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严鹏 蒋持平. 双周期平面裂纹问题的特征展开-变分方法[J]. 力学学报, 2009, 41(5): 681-687. DOI: 10.6052/0459-1879-2009-5-2008-117
引用本文: 严鹏 蒋持平. 双周期平面裂纹问题的特征展开-变分方法[J]. 力学学报, 2009, 41(5): 681-687. DOI: 10.6052/0459-1879-2009-5-2008-117
Peng YAN, Chiping Jiang. Analysis of doubly periodic in-plane cracks using the eigenfunction expansion-variational method[J]. Chinese Journal of Theoretical and Applied Mechanics, 2009, 41(5): 681-687. DOI: 10.6052/0459-1879-2009-5-2008-117
Citation: Peng YAN, Chiping Jiang. Analysis of doubly periodic in-plane cracks using the eigenfunction expansion-variational method[J]. Chinese Journal of Theoretical and Applied Mechanics, 2009, 41(5): 681-687. DOI: 10.6052/0459-1879-2009-5-2008-117

双周期平面裂纹问题的特征展开-变分方法

Analysis of doubly periodic in-plane cracks using the eigenfunction expansion-variational method

  • 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.

     

    Abstract: A variational functional for the unit cell for a doublyperiodic in-plane problem is presented, based on the variational principlein elasticity in conjunction with the double quasi-periodicity of thedisplacement field and the double periodicity of the stress and strainfields. Then by combining with the eigenfunction expansions of the complexstress functions satisfying the traction-free conditions on the cracksurfaces, an eigenfunction expansion-variational method for the unit cellmodel is developed. The general doubly periodic boundary conditions for aunit cell are considered, so the present method can be used to solve thegeneral doubly periodic crack problems. The convergency analysis of thenumerical results demonstrates the high efficiency and accuracy of thepresent method. Finally, for several general doubly periodic crack arrays,the influence of the stress intensity factors on the crack arrangement isexamined.

     

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