Algorithms of determining the rational parameters of units in numerical modeling of dynamic response mechanisms

Mathematics. Physics. Mechanics


Kasumov E. V.

Kazan National Research Technical University named after A.N. Tupolev, KNRTU-KAI, 10, Karl Marks str., Kazan, 420111, Russia



The purpose of this paper is stepwise development of complex of nonlinear mathematical models of design and checking calculations of aircraft mechanical systems.
The paper discusses techniques of numerical simulation using the finite element method for early stages of mechanical system design for aircrafts.
Mathematical models of kinematic and power analysis of mechanical system with flexible links are considered as a basis for determination of preliminary data of design parameters calculation of links including the load-bearing surface.
This paper concerns issues of determination of preliminary endurance of aircraft mechanical system elements at early stages of design thereof. The technique of design calculation is built on usage of numerical methods for determination of load amplitude spectrum.
Examples of calculation of load-bearing surface made of composite materials, lightweight helicopter control system mechanisms are presented. Application possibilities of nonlinear problems solution at initial stages of aircraft development are examined.
The obtained function of face panels thickness is determined as a rational function of material distribution in design calculation at preset field of loads and temperatures.
Approaches to calculations of structure rational parameters are considered with which the most smooth and level low stress field is obtained. This allows enhancing fatigue strength characteristics. On the basis of calculation results the determination of preliminary endurance for idealized structure of aircraft assemblies is performed. Main assumptions in preliminary endurance calculation are a uniformity of material properties, surface smoothness, and absence of processing defects. Results of tests of laboratory patterns of materials used in the structure are utilized in source data.
Mathematical models for design calculation of load-bearing surface made of composite materials are intended for determination of rational values of maximum stiffness.
Component simulation of forthcoming bench and flight testing on the stage of flying vehicle designing allows to increase efficiency of full-scale test as well as to define optimal design parameters more precisely.


the mathematical model, numerical simulation, kinematic analysis, power analysis, designing


  1. Bate K., Vilson E. Chislennye metody analiza i metod konechnyh jelementov (Numerical methods in finite element analysis), Moscow, Strojizdat, 1982, 448 p.
  2. Craig R.R., Bampton M. C.C. AIAA Journal, 1968, no.6(7), pp.1313-1319.
  3. Dmitriev I.S., Esaulov S.Ju. Sistemy upravlenija odnovintovyh vertoletov (Control system of one-screw helicopters), Moscow, Mashinostroenie, 1969, 220 p.
  4. Kolosov S.P., Stromilov V.M. Osnovy avtomaticheskogo pilotirovanija (Basis of automatic piloting ), Moscow, Oborongiz, 1959, 233 p.
  5. Golovanov A.I., Kasumov E.V., Shuvalov V.A. Uchenye zapiski CAGI, 2010, no. 4, vol. XLI, pp. 86-104.
  6. Golovkin M.A., Tarasov N.N. Uchenye zapiski CAGI, 2009, no.4, vol. XL, pp. 56-85.
  7. V.A. Leont'ev. Uchenye zapiski CAGI, 2010, no.5, vol. XII, pp. 67-79.
  8. Gajnutdinov V.G., Kasumov E.V. Vestnik Kazanskogo gosudarstvennogo tehnicheskogo universiteta, 1998, no.3, pp.6-8.
  9. Gajnutdinov V.G., Kasumov E.V. Izv. vuzov. Aviacionnaja tehnika, 1999, no.4, pp.13-15.
  10. Boldyrev A.V., Komarov V.A., Lapteva M.Ju., Popovich K.F. Polet, Moscow, 2008, no.1, pp.34-39.
  11. Boldyrev A.V., Komarov V.A., Lapteva M.Ju. Vestnik Kazanskogo gosudarstvennogo tehnicheskogo universiteta , 2009, no.3, pp. 13-15.
  12. Kuznetsov A.S. Izvestija Samarskogo nauchnogo centra Rossijskoj akademii nauk, 2011, no.1(2), vol.13 (39), pp.318-321.
  13. Gajnutdinov V.G., Ramazanov R.V., Coj A.S. Vestnik Kazanskogo gosudarstvennogo tehnicheskogo universita, 2003, no.2, pp.8-9.

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