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复合材料的研究中经常遇到具有周期孔洞结构的材料,由于区域的小周期性及剧烈振荡性,用传统的有限元计算方法来计算这些材料对应的问题时需要大量的计算机存储空间及计算时间.对这类材料的热力耦合问题给出了一种新型的高阶双尺度渐近解,得到了对应的均匀化常数、均匀化方程及对应的有限元算法.数值算例表明,周期单胞的局部结构对局部应力与应变有较大的影响.算法对数值模拟这类材料的力学行为是高效和可行的.
Due to the small periodicity and violent oscillation of the region, the traditional finite element calculation method to calculate the corresponding problems of these materials requires a large amount of computer storage space and calculation time A new type of high - order two - scale asymptotic solution is given for the thermodynamic coupling problem of these materials, and the corresponding uniformization constant, the homogenization equation and the corresponding finite element method are obtained. Numerical examples show that the periodic unit cell The local structure of the local stress and strain have a greater impact.The algorithm for numerical simulation of the mechanical behavior of such materials is efficient and feasible.