Geodesic
Analysis of stress-strain state of the naturally twisted rod bending by transverse force on the basis of the finite element method
Vladikavkazskij matematičeskij žurnal, Tome 15 (2013) no. 3, pp. 45-53 Cet article a éte moissonné depuis la source Math-Net.Ru

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Numeric solution based on homogeneous solutions method and numeric integration by finite element method of two-dimension boundary problems, which are described Saint-Venant's solutions on pure bending and bending by transverse force of the naturally twisted rod with rectangular cross-section was constructed. The analysis of stress-strain state of the rod was realized for different values of parameter $\tau_0$. 
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N. V. Kurbatova; Yu. A. Ustinov; E. S. Chumakova. Analysis of stress-strain state of the naturally twisted rod bending by transverse force on the basis of the finite element method. Vladikavkazskij matematičeskij žurnal, Tome 15 (2013) no. 3, pp. 45-53. http://geodesic.mathdoc.fr/item/VMJ_2013_15_3_a4/

[1] Riz P. M., “Deformatsiya estestvenno zakruchennykh sterzhnei”, Dokl. AN SSSR, 23:1 (1939), 18–21 | MR

[2] Dzhanelidze G. Yu., Lure A. I., “Zadachi Sen-Venana dlya estestvenno skruchennykh sterzhnei”, Dokl. AN SSSR, 24:1 (1939), 23–26

[3] Dzhanelidze G. Yu., Lure A. I., “Zadachi Sen-Venana dlya estestvenno skruchennykh sterzhnei”, Dokl. AN SSSR, 24:3 (1939), 226–228

[4] Dzhanelidze G. Yu., Lure A. I., “Zadachi Sen-Venana dlya estestvenno skruchennykh sterzhnei”, Dokl. AN SSSR, 24:4 (1939), 325–326

[5] Uzdalev A. I., Inozemtsev G. G., Zubkov A. V., Alakhazova O. V., “Napryazhennoe sostoyanie estestvenno zakruchennogo sterzhnya”, PMM, 24:11 (1988), 103–108 | Zbl

[6] Eliseev V. V., “Izgib estestvenno-zakruchennogo sterzhnya”, Tr. Leningr. politekhn. in-ta, 425, 1988, 44–46

[7] Zametalina N. P., Prokopov V. K., “Napryazhennoe sostoyanie estestvenno skruchennykh sterzhnei tipa spiralnykh sverl”, Izv. AN ArmSSR, 27:3 (1974), 3–9

[8] Korolkov V. I., “K resheniyu zadachi o rastyazhenii estestvenno zakruchennogo sterzhnya proizvolnogo poperechnogo secheniya v trekhmernoi postanovke”, PMM, 4:12 (1988), 113–115

[9] Shorr B. F., “K teorii zakruchennykh neravnomerno nagretykh sterzhnei”, Izv. AN SSSR. Mekhanika i mashinostroenie, 1960, no. 1, 141–151 | Zbl

[10] Druz A. N., Polyakov N. A., Ustinov Yu. A., “Odnorodnye resheniya i zadachi Sen-Venana dlya estestvenno zakruchennogo sterzhnya”, PMM, 60:4 (1996), 660–668 | MR | Zbl

[11] Ustinov Yu. A., Zadachi Sen-Venana dlya psevdotsilindrov, Nauka, M., 2003, 128 pp.

[12] de Saint-Venant A. J.-C. B., “Memoire sur la torsion des prisms, avec des conciderations sur leur flexion, ainsi que sur l'equilibre interieur des solides elastiques en general, et des formules pratiques pour le calcul de leur resistance a divers efforts s'exercant simultanement”, Mem. Savants Etrang., 14 (1856), 233–560

[13] de Saint-Venant A. J.-C. B., “Memoire sur la flexion des prismes”, Liouville J. Math., 1 (1856), 89–189

[14] Sen-Venan V., Memuar o kruchenii prizmy. Memuar ob izgibe prizmy, Fizmatlit, M., 1961, 518 pp.

[15] Berdichevskii V. L., Staroselskii L. A., “Izgib, rastyazhenie i kruchenie estestvenno-zakruchennykh sterzhnei”, PMM, 49:6 (1985), 978–991 | MR

[16] Ustinov Yu. A., Kurbatova N. V., “Zadachi Sen-Venana dlya sterzhnei s fizicheskoi i geometricheskoi anizotropiei”, Izv. vuzov. Sev.-Kavk.region. Estestv. nauki. Mat. model., 2001, Spetsvypusk, 154–157

[17] Natalya V. Kurbatova, “On a stretching-torsion of a naturally twisted rod”, Advanced Problems in Mechanics, 2005, 59–60

[18] Kurbatova N. V., Romanova N. M., “Konechno-elementnoe reshenie zadachi izgiba dlya estestvenno-zakruchennogo sterzhnya”, Tr. IX mezhdunar. konf. “Sovremennye problemy mekhaniki sploshnoi sredy”, v. 1, Izd-vo TsVVR, Rostov n/D., 2005, 123–126

[19] Ustinov Yu. A., “Obosnovanie printsipa Sen-Venana dlya estestvenno-zakruchennogo sterzhnya”, Vladikavk. mat. zhurn., 12:1 (2010), 53–67 | MR | Zbl

[20] Vorobev Yu. S., Shorr B. F., K teorii zakruchennykh neravnomerno nagretykh sterzhnei, Naukova dumka, Kiev, 1983, 188 pp.

[21] Timoshenko S. P., Guder Dzh., Teoriya uprugosti, Nauka, M., 1975, 575 pp.

[22] Kurbatova N. V., “Effektivnye skhemy konechno-elementnoi diskretizatsii”, Sovremennye problemy mekhaniki sploshnoi sredy, v. 2, Izd-vo YuFU, Rostov n/D., 2010, 189–193

[23] Kurbatova N. V., Chumakova E. S., “Sravnitelnyi analiz napryazhenno-deformirovannogo sostoyaniya v zadache izgiba estestvenno zakruchennogo sterzhnya”, Sovremennye problemy mekhaniki sploshnoi sredy, v. 2, Izd-vo YuFU, Rostov n/D., 2009, 129–133

[24] Birger I. A., Panovko Ya. G., Prochnost. Ustoichivost. Kolebaniya, v. 1, Mashinostroenie, M., 1968, 831 pp.