中文摘要：

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．

英文摘要：

The problems of composite structures containing small periodic perforated configurations are often encountered in the development of composite materials. These structures often consist of material with very fine micro-structures and vary sharply within a very small periodic domain. The traditional simulation of these structures involving multi-scale is very difficult because of the requirement for a tremendous amount of computer memory and CPU running time. The two-scale formal asymptotic expansions of the increment of temperature and the displacement for the structure with small periodic perforated configuration of composite material are given. The two-scale finite element algorithm is described, and simple numerical results are evaluated by two-scale finite element computational method. The numerical results show that the basic configuration and the increment of temperature strongly affect local strains and local stresses inside basic cell. A new effective numerical method is presented for thermoelastic problem in a periodic perforated domain.