Analysis for Beam/Bar Structures Based on Homogenization Method.
Analysis for Beam/Bar Structures Based on Homogenization Method.
复制标题
基于均匀化方法的梁/杆结构分析。
DOI：
10.1299/kikaia.67.933
复制
发表时间：
2001
期刊：
影响因子：
--
通讯作者：
N. Kumazawa
中科院分区：
文献类型：
--
作者：
H. Okada;Shutatsu Fujitani;Y. Fukui;N. Kumazawa
本文提出了一种基于有限元法的均匀化方法，用于分析受扭转、弯曲和轴向拉/压作用的梁/杆结构。梁/杆结构的详细配置被假定为周期性的。它们由重复的单位单元组成。用三维有限元模型表示单胞。将基于三维有限元模型的单元位移场、基于Euler-Bernoulli假设的梁弯曲变形位移场和基于圆杆扭转位移场叠加，得到结构内部完整的变形场。严格地说，当梁/杆结构的横截面尺寸在极限意义上接近零时，建议的公式是有效的。然而，作为近似，该理论可以应用于梁/杆结构的横截面是有限的，但与它们的长度相比是小的情况。数值算例验证了该方法的有效性。该均匀化方法不仅适用于复合材料梁/杆的分析，也适用于具有复杂内部结构的其它类型的结构，如复杂形状的孔、复杂截面形状的孔等。
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.