求解双材料裂纹结构全域应力场的扩展边界元法

Computation of Total Stress Fields for Cracked Bi-Material Structures With the Extended Boundary Element Method

在线弹性理论中,复合材料裂纹尖端具有多重应力奇异性,常规数值方法不易求解.该文建立的扩展边界元法(XBEM)对围绕尖端区域位移函数采用自尖端径向距离r的渐近级数展开式表达,其幅值系数作为基本未知量,而尖端外部区域采用常规边界元法离散方程.两方程联立求解可获得裂纹结构完整的位移和应力场.对两相材料裂纹结构尖端的两个材料域分别采用合理的应力特征对,然后对其进行计算,通过计算结果的对比分析,表明了扩展边界元法求解两相材料裂纹结构全域应力场的准确性和有效性.

According to the theory of linear elasticity,the conventional numerical methods are difficult to calculate the singular stress fields of cracked bi-material structures. An extended boundary element method ( XBEM) was proposed to calculate the singular stress fields near crack tips. Firstly,a small sector around the crack tip was removed from the cracked structure. The displacement and stress components in the small sector were expressed as asymptotic series expansions with respect to the radial coordinate from the tip. The amplitude coefficients in the asymptotic series expansions were taken as the basic unknowns. Secondly,the boundary element method was used to analyze the cracked structure without the small sector. Consequently,the complete displacement and stress fields of the cracked structure were solved through combination of the boundary element analysis and the asymptotic series expansions near the tip. For the 2 domains near the crack tip of a bonded bi-material,reasonable terms shall be chosen in the asymptotic series expansions respectively. The computation results show the accuracy and effectiveness of the XBEM for determining the stress fields of the cracked bi-material structures.