-146
Received: January 15, 2018
Pidstryhach Institute for Applied Problems of Mechanics and Mathematics National Academy of Sciences of Ukraine
Pidstryhach Institute for Applied Problems of Mechanics and Mathematics National Academy of Sciences of Ukraine
Centre of Mathematical Modelling IAPMM of Ukrainian National Academy of Sciences
Lviv Polytechnic National University

A mathematical model is constructed and a problem of optimization of annealing regimes of thermosensitive glass elements of constructions with the use of numerical methods and variational calculus is solved. As an example, the optimal regimes of annealing of specific glass plates for different values of permissible stresses are constructed and analyzed.

  1. Grigolyuk E., Podstrigach Ya., Burak Ya. Optimization of heating of shells and plates. Kiev, Naukova dumka (1979), (in Russian).
  2. Biswas P. Thermal Stresses, Deformations and Vibrations of Plates and Shells -- A Nonlinear Approach. Procedia Engineering. 144, 1023–1030 (2016).
  3. Podstrigach Ya., Kolyano Yu., Semerak M. Temperature fields and stresses in elements of electrovacuum devices. Kiev, Naukova dumka (1981), (in Russian).
  4. Carrera E., Fazzolari F., Cinefra M. Thermal Stress Analysis of Composite Beams, Plates and Shells. Computational Modelling and Applications. Massachusetts, Academic Press (2016).
  5. Bartenev H. Mechanical properties and heat treatment of glass. Moscow, Stroyizdat (1960), (in Russian).
  6. Bartenev H. High-strength and highly-strength inorganic glasses. Moscow, Stroyizdat (1974), (in Russian).
  7. Pukh V. Strength and destruction of glass. Moscow, Nauka (1973), (in Russian).
  8. Solntsev S., Morozov E. The destruction of glass. Moscow, Mechanical Engineering (1978), (in Russian).
  9. Budz S., Gachkevich N. Optimization of heat treatment of piecewise homogeneous shells of ELB with allowance for the temperature dependence of the material characteristics. Physico-chemical mechanics of materials. 5, 111–113 (1987), (in Russian).
  10. Chernousko F., Banichuk N. Variational problems of mechanics and control. Moscow, Nauka (1973), (in Russian).
  11. Norry D., Freese J. An Introduction to the Finite Element Method. Moscow, Mir (1981).
  12. Gachkevich O., Gachkevich M., Budz S. Optimization under the stress state of the heating modes of glass lump-homogeneous membranes. Lviv, Pidstryhach Institute for Applied Problems of Mech. and Math., National Academy of Sciences of Ukraine (2014), (in Ukrainian).
  13. Korn G., Korn T. Reference on mathematics. Moscow, Nauka (1974).
  14. Marchuk G. Methods of computational mathematics. Moscow, Nauka (1977), (in Russian).
  15. Gachkevich M., Gachkevich O., Torskyy A., Dmytruk V. Mathematical models and methods of optimization of technological heating regimes of the piecewise homogeneous glass shell. State-of-the-art investigations. Mathematical Modeling and Computing. 2 (2), 140–153 (2015).
  16. Baranovsky V., Gusev V., Ivanov V. and others. Production of color kinescopes. Ed. Baranovsky V. Moscow, Energia (1978), (in Russian).
Math. Model. Comput. Vol. 5, No. 2, pp. 134-146(2018)