裂纹的扩展有限元数值模拟研究  

Numerical simulation of extended finite elements of cracks

作　　者：应宗权[1] 王友元[1] 杜成斌[2] 

机构地区：[1]中交四航工程研究院有限公司,广东广州510230 [2]河海大学土木工程学院,江苏南京210098

出　　处：《水运工程》2010年第1期10-14,共5页Port & Waterway Engineering

基　　金：国家自然科学基金重点项目(50539030-1-1);国家自然科学基金项目(50779011)

摘　　要：扩展有限元方法中,结构的不连续模拟通过单位分解的方法对位移模式的局部富集来实现,这个技术可以使得裂纹的不连续性独立于结构的单元划分。阐述了富集函数的构造、支配方程的建立、数值积分方案及程序实现等。对于线弹性体裂纹的模拟,通过一个跳跃函数和二维裂纹尖端位移渐进场来考虑裂纹的不连续性和奇异性。通过编制扩展有限元程序,模拟了各向同性介质中的二维裂纹。最后通过算例的模拟结果证明了该方法的精确性和实用性。The discrete simulation of a structure is achieved by partial enrichment in displacement mode with unity partition method in extended finite element approach. This technology can make the crack discontinuity independent of the unity partition of structure. This paper describes the composition enrichment functions, establishment of governing equation, numerical integration programs and program implementation, etc. For the linear elastic body simulation of crack, the discontinuity and singularity of a crack is considered by a jump function and 2D crack-tip incremental displacement field. The 2D crack in isotropic medium is simulated by compiling the extended finite program. Finally, the simulation results of examples have proved the accuracy and practicability of this method.

关 键 词：裂纹 扩展有限元方法 数值积分 应力强度因子 

分 类 号：O242[理学—计算数学]