摘要
自然单元法是一种新兴的无网格数值计算方法,但应用于裂纹问题计算时,其近似函数并不能准确反映裂纹尖端渐进应力场的奇异性,为获得足够的计算精度,需要在缝尖附近增大结点的布置密度。针对裂纹问题提出一种增强的自然单元法,将缝尖渐近位移场函数嵌入到自然单元法近似函数中,给出了增强试函数的构造方法,推导了总体刚度矩阵和荷载列阵的相关列式。应力强度因子可以作为附加未知量直接算得,也可用J积分或相互作用能量积分方法进行计算,对增强区域的选择和影响进行了分析。算例结果表明,基于增强自然单元法采用围线积分方法计算应力强度因子具有很高的精度,但直接以附加结点自由度形式计算则精度有所降低。
The natural element method（NEM） is a recently developed meshless method, but in analysis of fracture problems, the trial functions can not reflect the singular stress fields correctly. Therefore, refined array of nodes around a crack tip adequately is required to obtain sufficient accuracy. An enriched NEM formulation for fracture problems is proposed, in which the asymptotic displacement fields near crack tip are added to the NEM approximation, the construction of the enriched trial functions are pres- ented, the corresponding formulas of global stiffness matrix and load vector have been deduced. In this method, the stress intensity factors can be calculated directly as the additional unknowns, and can also be computed using the J integral or interaction integral method. In addition, the effects of different enriched regions on the solutions for stress intensity factors are discussed. Numerical results illustrate that the contour integral method in the calculation of stress intensity factors has high accuracy, while the method using the stress intensity factors as the additional unknowns produces lower accuracy.
出处
《计算力学学报》
EI
CAS
CSCD
北大核心
2010年第2期264-269,共6页
Chinese Journal of Computational Mechanics
基金
国家自然科学基金(10972072
50679022)
国家重点基础研究发展计划(2007CB714104)资助项目
关键词
固体力学
自然单元法
增强位移近似
缝尖渐近位移场
应力强度因子
solid mechanics
natural element method
enriched displacement approximation
crack tip asymptotic displacement field
stress intensity factor
