扩展无网格法分析功能梯度材料断裂问题  

Enriched Meshless Analysis of Cracks in Functionally Graded Materials

作　　者：张保文[1] 马文涛[1] 黄凌霄[1] 

机构地区：[1]宁夏大学数学计算机学院,宁夏银川750021

出　　处：《安徽师范大学学报（自然科学版）》2016年第3期230-236,共7页Journal of Anhui Normal University(Natural Science)

基　　金：国家自然科学基金(51269024;41204041)

摘　　要：提出一种扩展无网格法模拟二维功能梯度材料I、II型复合断裂问题.基于单位分解思想,在EFGM近似函数中分别添加阶跃函数和奇异函数,依次表征不连续位移场和裂尖奇异应力场.结合一种不需要求解梯度材料参数的互作用积分的域形式计算了复合型应力强度因子.两个功能梯度板的数值算例验证了单位分解扩展无网格法的可行性和有效性.An enriched meshless method was presented for analysing the mixed mode I and mode II fracture problem in two-dimension functionally graded materials. Both enriched functions, including jump function and crack tip singularity function, were added in the approximation of EFGM based on partition of unity. The mixed mode stress intensity factors for cracks in functionally graded materials were numerically evaluated using the modified domain form of interaction integral. The integrand does not involve any derivatives of materials properties. The numerical results were obtained for edge and center cracks, and were found to be in good with the reference solutions for the functionally graded material crack problems.

关 键 词：功能梯度材料 EFGM 扩展无网格法 应力强度因子 

分 类 号：TB301[一般工业技术—材料科学与工程]