Structural Engineering and Mechanics

  • 제4권6호
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  • Pages.613-630
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  • 1996
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Use of homogenization theory to build a beam element with thermo-mechanical microscale properties

  • Schrefler, B.A. (Instituto di Scienza e Tecnica delle Costruzioni, University of Padova) ;
  • Lefik, M. (Department of Mechanics of Materials, Technical University of Lodz)
  • 발행 : 1996.11.25
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초록

The homogenization method is used to develop a beam element in space for thermo-mechanical analysis of unidirectional composites. Local stress and temperature field in the microscale are described using the function of homogenization. The global (macroscopic) behaviour of the structure is supposed to be that of a beam. Beam-type kinematical hypotheses (including independent shear rotations) are hence applied and superposed on the microdescription. A macroscopic stiffness matrix for such a beam element is then developed which contains the microscale properties of the single cell of periodicity. The presented model enables us to analyse without too much computational effort complicated composite structures such as e.g. toroidal coils of a fusion reactor. We need only a FE mesh sufficiently fine for a correct description of the local geometry of a single cell and a few of the newly developed elements for the description of the global behaviour. An unsmearing procedure gives the stress and temperature field in the different materials of a single cell.

키워드

참고문헌

  1. Bensoussan, A., Lions, J.L. and Papanicolau, G. (1976), "Asymptotic analysis for periodic structures", North-Holland, Amsterdam.
  2. Dumontet, H. (1990), "Homogeneisation et effets de bords dans les materiaux composites", (These de Dovtorat d'Etat), Universite Pierre et Marie Curie Paris 6.
  3. Ladeveze, P. (1985), Local Effects in the Analysis of Structures, P. Ladeveze Ed., Elsevier Publishers.
  4. Lefik, M. and Schrefler, B. A. "FE modelling of boundary layer correctors for composties, using the homogenization theory", Engineering Computations, 13(6), 31-42.
  5. Lefik, M. and Schrefler, B. A. (1994), "3D finite element analysis of composite beams with parallel fibres based on the homogenization theory", Computational Mechanics, 14, 2-15. https://doi.org/10.1007/BF00350153
  6. Lefik, M. and Schrefler, B.A. (1994), "Application of the homogenization method to the analysis of superconducting coils", Fusion Engineering and Design, 24, 231-255. https://doi.org/10.1016/0920-3796(94)90024-8
  7. Sanchez-Palencia, E. (1980), Non-Homogeneous Media and Vibration Theory, Berlin, Springer V.
  8. Schrefler, B.A. and Lefik, M. (1995), "F.E. Application of homogenization theory to thermoelastic analysis of composite superconducting coils for nuclear fusion device", Proceedings of IX Conference on Thermal Problems ATLANTA'95, 1183-1194.
  9. Schrefler, B.A. and Lefik, M. (1995), "Use of homogenization method to build element which capture microscale properties", Proceedings of Conf. on Educational Practice and Promotion of Computational Methods in Engineering Using Small Computers, Macao, August 1995, 177-188.
  10. Zienkiewicz, O.C. (1989), The Finite Element Method,London, McGraw-Hill.

피인용 문헌

  1. A multilevel homogenised model for superconducting strand thermomechanics vol.45, pp.4, 2005, https://doi.org/10.1016/j.cryogenics.2004.09.005
  2. Finite element linear and nonlinear, static and dynamic analysis of structural elements – an addendum – A bibliography (1996‐1999) vol.17, pp.3, 2000, https://doi.org/10.1108/02644400010324893
  3. Thermo-Mechanics of the Hierarchical Structure of ITER Superconducting Cables vol.17, pp.2, 2007, https://doi.org/10.1109/TASC.2007.897759
  4. Multi-scale computational homogenization: Trends and challenges vol.234, pp.7, 2010, https://doi.org/10.1016/j.cam.2009.08.077