求解双材料裂纹结构全域应力场的扩展边界元法

Abstract

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.