Local enrichment of the finite cell method for problems with material interfaces
Local enrichment of the finite cell method for problems with material interfaces
复制标题
DOI：
10.1007/s00466-013-0853-8
复制
发表时间：
2013-10
影响因子：
4.1
通讯作者：
Meysam Joulaian;A. Düster
中科院分区：
文献类型：
--
作者：
Meysam Joulaian;A. Düster
本文提出了一种有效的，分层高阶富集方法的有限单元法应用于固体力学问题的不连续性和奇异性。与标准的扩展有限元方法相比，其中新的自由度被引入到位于富集区的所有有限元中，我们定义了所谓的叠加网格上的富集，该叠加网格叠加在基础网格上。在基本网格上采用有限单元法进行逼近，在覆盖网格上采用hp-d方法进行层次扩展。我们提出了两种不同的策略来定义叠加叠加网格上的富集。在第一种方法中，富集是基于局部的，p-orhp-细化，利用有限元法上的覆盖网格。或者，丰富的构造通过划分的统一方法引入精心选择的富集功能，适合手头的问题。我们的研究结果表明，该方法提高了有限单元法的精度显着，只有最小数量的额外的自由度。在本文中，我们将集中在与材料接口的例子，虽然该方法也可以应用到涉及强不连续性和奇异性的问题。精确的应力分布和指数收敛速度是该方法的两个显著特点。由于分层的方法，它铺平了道路，使用不同的方法近似的基础和覆盖网格，因此允许多尺度问题得到解决。
This paper proposes an efficient, hierarchical high-order enrichment approach for the finite cell method applied to problems of solid mechanics involving discontinuities and singularities. In contrast to the standard extended finite element method, where new degrees of freedom are introduced for all finite elements located in the enrichment zone, we define the enrichment on a so-called overlay mesh which is superimposed over the base mesh. The approximation on the base mesh is obtained by means of the finite cell method where thehp-dmethod is employed to introduce the hierarchical extension on the overlay mesh. We present two different strategies for defining the enrichment on the superimposed overlay mesh. In the first approach, the enrichment is based on a localh-,p- orhp-refinement utilizing the finite element method on the overlay mesh. Alternatively, the enrichment is constructed by means of the partition of unity method introducing carefully selected enrichment functions suitable for the problem at hand. Our results reveal that the proposed method improves the accuracy of the finite cell method significantly with only a minimum number of additional degrees of freedom. In this paper we will focus on examples with material interfaces although the method can also be applied to problems involving strong discontinuities and singularities. Accurate stress distribution and an exponential rate of convergence are the two striking characteristics of the proposed method. Due to the hierarchical approach it paves the way to using different approaches for the approximation on the base and the overlay mesh and accordingly allows multiscale problems to be addressed as well.