Application of perturbation method and sensitivity functions to the problem of optimizing the systems with distributed parameters
Published: 22.10.2015
Authors: Bushuev A.Yu.
Published in issue: #6(42)/2015
DOI: 10.18698/2308-6033-2015-6-1411
Category: Mechanics | Chapter: Mechanics of Deformable Solid Body
Creating of effective optimization methods is important for solving real engineering problems. In this paper we developed a method for constructing the sensitivity function to solve the problem of optimizing of the elastic construction. Moreover, for optimizing of the systems we offer an iterative algorithm, which is based on the linearization procedure and the sensitivity function. The quality of these systems is described by a fractional-linear functional with control restrictions.
References
[1] Hog E., Choi K., Komkov V. Analiz chuvstvitelnosti pri proektirovanii konstruktsiy [The sensitivity analysis in the structures design]. Moscow, Mir Publ., 1988 [in Russian].
[2] Banichuk N.V., Karpov I.I., Klimov D.M. Mekhanika bolshikh kosmicheskikh konstruktsiy [The mechanics of large space structures]. Moscow, Factorial Publ., 1997.
[3] Bushuev A.Yu., Gorskiy V.V. Inzhenerno-fizicheskiy zhurnal - Journal of Engineering Physics and Thermophysics, 2000, vol. 73, no. 1, pp. 155-159.
[4] Troitskiy A.V. Matematicheskie modeli i metody analiza chuvstvitelnosti v zadachakh optimizatsii konstruktsiy rotorov. Diss kand. tekhn. nauk [Mathematical models and methods of sensitivity analysis in optimization problems of rotor construction. Cand. eng. sci. diss.]. Moscow, 2006.
[5] Tushev O.N., Berezovskiy A.V. Oboronnaya tekhnika - Defense Engineering, 2007, no. 3-4, pp. 87-93.
[6] Pavlov S.P. Matematicheskoe modelirovanie i optimizatsiya formy termouprugikh tel. Diss dokt. fiz.-mat. nauk [Mathematical modeling and optimization of thermoelastic bodies form. Doct. phys.- math. sci. diss.]. Saratov, 2009.
[7] Pupko V.Ya., Zrodnikov A.V., Likhachev Yu.I. Metod sopryazhennykh funktsiy v inzhenerno-fizicheskikh issledovaniyakh [The method of conjugate functions in engineering physics research]. Moscow, Energoatomizdat Publ., 1984.
[8] Bushuev A.Yu., Yakovlev D.O. Vestnik MGTU im. N.E. Baumana. Ser. Estestvennye nauki - Herald of Bauman Moscow State Technical University. Ser. Natural Sciences, 2011, special issue "Mathematical modeling", pp. 66-69.
[9] Bushuev A.Yu., Farafonov B.A. Matematicheskoye modelirovaniye i chislennye metody - Mathematical Modeling and Computational Methods, 2014, vol. 2, no. 2 (2), pp. 101-114.
[10] Gorodetskiy Yu.I. Funktsii chuvstvitelnosti i dinamika slozhnykh mekha-nicheskikh system [Sensitivity function and dynamics of complex mechanical systems]. Nizhniy Novgorod, 2006.
[11] Dimitrienko Yu.I., Drogolub A.N., Gubareva E.A. Nauka i obrazovanie. Elektronnoe izdanie - Science and Education. Electronic Journal, 2015, no. 2. doi: 10.7463/0215.0757079 http://technomag.bmstu.ru/doc/757079.html
[12] Marchuk G.I. Sopryazhennye uravneniya i analiz slozhnykh system [Conjugate equations and complex systems analysis]. Moscow, Nauka Publ., 1992.
[13] Filippov A.P. Prikladnaya mekhanika - Applied mechanics, Academy of Sciences of Ukraine, 1971, vol. 7, issue 10.
[14] DimitrienkoYu.I. Mekhanika sploshnoy sredy. Tom 4. Osnovy mekhaniki tverdogo tela [Continuum mechanics. Vol. 4. Fundamentals of solid mechanics]. Moscow, BMSTU Publ., 2013, 624 p.