求解受钉传载荷含双边非对称边缘裂纹各向异性板的解析－变分方法

AN ANALYTICAL-VARIATIONAL METHOD FOR ANISOTROPIC PLATES WITH UNSYMMETRIC DOUBLE EDGE CRACKS SUBJECTED TO PIN LOADS

以单边边缘裂纹二维应力场与位移场展开式为基础，采用分区广义变分原理研究受钉传载荷含双边非对称边缘裂纹各向异性板应力强度因子。首先建立精确满足各向异性板基本微分方程和绕钉孔的合力平衡条件及位移单值条件的应力场和位移场的级数表达式，然后应用分区广义变分方法满足边界条件及子域间的交界条件并由此确定应力强度因子。在变分方程中只存在沿板边界的线积分，简化了计算程序和输入数据，且计算结果收敛迅速、准确。给出了求解非对称边缘裂纹问题的系统计算曲线。

Based upon the use of two dimensional theory of anisotropic elasticity the stress and displacement series are developed for the cracked plate subjected to pin loads.The series satisfy all basic equations,the condition of prescribed resultants and single valued condition of dis- placements at pin holes. A generalized variational principle about multi-regions is applied to consider the boundary conditions and interface conditions between subregions.Only line integra- tions exist in variational equations.Numerical studies reveal that convergent results are given by arelatively simple program which reduces data manipulation and CPU time.