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Section Mechanics
Title Principles of flexible body general dynamic equations derivation based on the Craig-Bampton model and of their practically significant approximations
Author(-s) Yudakov A.A.a
Affiliations ZAO (Close Corporation) “Avtomekhanika’’a
Abstract In the article dynamic equations of motion of flexible bodies' large displacement within a multibody system with small deformations are given. In the process of derivation finite element method (FEM) and the Craig-Bampton method of FEM model's matrices reduction are used. No additional approximations are involved, thus obtaining the most general equations in given problem definition. Analysis of difficulties arising in practical using of the derived general dynamic equations is conducted, and ways to overcome those are suggested. Modified equations derivation using more general approximation than is assumed in literature is presented. An example of derived flexible structures' dynamic equations software realization is given.
Keywords flexible body, finite element method, Craig-Bampton model, modal matrix, dynamic equations, constraint equations, multibody system
UDC 539.3
MSC 74H10, 70E55
DOI 10.20537/vm120312
Received 28 April 2012
Language Russian
Citation Yudakov A.A. Principles of flexible body general dynamic equations derivation based on the Craig-Bampton model and of their practically significant approximations, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2012, issue 3, pp. 126-140.
  1. Obraztsov I.F., Savel'ev L.M., Khazanov Kh.S. Metod konechnykh elementov v zadachakh stroitel'noi mekhaniki letatel'nykh apparatov (Finite element method in the problems of aircraft structural mechanics), Moscow: Vysshaya Shkola, 1985, 392 p.
  2. Zenkevich O. Metod konechnykh elementov v tekhnike (Finite element method in engineering), Moscow: Mir, 1975, 542 p.
  3. Bathe K.-J., Wilson E.L. Numerical methods in finite element analysis, New Jersey: Prentice-Hall, 1976, 528 p. Translated under the title Chislennye metody analiza i metod konechnykh elementov, Moscow: Stroiizdat, 1982, 448 p.
  4. Shabana A.A. An absolute nodal coordinate formulation for the large rotation and large deformation analysis of flexible bodies, Techn. Rep. No. MBS96-1-UIC, Dept. of Mech. Eng., Univ. of Illinois at Chicago, 1996.
  5. Mikheev G.V. Computer simulation of rigid and flexible multibody system dynamics with small deformations, Cand. Sci. (Eng.) Dissertation, Bryansk, 2004, 153 p.
  6. MSC.Adams/Flex software documentation.\&id=DOC10098\&cat=1VMO50\&actp=LIST.
  7. Yudakov A.A. General equations of flexible bodies motion, based on finite element method and Craig-Bampton model, High Technologies, Education, Industry: Trans. Of XI Int. Sci.-Pract. Conf., Saint Petersburg State University, St. Petersburg, 2011, vol. 4, pp. 135-142.
  8. Boikov V.G., Yudakov A.A. Simulation of rigid and flexible multibody system dynamics with EULER software, Inform. Tekhn. Vych. Sist., 2011, no. 1, pp. 42-52.
  9. Craig R.R., Bampton M.C. Coupling of substructures for dynamic analysis, AIAA Journal, 1968, vol. 6, no. 7, pp. 1313-1319.
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