单位分解增强自然单元法计算应力强度因子  

COMPUTING STRESS INTENSITY FACTOR USING PARTITION OF UNITY ENRICHED NATURAL ELEMENT METHOD

作　　者：江涛[1,2] 章青[1] 

机构地区：[1]河海大学工程力学系,南京210098 [2]安徽工业大学土木工程系,马鞍山243000

出　　处：《工程力学》2009年第6期52-57,64,共7页Engineering Mechanics

基　　金：国家自然科学基金项目(50679022);国家重点基础研究发展计划项目(2007CB714104)

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附近应力场的奇异性,需要在缝尖附近增大结点布置密度以获得一定的计算精度。在单位分解框架下将缝尖渐近位移场函数嵌入到自然单元法近似函数中,应用伽辽金过程获得平衡方程的离散线性方程,用相互作用能量积分方法计算了混合模式裂纹的应力强度因子。算例分析表明:单位分解增强自然单元法可以方便地处理裂纹问题,在不增加结点布置密度的情况下可有效提高应力强度因子的计算精度。The natural element method （NEM） is a recently developed meshless method, but in the analysis of fracture problems, the trial functions are not able to reflect the singular stress fields correctly, thusly the refined array of nodes around a crack tip adequately is required to obtain sufficient accuracy. A new method is proposed in this article, the near-tip asymptotic displacement fanctions are added to the NEM approximation using the framework of partition of unity, and the enriched approximation will be used in Galerkin procedure to obtain the linear discrete system of equilibriam differential equations. The mixed-mode stress intensity factors are evaluated by the interaction integral method. Numerical simulations illustrate that proposed technique can deal with problems containing cracks easily, and can increase accuracy compared with the non-enriched natural element method in the same discretization of nodes.

关 键 词：固体力学 自然单元法 单位分解 缝尖渐近位移场 应力强度因子 无网格法 

分 类 号：O302[理学—力学]