【作者】 吴世平； 梁军； 杜善义；

【Author】 WU Shiping, LIANG Jun, DU Shanyi (Center for Composite Materials and Structures. Harbin Institute of Technology, Harbin 150001, China)

【机构】 哈尔滨工业大学复合材料与结构研究所；

【摘要】 基于均匀化理论建立了复合材料线弹性问题的双尺度渐近分析方法,其实质就是通过宏观结构和非均质的周期细观结构来共同描述原结构。所有的力学量将表示成宏观尺度x和细观尺度y的函数,通过小参数ε展开,将原弹性力学问题转化为宏观均匀场u0(x)问题和单胞上的特征位移xα1(y),xα1α2(y)问题。由展开式得到了弹性力学问题的高阶位移场,最先得出了一价应力场,其结果反映出了由于材料不均匀性引起的应力的局部涨落。最后通过算例和有限元进行了比较,说明了此方法的有效性和优越性。更多还原

【Abstract】 A two-scale asymptotic analysis method of the linear problem for periodic composites is presented based on the homogenization theory. The previous composite structures have been described by a homogeneous problem and a periodical heterogeneous microstructure. All physical quantities are functions of macroscopic coordinate x and meso-microscopic coordinate y. The original problem is transformed into macroscopic homogeneous field u0(x) and the characteristic displacement xα1 (y) ,xα1α2 (y)on the cell by the expansion of a small parameter. The high order displacements are determined; moreover the method is first applied to calculate the first order stress field and the obtained results show the stress oscillating caused by the heterogeneous materials. Finally, the results are compared with finite element calculation, therefore the method can be proved feasible and has superiority.更多还原