An eigenfunction expansion-variational method based on a unit cell in analysis of a generally doubly periodic array of cracks
An eigenfunction expansion-variational method based on a unit cell in analysis of a generally doubly periodic array of cracks
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DOI：
10.1007/s00707-009-0198-8
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发表时间：
2010-02
期刊：
影响因子：
2.7
通讯作者：
P. Yan;C. Jiang
中科院分区：
文献类型：
--
作者：
P. Yan;C. Jiang
通过将位移场的拟周期性和应力应变场的周期性引入到应变能泛函中，构造了一种新的具有周期性微结构的非均匀固体单胞变分泛函.该泛函可以适应广泛的周期性结构，包括其中可能不存在单位晶胞的对称性或反对称性的情况。然后将该泛函应用于平面和反平面载荷作用下的双周期裂纹阵列问题。结合裂纹面上满足无力条件的复势函数的本征函数展开式，发展了一种基于单胞的本征函数展开-变分法。数值算例表明，该方法具有较高的精度和效率，适用范围广。揭示和讨论了裂纹对称排列时不存在的多裂纹相互作用的一些有趣现象。
A new variational functional for a unit cell of a heterogeneous solid with periodic microstructures is constructed by incorporating the quasi-periodicity of the displacement field and the periodicity of the stress and strain fields into the strain energy functional. The functional can accommodate a broad class of periodic structures including the case where symmetry or antisymmetry properties of the unit cell may not exist. Then the functional is applied to deal with a doubly periodic array of cracks under plane and anti-plane loading. By combining with the eigenfunction expansions of the complex potentials satisfying the traction-free condition on the crack surfaces, an eigenfunction expansion-variational method based on a unit cell is developed. Numerical examples are presented and compared with existing results to demonstrate the high accuracy and efficiency, and wide application scope of the present method. Some interesting phenomena of multi-crack interaction, which do not occur in the case of symmetrical arrays of cracks, are revealed and discussed.