Parameter optimization decomposition and synthesis algorithm for a bundle of rotation shells connected with a ring frame

The method of weight optimization of a shell structure consisting of a power ring frame connected to it on each side of non-homogeneous shells of rotation with variable wall thickness under the action of a spatially asymmetric load is presented. The construction decomposition algorithm is applied. The optimization of shells is carried out based on the necessary Pontryagin's optimality conditions with phase constraints. Finite-dimensional optimization methods are used to seek the optimal configuration of the ring frame. The synthesis of the construction is carried out by the method of successive approximations. Numerical optimization results are presented.

  1. Mossakovsky V. I., Gudramovich V. S., Makeev E. M.  Contact interactions of elements of shell structures. Kyiv, Naukova Dumka (1988).
  2. Myachenkov V. I., Grigoryev I. V.  Calculation of compound shell structures on a computer: Reference. Moscow, Mashinostroenie (1981).
  3. Hudramovich V. S., Dzyuba A. P.  Contact interaction and optimization of locally loaded shell structures.  Journal of Mathematical Science.  162, 231–245 (2009).
  4. Degtyarev A. V.  Problems and prospects. Missile technology.  Dnipro, Art-Press (2014).
  5. Troshin V. G.  On one method of calculation of composite shells of revolution supported by power transverse ribs.  Structural mechanics and calculation of structures.  4, 41–46 (1991).
  6. Dziuba A. P., Levitina L. D., Sadovnikov S. S.  Calculation and optimal design of a beam of rotation connected by a frame under asymmetric loading.  Visn. Dnipropetrovsk University. Ser.: Mechanics.  7 (2), 39–51 (2003), (in Ukrainian).
  7. Himmelblau D.  Applied Nonlinear Programming. McGrow-Hill Book Comp. (1972).
  8. Rekleitis G., Reyvindran A., Ragsdell K.  Optimization in technology: in 2 books. Wiley-Interscience Publ. (1983).
  9. Grigorenko Ya. M., Vasilenko A. T.  Methods for calculating shells, Theory of shells of variable rigidity. Vol. 4. Kyiv, Naukova Dumka (1981).
  10. Dziuba A. А., Dziuba A. P., Levitina L. D., Safronova I. А.  Mathematical simulation of deformation  for the rotation shells with variable wall thickness.  Journal of Optimization, Differential Equations and Their Applications.  29 (1), 79–95 (2021).
  11. Dziuba A. P., Sirenko V. N., Klymenko D. V., Levityna L. D. Cherenkov D. A.  Optimization of composite revolution shells by methods of the theory of optimal processes.  Space Science and Technology.  26 (5), 28–37 (2020), (in Ukrainian).
  12. Pontryagin L. S., Bolteanskii V. G., Gamkrelidze R. V., Mishchenko E. F.  The Mathematical Theory of Optimal Processes. Interscience: New York. NY, USA (1962).
  13. Bryson A. E., Yu-Shi Ho.  Applied theory of optimal control. Blaisdell Publ. comp. (1969).
  14. Bogomolov S. I., Nazarenko S. A., Simson E. A.  Calculation and optimization of shells of general shape based on the mixed approach of the finite element method.  Dynamics and strength of heavy machines.  91–97 (1986).
  15. Gaydaychuk V. V., Kosheviy O. O. Kosheviy O. P.  Optimal design and strength calculation of shells under combined leads in the program complex Femap Nastran.  Modern problems of architecture and urban planning.  50, 314–324 (2018).
  16. Dzyuba A., Torskyy A.  Algorithm of the successive approximation method for optimal control problems with phase restrictions for mechanics tasks.  Mathematical Modeling and Computing.  9 (3), 734–749 (2022).
  17. Malkov V. P., Ugodchikov A. G.  Optimization of elastic systems. Moscow, Nauka (1981).
  18. Grigorenko Ya. M., Vlaikov G. G., Grigorenko A. Ya.  Numerical-analytical solution of shell mechanics problems based on various models.  Kiev, Academicperiodical (2006).
  19. Biderman V. L.  Mechanics of thin-walled structures. Мoscow, Mashinostroenie (1977).
  20. Emel'yanov I. G.  Application of discrete Fourier series to the stress analysis of shell structures.  Computational Continuum Mechanics.  8 (3), 245–253 (2015).
  21. Dziuba A. P., Safronova I. A., Levitina L. D.  Algorithm for computational costs reducing in problems of calculation of asymmetrically loaded shells of rotation.  Strength of Materials and Theory of Structures.  105, 99–113 (2020).
  22. Strength. Sustainability. Oscillations: Handbook Vol. 1, ed. I. A. Birger, Ya. G. Panovko.  Moscow, Mashinostroenie (1968).
Mathematical Modeling and Computing, Vol. 10, No. 3, pp. 976–987 (2023)