Optimization of composite revolution shell by methods of theory of the optimal process

1Dzyuba, AP, 2Sirenko, VN, 2Klymenko, DV, 1Levytina, LD, 2Cherenkov, DA
1Oles Honchar National University of Dnipro, Dnipro, Ukraine
2Yangel Yuzhnoye State Design Office, Dnipro, Ukraine
Space Sci. & Technol. 2020, 26 ;(5):028-037
Publication Language: Ukrainian
We considered the problem of weight optimization of parameters of multi-layer composite shell produced by the method of continuous cross-winding under axisymmetric loading. Shell layers are placed symmetrically relative to the middle surface. The angles of the reinforcing material winding variable along the meridian and the thickness of layers are taken as the variation parameters. We propose an algorithm of the automated determination of the elastic constants of a composite material variable along the shell meridian anisotropy. The connection of the composite structure with the technological process of shell manufacturing by winding with a reinforcing tape under different angles to the axis of rotation is taken into account. The values of four elastic constants obtained as a result of experimental testing of witness specimens of the composite material along and orthogonal to the reinforcement are used as output.
         The equations of state of the moment theory of shells of the variable along the meridian orthotropy and wall thickness are obtained as a boundary value problem for a system of ordinary differential equations with variable coefficients. The use of the necessary optimality conditions in the form of the principle maximum of Pontryagin in the presence of arbitrary phrasal restraints made it possible to reduce the emerging multiparameter problem to a sequence of extreme problems of a significantly smaller dimension. This approach greatly simplifies taking into account the conditions of strength reliability, and technological and structural requirements of real design, and the process of finding an optimal project as a whole. The results of the optimization of a two-layer fiberglass shell of rotation are presented in the form of a change in the distribution of layers’ thickness and the glass fiber winding angle. Materials of research can be used to reduce the material consumption of structural elements in rocket and space technology and other branches.
Keywords: angles of winding, composite revolution shell, medalling of mechanical characteristics, principle maximum of Pontryagin, thickness of layers, weight optimization
1. Ambartsumjan S. A. (1974). General theory of anisotropic shells. Moscow: Nauka, 446 p.
2. Biderman V. L. (1977). Mechanics of the thin-walled constructions. Moscow: Mashi nostroenie, 488 p.
3. Brajson Ho Yu-shy. (1972). Applied theory of optimal management. Moscow: Mir, 544 p.
4. Golushko S. K., Nemirovsky Yu. V. (2008). Di rect and reverse tasks of mechanics of resilient composite plastins and shells of rotation. Moscow: Fizmatlit, 432 p.
5. Grebenyuk S. N. (2011). Resilient descriptions of composite material with a transtropna matrix and fibre. Методs of decision of the applied tasks of mechanics of the deformed solid: col. of sci. art. Dnepropetrovsk: Lira. Iss. 12, 62—68.
6. Grebenyuk S. N. (2012). Determination of the maximum module of resiliency on the basis of power condition of concordance. Bull. Kherson NTU, Iss. 2(45), 106—112.
7. Grebenyuk S. N., Klimenko M. I. (2014). Determination of the effective module of resiliency of composite at normal distribution of the modules of resiliency of fibre and matrix. Bull. Kherson NTU, Iss. 3(50), 254—258.
8. Dzyuba A. P. (1999). A method of the successive approximations untiing of tasks of optimal management is with limit phase coordinates for optimization of power elements of constructions. Problems of computational mechanics and strength of syructures. Dnepropetrovsk: Navchalyna kniga. Iss. 5, 61—85.
9. Dzyuba A. P., Sirenko V. N., Dzyuba P. A., Safronova I. A. (2018). Models and algorithms of optimization of elements of heterogeneous shell constructions. Actual problems of mechanics: monograph. Und. ed. N. V. Poljakov. Dnipro: Lira, 452 p.
10. Mechanics of compos: monograph in 12 vol. Und. the ed. A. N. Guzja. Kiev: Naukova Dumka, 1993—2003 rr. Vol. 8. Statics of elements of constructions. Und. the ed. Ja. M. Grigorenko. 1999. 379 p.
11. Obrazstov I. F., Vasilyev V. V., Bunakov V. A. (1977). Optimal re-enforcement of shells of rotation from composition materials. Moscow: Mashinostroenie, 144 p.
12. Pobedrya B. E. (1984). Mechanics of composition materials: Monograph. Moscow: Nauka, 400 p.
13. Solomonov Yu. S., Georgievsky V. P., Nedbay A. Ya., Andryushin V. A. (2013). Applied tasks of mechanics of composite cylindrical shells. Moscow: Fizmatlit, 406 p.
14. Uitni D. M. (1967). Resilient properties of the shells reinforced by fibres. Misselry and cosmonautics. No. 5, 170—173.
15. Hashin Z., Rozen B. (1964). Resilient modules of the materials reinforced by fibres. Appl. mech. (Trans ASME), No. 2, 71—82.
16. Hill R. (1966). Theory of mechanical properties of fibred composite materials. Mechanics IL, No. 2, 131—149.
17. Shvabyuk D. I., Rotko C. V. (2015). Linear deformation, durability and firmness of composite shells of middle thickness: Monograph. Lutsk: LNTU, 254 p.
18. Grebenyuk S. N. (2014). The shear modules of composite material with isotropic matrix and a fibre. J. Appl. Math. and Mech., 78, No. 2, 270—276.