Structural Engineering and Mechanics

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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)
  • Published : 1996.11.25
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Abstract

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.

Keywords

References

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  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