624.04 A new method for calculating the torsional stiffness of a naturally twisted bar

Temis Y. M. (Центральный институт авиационного моторостроения им. П.И. Баранова), Ziyatdinov I. Z. (Центральный институт авиационного моторостроения им. П.И. Баранова)

BEAM MODELS, TORSIONAL STIFFNESS, TECHNICAL THEORY OF NATURALLY TWISTED BEAMS


doi: 10.18698/2309-3684-2023-1-6480


At the initial stages of designing compressor blades, screws, cutting tools, it is advisable to use a finite element model based on a model of a naturally twisted beam. This model takes into account the influence of the angle of natural twist on the rigidity of the part. The torsional stiffness of a bar significantly affects the stiffness parameters of the finite element model. It is shown that the torsional stiffness correction obtained on the basis of the relations of the technical theory of naturally twisted beams makes it possible to obtain results at small angles of natural twist that are in good agreement with the three-dimensional calculation of a twisted FEM beam. At large specific angles of initial twist, the technical theory gives overestimated values of the torsional stiffness. The article proposes a modification of the relations of the technical theory to determine the torsional rigidity, taking into account large angles of initial twist.


Temis Yu.M., Karaban V.V. Trudy CIAM. No 1319: Geometricheski nelinejnaya konechno-elementnaya model' zakruchennogo sterzhnya v zadachah staticheskogo i dinamicheskogo rascheta lopatok [Proceedings of CIAM. No. 1319: Geometrically nonlinear finite element model of a twisted rod in problems of static and dynamic calculation of blades]. Moscow, CIAM, 2019, 19 p.
Vorobyev Yu.S., Shorr B.F. Teoriya zakruchennyh sterzhnej [Theory of twisted rods]. Kiev, Naukova dumka Publ., 1983, 186 p.
Vlasov V.Z. Tonkostennye uprugie sterzhni [Thin-walled elastic rods]. Moscow, Fizmatgiz Publ., 1959, 568 p.
Svetlitsky V.A. Mekhanika gibkih sterzhnej i nitej [Mechanics of flexible rods and threads]. Moscow, Mashinostroenie Publ., 1978, 222 p.
Lurie A.I., Janelidze G.Yu. Zadacha Sen-Venana dlya estestvenno-skruchennyh sterzhnej [The Saint-Venant problem for naturally twisted rods]. Doklady Akademii nauk SSSR, 1939, vol. 24, no. 1-9, pp. 23–26.
Riz P.M. On the deformations and stresses of naturally twisted bars. Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, 1939, vol. 3, iss. 4, pp. 449–476.
Temis J.M., Fyodorov I.M. A comparison of methods for the stability analysis of beams with varying cross sections under nonconservative loading. Proceedings. 2005 International Conference Physics and Control, St. Petersburg, Russia, 2005, pp. 306-311. DOI: 10.1109/PHYCON.2005.1513998
Panasenko N.N., Yuzikov V.P., Sinelshchikov A.V. Finite element model of the spatial structures from thin-walled open section bars in 2 parts. Part 1. Vestnik of Astrakhan State Technical University. Series: Marine engineering and technologies, 2015, no. 2, pp. 89–100.
Meier C., Popp A., Wall W.A. Geometrically exact finite element formulations for slender beams: Kirchhoff–Love theory versus Simo–Reissner theory. Archives of Computational Methods in Engineering, 2019, vol. 26, pp. 163–243.
Chai T.Y. Warping behavior of cantilever steel beam with openings. Diss. of Master of Engineering (Civil-Structure). Malaysia, 2005.
Lisi D. A beam finite element model including warping. Application to the dynamic and static analysis of bridge decks. Diss. of Master of Civil Engineering. Italy, Milan, 2012.
Kourtis L.C., Kesari H, Carter D.R., Beaupré G.S. Transverse and torsional shear stresses in prismatic bodies having inhomogeneous material properties using a new 2D stress function. Journal of Mechanics of Materials and Structures, 2009, vol. 4, no. 4, pp. 659–674.
Malcolm D.J., Laird D.L. Modeling of blades as equivalent beams for aeroelastic analysis. ASME 2003 Wind Energy Symposium, 2003, art. no. WIND2003-870, pp. 293–303.
Branner K., Blasques J.P.A.A., Kim T., Fedorov V., Berring P., Bitsche R., Berggreen C. Anisotropic beam model for analysis and design of passive controlled wind turbine blades. DTU Wind Energy, 2012, art. no. 0001.
Bitsche P., Berggreen R., Temis J.M. Multidisciplinary technology for blade bending-torsion flutter prediction. 8th IFToMM International Conference on Rotor Dynamics, 2010, pp. 530–537.
Couturier Ph. Structural modelling of composite beams with application to wind turbine rotor blades. Diss. of Ph.D. degree Kgs. Lyngby, DTU Mechanical Engineering, 2016, 202 p.
Birger I.A., Mavlyutov R.R. Soprotivlenie materialov [Resistance of materials]. Moscow, Nauka Publ., 1986, 560 p.
Dubrovin V.M., Butina T.A. Modeling the stability of compressed and twisted rods in precise problem statement. Маthematical Modeling and Coтputational Methods, 2015, no. 3, pp. 3–16.
Karaban V.V. Avtomatizirovannaya sistema opredeleniya geometricheskih harakteristik proizvol'nyh odno- i mnogosvyaznyh sechenij [Automated system for determining the geometric characteristics of arbitrary single- and multiconnected sections]. Aktual'nye problemy matematicheskogo modelirovaniya i avtomatizirovannogo proektirovaniya v mashinostroenii: tezisy dokladov mezhdunarodnoj nauchno-tekhnicheskoj konferencii. Sekciya 5 [Actual problems of mathematical modeling and computer-aided design in mechanical engineering: abstracts of reports of the international scientific and technical conference. Section 5], Kazan, 1995, pp. 56–58.
Temis Yu.M., Karaban V.V. Opredelenie geometricheskoj zhestkosti na kruchenie odno- i mnogosvyaznyh mashinostroitel'nyh i lopatochnyh profilej s osobennostyami s ispol'zovaniem MGE [Determination of geometric torsional stiffness of single- and multi-connected machine-building and blade fillets with features using MGE]. Prikladnye problemy prochnosti i plastichnosti. Chislennoe modelirovanie fiziko-mekhanicheskih processov: mezhvuzovskij sbornik [Applied problems of strength and plasticity. Numerical modeling of physical and mechanical processes: Intercollegiate Collection], 1997, issue 55, pp. 137-149


Темис Ю.М., Зиятдинов И.З. Новый метод вычисления жесткости на кручение в модели естественно-закрученного стержня. Математическое моделирование и численные методы, 2023, No 1, с. 64–80



Download article

Количество скачиваний: 116