中文摘要：

根据弹性力学的变分原理,利用双周期问题位移场的双准周期性质和应力应变场的双周期性质,构造了双周期平面问题的单胞泛函变分表达式.然后结合针对裂纹问题的复应力函数特征展开式,发展了基于单胞模型的双周期裂纹平面问题的特征展开-变分方法.由于该方法考虑了最一般的双周期边界条件,因而能够分析一般非对称排列的双周期裂纹问题.通过结果的收敛性分析说明了该方法具有计算效率和精度都高的优点.最后,对于裂纹呈平行四边形排列的情况,分析了不同的裂纹排列对应力强度因子的影响.

英文摘要：

A variational functional for the unit cell for a doubly periodic in-plane problem is presented, based on the variational principle in elasticity in conjunction with the double quasi-periodicity of the displacement field and the double periodicity of the stress and strain fields. Then by combining with the eigenfunction expansions of the complex stress functions satisfying the traction-free conditions on the crack surfaces, an eigenfunction expansion-variational method for the unit cell model is developed. The general doubly periodic boundary conditions for a unit cell are considered, so the present method can be used to solve the general doubly periodic crack problems. The convergency analysis of the numerical results demonstrates the high efficiency and accuracy of the present method. Finally, for several general doubly periodic crack arrays, the influence of the stress intensity factors on the crack arrangement is examined.