A novel hybrid finite element analysis of inplane singular elastic field around inclusion corners in elastic media
A novel hybrid finite element analysis of inplane singular elastic field around inclusion corners in elastic media
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DOI：
10.1016/j.ijsolstr.2008.08.030
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发表时间：
2009-06
影响因子：
3.6
通讯作者：
Meng-Cheng Chen;X. Ping
中科院分区：
文献类型：
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作者：
Meng-Cheng Chen;X. Ping
本文用特别混合应力有限元法研究了弹性介质中包含角的面内奇异弹性场问题。首先采用基于一维有限元法的特征分析方法，确定了反映夹杂角周围弹性行为的应力场和位移场的奇异阶次和角依赖性。这些数值特征解随后被用来建立一个超级单元来模拟包含角周围的弹性行为。最后，将超单元与标准的四节点混合应力单元结合，建立了一种用于夹杂角局部奇异应力场分析的混合应力有限元方法。奇异应力场由包含角处定义的广义应力强度因子表示。采用特别有限元法研究了纵向拉伸作用下各向同性材料中单个矩形或菱形夹杂的问题。与已有的数值计算结果对比表明，该方法是一种有效的网格减少方法，可以得到精确的近场应力分布。作为应用，将现有的特设有限元方法推广到讨论各向异性材料中单个矩形或菱形夹杂的面内奇异弹性场问题，以及各向同性材料中两个相互作用的矩形夹杂的面内奇异弹性场问题。在数值分析中，系统地计算了受拉剪作用的板中一个或两个夹杂物在不同材料类型、刚度比、形状和间距位置下的角部广义应力强度因子。
This paper deals with the inplane singular elastic field problems of inclusion corners in elastic media by an ad hoc hybrid-stress finite element method. A one-dimensional finite element method-based eigenanalysis is first applied to determine the order of singularity and the angular dependence of the stress and displacement field, which reflects elastic behavior around an inclusion corner. These numerical eigensolutions are subsequently used to develop a super element that simulates the elastic behavior around the inclusion corner. The super element is finally incorporated with standard four-node hybrid-stress elements to constitute an ad hoc hybrid-stress finite element method for the analysis of local singular stress fields arising from inclusion corners. The singular stress field is expressed by generalized stress intensity factors defined at the inclusion corner. The ad hoc finite element method is used to investigate the problem of a single rectangular or diamond inclusion in isotropic materials under longitudinal tension. Comparison with available numerical results shows the present method is an efficient mesh reducer and yields accurate stress distribution in the near-field region. As applications, the present ad hoc finite element method is extended to discuss the inplane singular elastic field problems of a single rectangular or diamond inclusion in anisotropic materials and of two interacting rectangular inclusions in isotropic materials. In the numerical analysis, the generalized stress intensity factors at the inclusion corner are systematically calculated for various material type, stiffness ratio, shape and spacing position of one or two inclusions in a plate subjected to tension and shear loadings.