基于Kirchhoff板中裂纹尖端辛本征解的有限元应力恢复方法

对于含穿透裂纹的板结构，裂纹尖端应力场及应力强度因子的计算精度对评估板的安全性具有非常重要的影响。基于含裂纹Kirchhoff板弯曲问题中裂纹尖端场的辛本征解析解，该文提出了一个提高裂纹尖端应力场计算精度的有限元应力恢复方法。首先利用常规有限元程序对含裂纹板弯曲问题进行分析，得到裂纹尖端附近的单元节点位移；然后根据节点位移确定辛本征解中的待定系数，得到裂纹尖端附近应力场的显式表达式。数值结果表明，该方法给出的应力分析精度得到较大提高，并具有良好的数值稳定性。

A STRESS RECOVERY METHOD FOR CRACKS IN KIRCHHOFF PLATE BASED ON THE SYMPLECTIC EIGENSOLUTIONS NEAR THE CRACK TIPS

For a plate structure with through cracks, the calculation accuracy of the stress field and the stress intensity factor near the crack tips has important influence on the safety evaluation of the plate. Based on the analytical symplectic eigen-solutions of the crack tip field in the Kirchhoff plate bending problem with cracks, a finite element stress recovery method is proposed to improve the calculation accuracy of the stress field near the crack tips. Firstly, the bending problem of the cracked plate is analyzed by using the conventional finite element program, and the nodal displacements near the crack tip are obtained. Secondly, the undetermined coefficients in the symplectic eigen-solutions are determined by using nodal displacements, and the explicit expression of the stress field near the crack tip is obtained. The numerical results show that the present approach can present the stress results with more precision and has good numerical stability.