一种新的计算各向异性材料裂纹尖端应力强度因子杂交元法  

Stress intensity factors near crack tip of anisotropic material with a new hybrid finite element method

作　　者：梁平英[1] 陈梦成[1] 

机构地区：[1]华东交通大学土木工程学院,江西南昌330013

出　　处：《计算力学学报》2007年第2期209-214,共6页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(10362002);江西省自然科学基金(0512003);华东交通大学校立科研基金资助(06ZKTM03);江西省道路与铁道工程重点实验室资助项目

摘　　要：利用有限元特征分析法研究了平面各向异性材料裂纹端部的奇性应力指数以及应力场和位移场的角分布函数,以此构造了一个新的裂纹尖端单元。文中利用该单元建立了研究裂纹尖端奇性场的杂交应力模型,并结合Hellinger-Reissner变分原理导出应力杂交元方程,建立了求解平面各向异性材料裂纹尖端问题的杂交元计算模型。与四节点单元相结合,由此提出了一种新的求解应力强度因子的杂交元法。最后给出了在平面应力和平面应变下求解裂纹尖端奇性场的算例。算例表明,本文所述方法不仅精度高,而且适应性强。In this paper a finite element eigen-analysis method is applied to solve the stress singularities, also is used to calculat the angular dependences of the stress and displacement fields near crack tip of anisotropic material under in-plane loading. Consequently, They are used to constructs a new singular tip element. With the tip element, a hybrid-stress finite element equation is educed combining Hellinger-Reissner principal, accordingly a hybrid-stress finite element model is developed. Combined with general four-node element around crack tip element, a new hybrid finite element method to study stress intensity factors for interfacial crack is introduced. To illustrate the efficacy of the suggested procedure, some numerical examples are presented, which are computed stress intensity factors for crack tip in anisotropic material under the conditions of in-plane stress and strain. All calculations show that present method yields more accurate results than those of the existing analytical/reference solutions, and the method can be applied to study more complex structures in engineering.

关 键 词：有限元特征分析法 各向异性 奇性应力指数 杂交元法 应力强度因子 

分 类 号：TU339[建筑科学—结构工程] O242[理学—计算数学]