The present work is to develop the FMBEM with quadratic elements to the analysis of 3-D linear elastic structures containing subdomains. To the numerical integration, an adaptive method with subdivision of elements is applied. The BEM formulation for perfectly bonded subdomains, in which interface traction forces are eliminated from the system of equations is implemented. The method is applied to problems of solids with spherical inclusions: a single inclusion, two interacting inclusions, many regularly distributed inclusions and randomly distributed inclusions. Different values of volume fraction of inclusions, up to 0.5 for the cubic arrangement of inclusions, and contrast in elastic properties between the matrix and inclusions, up to 1000 for the ratio of Young’s moduli of the constituents, are considered. Stresses or effective elastic constants are computed. The results are compared to analytical models and a good agreement is observed. The proposed method shows a perspective of modelling 3-D composites efficiently.

目前的工作是开发具有二次元的FMBEM，以分析包含子域的3-D线性弹性结构。对于数值积分，应用了一种将元素细分的自适应方法。实施了完美结合子域的BEM公式，其中从方程组中消除了界面牵引力。该方法适用于具有球形夹杂物的固体问题：单个夹杂物，两个相互作用的夹杂物，许多规则分布的夹杂物和随机分布的夹杂物。考虑了不同的夹杂物体积分数值，对于夹杂物的立方排列，最大为0.5，对于基质和夹杂物之间的弹性性能的对比度，对于成分的杨氏模量比，最大为1000。计算应力或有效弹性常数。将结果与分析模型进行比较，并观察到良好的一致性。所提出的方法展示了有效地建模3-D复合材料的观点。