Analysis for Beam/Bar Structures Based on Homogenization Method.

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  • 均質化法によるはり・軸構造の解析
  • キンシツカホウ ニ ヨル ハリ ジク コウゾウ ノ カイセキ

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A homogenization method based on the finite element method for beam/bar structures subject to torsion, bending and axial stretch/compression, is derived. The detailed configurations of the beam/bar structures are assumed to be periodic. They are composed of repeating unit cells. The unit cell is represented by three dimensional finite element model. Displacement fields based on the three dimensional finite element model for the unit cell and those based on Euler-Bernoulli hypotheses for the bending deformation of beam and also based on the torsion of circular bar, are superposed, representing a complete deformation field within the structures. Proposed formulation is, in rigorously speaking, valid when the size of the cross section of the beam/bar structure approaches zero in limiting sense. However, as an approximation, the theory can be applied to the case that the cross section of the beam/bar structure is finite but is small compared with their length. Some numerical examples are presented to discuss the validity of the proposed method. The proposed homogenization technique can be applied to analyses for composite beam/bar and also for other types of structures having complex internal structures, such as holes of complex shape, complex cross sectional shape, etc.

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