尖锐夹杂角端部局部应力场杂交有限元分析  

A Hybrid FEM Analysis of Singular Stress Fields Around a Sharp Inclusion Corner

作　　者：平学成[1] 陈梦成[2] 

机构地区：[1]华东交通大学机电工程学院,江西南昌330013 [2]华东交通大学土木建筑学院,江西南昌330013

出　　处：《力学季刊》2010年第1期138-144,共7页Chinese Quarterly of Mechanics

基　　金：国家自然基金资助项目(10662004;10362002);江西省自然基金资助项目(2007GZW0862)

摘　　要：本文首先利用作者曾提出的一维有限元特征分析方法计算所得到的尖锐夹杂角端部应力奇异指数和奇异应力场、位移场角分布函数,并依据Hellinger-Reissner原理,开发出了一个特殊的、能够反映夹杂角端部局部弹性现象的n结点多边形超级角端部单元,然后将该超级单元与标准的4结点杂交应力单元耦合在一起构建了一种分析异形夹杂角端部奇异弹性场的新型特殊杂交应力有限元方法。文中给出了两个应用算例,算例结果表明:本文方法不仅使用单元少、计算结果精度高,而且适用范围广,可拓展应用于分析复合材料微结构组织与力学行为关系。A super n-noded polygonal element was first developed to simulate local elastic behavior around an inclusion corner by one-dimensional finite element method based on the eigen analysis and Hellinger-Reisnner principle. The super element was 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. Two numerical examples were finally given. Comaprison with available numerical results shows that the present method is an efficient mesh reducer and yields accurate stress distribution in the near-field region. Versatility and applicability of the developed method are also demonstrated for solving mechanical behavior of microstructures in composite materials or other nanomechanical problems.

关 键 词：夹杂角端部 应力奇异性 广义应力强度因子 杂交应力有限元 

分 类 号：O346.1[理学—固体力学]