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Optimization problems of the stress-deformed state of thermoelastic shells

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Abstract

We discuss general questions about the choice of optimization criteria for the stressed state of thermoelastic shells taking account of the functional measures of the space-time variability of its characteristics. The efficiency of the proposed approach is illustrated using the example of the solution of a problem for an axisymmetrically heated cylindrical shell.

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Literature cited

  1. L. P. Besedina and Ya. I. Burak, “On the optimal conditions of local thermal treatment of a cylindrical shell of finite length under various methods of fastening the end sections,”Fiz.-Khim. Mekh. Mater., No 5, 621–624 (1969).

    Google Scholar 

  2. L. P. Besedina, Ya. I. Burak, and Ya. S. Podstrigach, “On the optimal heating of nonuniform shells of revolution,”Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 6, 110–116 (1973).

    Google Scholar 

  3. L. P. Besedina and Ya. P. Romanchuk, “The influence of fastening conditions on the optimal heating of an nonuniform cylindrical shell,”Mat. Met. i Fiz.-Mekh. Polya, No. 2, 102–106 (1975).

    Google Scholar 

  4. L. P. Besedina and N. N. Timoshenko, “Optimal plastic deformations in a slanted spherical shell with a circular welded seam,”Mat. Met. i Fiz.-Mekh. Polya, No. 1, 127–130 (1975).

    Google Scholar 

  5. B. L. Bozhenko, “Stress optimization of temperature fields in a cylindrical shell by the finite element method,”Mat. Met. i Fiz.-Mekh. Polya, No. 18, 89–92 (1983).

    Google Scholar 

  6. S. F. Budz, “Heat regimes of zonal annealing of a cylindrical shell that are optimal over stresses,”Fiz.-Khim. Mekh. Mater., No. 4, 116–118 (1974).

    Google Scholar 

  7. S. F. Budz, “On the determination of the optimal temperature fields under local heating of shells of revolution,”Mat. Met. i Fiz.-Mekh. Polya, No. 1, 122–127 (1975).

    Google Scholar 

  8. Ya. I. Burak, “Criteria for optimization of the stressed state of thermoelastic bodies,”Mat. Met. i Fiz.-Mekh. Polya, No. 24, 49–52 (1985).

    Google Scholar 

  9. Ya. I. Burak and L. P. Besedina, “Variable-thickness local temperature fields for removing the residual stresses in nonuniform cylindrical shells,Fiz.-Khim. Mekh. Mater., No. 2, 71–74 (1973).

    Google Scholar 

  10. Ya. I. Burak and L. P. Besedina, “Low-temperature thermal treatment of the zone of a circular seam in a plate with a circular hole,”Autom. Svarka, No. 5, 19–23 (1975).

    Google Scholar 

  11. Ya. I. Burak and B. L. Bozhenko, “Application of the finite element method to solve problems of the thermomechanics of thin shells,” in:All-Union School for Young Researchers on ‘Numerical Methods of Solving Problems of Mathematical Physics’,” [in Russian], Znanie, Moscow (1983), Pt. 2, pp. 15–16.

    Google Scholar 

  12. Ya. I. Burak and S. F. Budz, “On the determination of optimal regimes for heating a thin spherical shell,”Prikl. Mekh.,10, No. 2, 14–20 (1974).

    Google Scholar 

  13. Ya. I. Burak and B. V. Gera, “Optimization of regimes of force loading of a cylindrical shell,”Prikl. Mekh.,14, No. 12, 113–117 (1978).

    Google Scholar 

  14. Ya. I. Burak, E. I. Grigolyuk, and Ya. S. Podstrigach, “On the application of calculus of variations methods to solve problems on the optimal heating of thin shells,” in:Proc. 7th All-Union Conf. Th. Shells and Plates [in Russian], Dnepropetrovsk Univ. Press (1970), pp. 100–108.

  15. Ya. I. Burak and P. P. Domanskii, “Optimization of dynamic effects in shells of revolution with an axially symmetric force loading,”Prikl. Mekh.,18, No. 2, 7–14 (1982).

    Google Scholar 

  16. Ya. I. Burak and Yu. D. Zozulyak, “Extremal temperature fields and stresses under local heating of a spherical shell,”Prikl. Mekh.,6, No. 12, 74–81 (1970).

    Google Scholar 

  17. Ya. I. Burak and Yu. D. Zozulyak, “Determination of the optimal force loading under local heating of thin shells of revolution,”Tepl. Napr. v El. Konstr., No. 13, 71–75 (1973).

    Google Scholar 

  18. Ya. I. Burak, Yu. D. Zozulyak, and B. V. Gera,Optimization of Transitional Processes in Thermoelastic Bodies [in Russian], Naukova Dumka, Kiev (1984).

    Google Scholar 

  19. Ya. I. Burak and I. V. Ogirko, “The optimal heating of a cylindrical shell with variable material characteristics,”Mat. Met. i Fiz.-Mekh. Polya, No. 5, 63–68 (1977).

    Google Scholar 

  20. Ya. I. Burak, Ya. P. Romanchuk, and V. P. Morgun, “Optimization of the conditions for local heating of welded plates,”Fiz.-Khim. Mekh. Mater., No. 5, 98–102 (1978).

    Google Scholar 

  21. Ya. I. Burak, Ya. P. Romanchuk, A. A. Kazimirov, and V. P. Morgun, “Choosing an optimal temperature field for preliminary heating of plates in welding,”Avtom. Svarka, No. 5, 15–19 (1979).

    Google Scholar 

  22. Ya. I. Burak and Ya. S. Podstrigach, “On a class of variational problems for a conditional extremum,” in:Proc. Rep. Symp. Diff. Eqs. [in Russian], Odessa Univ. Press (1968), pp. 166–167.

  23. Ya. I. Burak and N. N. Timoshenko, “Determination of the optimal temperature fields for local heating of a slanted conical shell,”Fiz.-Khim. Mekh. Mater., No. 6, 107–109 (1970).

    Google Scholar 

  24. Ya. I. Burak and N. N. Timoshenko, “Determination of optimal temperature fields in problems on the local heating of slanted shells,”Fiz. i Khim. Obrab. Mater., No. 5, 29–36 (1973).

    Google Scholar 

  25. B. V. Gera, “Optimization of dynamic thermal stresses in a cylindrical shell,”Mat. Met. i Fiz.-Mekh. Polya, No. 9, 66–70 (1979).

    Google Scholar 

  26. B. V. Gera, “Optimization of regimes of intensive heating of a cylindrical shell,,Vych. i Prikl. Mat., No. 45, 13–21 (1981).

    Google Scholar 

  27. E. I. Grigolyuk, Ya. I. Burak, V. Yu. Krukevich, and Ya. S. Podstrigach, “On the determination of regimes of local thermal treatment of cylindrical shells with residual stresses,”Fiz.-Khim. Mekh. Mater., No. 3, 361–369 (1969).

    Google Scholar 

  28. E. I. Grigolyuk, Ya. I. Burak, and Ya. S. Podstrigach, “On an extremal problem of thermoelasticity for an infinite cylindrical shell,”Dokl. Akad. Nauk SSSR,174, No. 3, 534–537 (1967).

    Google Scholar 

  29. E. I. Grigolyuk, Ya. I. Burak, and Ya. S. Podstrigach, “Statement and solution of some variational problems of the thermoelasticity of thin shells in application to the choice of optimal regimes of local thermal treatment,”Zh. Prikl. Mekh. i Tekh. Fiz., No. 4, 47–54 (1968).

    Google Scholar 

  30. E. I. Grigolyuk, Ya. I. Burak, and Ya. S. Podstrigach, “On the statement and solution of a class of extremal problems of thermoelasticity for shells of revolution,” in:Theory of Plates and Shells [in Russian], Naukova Dumka, Kiev (1971), pp. 66–73.

    Google Scholar 

  31. E. I. Grigolyuk, B. L. Pelekh, and Ya. S. Podstrigach, “On the solution of a class of problems of optimal heating of three-layered shells with elastic filler,” in:Proc. IX All-Union Conf. Theory of Shells and Plates [in Russian], Nauka, Leningrad (1973), pp. 257–258.

    Google Scholar 

  32. E. I. Grigolyuk, B. L. Pelekh, and Ya. S. Podstrigach, “On the optimal heating of three-layered cylindrical shells with a light elastic filler,”Zh. Prikl. Mekh. i Tekh. Fiz., No. 2, 120–125.

  33. E. I. Grigolyuk, Ya. S. Podstrigach, and Ya. I. Burak,Optimization of the Heating of Shells and Plates [in Russian], Naukova Dumka, Kiev (1979).

    Google Scholar 

  34. P. P. Domanskii, “Optimization of the solutions of the equation of motion of shells of revolution in order to increase the parameters of dynamic stability,”Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 12, 12–14 (1982).

    Google Scholar 

  35. Yu. D. Zozulyak, “Optimization of the force load with narrow zones of local heating of a cylindrical shell,”Mat. Met. i Fiz.-Mekh. Polya, No. 1, 118–122 (1975).

    Google Scholar 

  36. Yu. D. Zozulyak, “Optimal temperature fields under local heating of a cylindrical shell conjugate with a dome,”Mat. Met. i Fiz.-Mekh. Polya, No. 2, 99–102.

  37. Yu. D. Zozulyak, “On the application of a force load in the welding process in order to optimize the residual stresses in a cylindrical shell,”Mat. Met. i Fiz.-Mekh. Polya, No. 4, 51–53 (1976).

    Google Scholar 

  38. Yu. D. Zozulyak, Yu. L. Ledyashov, “The methodology of determining rational schemes for spot welding thin-walled shells,”Avtom. Svarka, No. 2, 18–20 (1986).

    Google Scholar 

  39. V. N. Maksimovich and G. V. Plyatsko, “Temperature fields and stresses in the local relaxation of spiral welded seams in cylindrical shells,”Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 4, 188–192 (1972).

    Google Scholar 

  40. I. V. Ogirko, “The methodology of numerical optimization of thermal stresses in flexible rectangular slanted shells in a plane,”Mat. Met. i Fiz.-Mekh. Polya, No. 14, 79–81 (1981).

    Google Scholar 

  41. B. L. Pelekh, Ya. S. Podstrigach, and I. G. Sirenko, “Some general questions of the theory of thermoelasticity of transversally isotropic shells,”Izv. Akad. SSSR, Mekh. Tverd. Tela, No. 6, 81–88 (1971).

    Google Scholar 

  42. G. V. Plyatsko and V. N. Maksimovich, “On a method of determining the temperature field for local heating of cylindrical shells,”Dokl. Akad. Nauk SSSR, Ser. A, No. 9, 810–814 (1971).

    Google Scholar 

  43. G. V. Platsko, V. N. Maksimovich, and Z. I. Goryacheva, “A method of determining the temperature field in local relaxation of circular welded seams of cylindrical shells,”Svar. Proizv., No. 6, 25–27 (1973).

    Google Scholar 

  44. Ya. S. Podstrigach, Ya. I. Burak, and L. P. Besedina, “On the influence of the method of fastening the end sections of shells of revolution on the profile of the optimal temperature field under local thermal treatment,”Tepl. Napr. v El. Konstr., No. 10, 261–268 (1970).

    Google Scholar 

  45. Ya. S. Podstrigach, Ya. I. Burak, and L. P. Besedina, “On the optimal heating of an nonuniform cylindrical shell,”Fiz.-Khim. Mekh. Mater., No. 2, 67–74 (1974).

    Google Scholar 

  46. Ya. S. Podstrigach, Ya. I. Burak, S. F. Budz, et al.,Optimization and Control in Electrovacuum Production [in Russian], Naukova Dumka, Kiev (1980).

    Google Scholar 

  47. Ya. S. Podstrigach, Ya. I. Burak, and Yu. D. Zozulyak, “Determination of the extremal temperature overfalls in thickness during the axially symmetric heating of shells of revolution,”Tepl. Napr. v El. Konstr., No. 11, 26–31 (1971).

    Google Scholar 

  48. Ya. S. Podstrigach, Ya. I. Burak, and Yu. D. Zozulyak, “On the determination of the optimal force loading in the local heating of a cylindrical shell” [in Ukrainian],Dop. Akad. Nauk Ukr. RSR, Ser. A, No. 11, 1024–1028 (1972).

    Google Scholar 

  49. Ya. P. Romanchuk, “Optimization of the stressed state of a cylindrical shell using local heating,”Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 12, 1106–1109 (1976).

    Google Scholar 

  50. O. N. Shablii, V. I. Zaretskii, and Ya. R. Medynskii, “Optimal control of the temperature regime of a circular disk,”Izv. Vuzov, Mashinostroenie, No. 10, 78–82 (1978).

    Google Scholar 

  51. O. N. Shablii and Ya. R. Medynskii, “The problem of optimal control of the stressed state of physically nonlinear plates and shells,” in:Theory and Methods of Computing Nonlinear Plates and Shells [in Russian], Saratov Univ. Press (1981), pp. 75–77.

  52. O. N. Shablii and Ya. R. Medynskii, “On the problem of the formation of necessary residual stresses in a circular disk,”Prikl. Mekh.,17, No. 6, 90–93 (1986).

    Google Scholar 

  53. O. N. Shablii and Ya. R. Medynskii, “Optimal control of the formation of a residual stress-deformed state in solid thermoelastic bodies,” Preprint, Ukrainian Scientific/Technical Information, No. 965Uk (1984).

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Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 27, 1988, pp. 11–18.

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Burak, Y.I., Zozulyak, Y.D. Optimization problems of the stress-deformed state of thermoelastic shells. J Math Sci 62, 2499–2505 (1992). https://doi.org/10.1007/BF01099139

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  • DOI: https://doi.org/10.1007/BF01099139

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