Homogenization-based finite element analysis of unidirectional composites by classical and multiresolutional techniques
Homogenization-based finite element analysis of unidirectional composites by classical and multiresolutional techniques
复制标题
DOI：
10.1016/j.cma.2004.07.030
复制
发表时间：
2005-01-01
影响因子：
7.2
通讯作者：
Kaminski, M
中科院分区：
文献类型：
--
作者：
Kaminski, M
使用均匀化技术和有限元法对多分辨率周期性非均匀介质中的单向瞬态问题的计算研究记录如下。这种均匀化方法，是经典的两尺度渐近方法的扩展，并基于小波表示的复合材料参数，这里被用来计算有效的材料参数的复合材料。这种方法的效率进行了比较，对渐近均匀化技术和简单的空间平均的材料性能使用有限元解的一些瞬态传热和自由振动问题。另一方面，与复合材料的材料参数的多分辨率分解得到的解决方案的比较也。数值结果表明，均匀化的参数产生的新方法是有界的空间平均值和渐近方法的结果，这一结果也是有效的周期性和简支组合梁的特征值。提出的多分辨率均匀化似乎是特别有效的情况下，在结构中的周期性细胞的数量较少，而细胞的数量增加需要应用的渐近均匀化方法。进一步的计算研究是必要的，在这方面，但应用多分辨率技术是自然的，因为复合材料的多尺度特性。此外，该方法在一般符号有限元程序的实现中可能是非常有效的。(c)2004 Elsevier B.V.保留所有权利。
Computational studies of unidirectional transient problems in multiresolutional periodic heterogeneous media using homogenization technique and the finite element method are documented below. This homogenization method, being the extension of the classical two-scale asymptotic approach and based on the wavelet representation for composite parameters, is used here to calculate effective material parameters of a composite. Efficiency of this method is compared against asymptotic homogenization technique and simple spatial averaging of material properties using the FEM solution for some transient heat transfer and free vibration problems. On the other hand, a comparison with the solutions obtained for a multiresolutional decomposition of material parameters for composites is also made. Numerical results show that the homogenized parameters resulting from the new approach are bounded by spatial averages and by asymptotic method results; this result is valid also for the eigenvalues of a periodic and simply supported composite beam. The multiresolutional homogenization proposed appears to be especially efficient in case of smaller numbers of periodicity cells in the structure, while increased number of cells needs application of an asymptotic homogenization method. Further computational studies are necessary in this area, but the application of the multiresolutional technique is natural because of multiscale character of composites. Moreover, this method may be very efficient in common symbolic-FEM programs implementation. (c) 2004 Elsevier B.V. All rights reserved.