混凝土断裂力学虚拟裂缝模型的半解析有限元法  

Semi-Analytical Finite Element Method for Fictitious Crack Model in Fracture Mechanics of Concrete

作　　者：王承强[1] 郑长良[1] 

机构地区：[1]大连理工大学工程力学系,大连116023

出　　处：《应用数学和力学》2004年第11期1157-1162,共6页Applied Mathematics and Mechanics

基　　金：国家教育部博士点专项基金资助项目(20010141024);教育部留学回国人员科研启动基金资助项目(教外司留[2001]498);辽宁省博士启动基金资助项目(2001102093);2001年国家高技术研究发展计划资助项目(2001AA412220)

摘　　要：　利用平面扇形域哈密顿体系的方程,通过分离变量法及共轭辛本征函数向量展开法,以解析的方法推导出基于混凝土断裂力学中虚拟裂缝模型的平面裂纹解析元列式·　将该解析元与有限元相结合,构成半解析的有限元法,可求解任意几何形状和荷载混凝土平面裂纹的虚拟裂缝模型计算问题·　数值计算结果表明方法对该类问题的求解是十分有效的。Based on the Hamiltonian governing equations of plane elasticity for sectorial domain, the variable separation and eigenfunction expansion techniques were employed to develop a novel analytical finite element for the fictitious crack model in fracture mechanics of concrete. The new analytical element can be implemented into FEM program systems to solve fictitious crack propagation problems for concrete cracked plates with arbitrary shapes and loads. Numerical results indicate that the method is more efficient and accurate than ordinary finite element method.

关 键 词：半解析有限元法 平面裂纹 展开法 本征函数 哈密顿体系 分离变量法 共轭 混凝土 荷载 断裂力学 

分 类 号：O346.1[理学—固体力学] O175[理学—力学]