In this paper, formulations for asymptotic homogenization method based on the boundary element method (BEM) are presented for the estimations for effective parameters of unidirectional fiber reinforced composites in the 2D plane strain case. The boundaries are discretized by shape functions of non-uniform rational B-splines (NURBS) according to the features of isogeometric analysis and the related isogeometric boundary element method is established. The strongly and weakly singular integrals in the boundary integral equations are precisely calculated in direct schemes. Comprehensive comparisons for the obtained effective parameters by the current method are conducted with the existing ones by conventional BEM and the ones by finite element method (FEM). It is found that the estimations in present work are more accurate than the ones by conventional BEM with fewer control points and are also more accurate than the ones by FEM for fibers with more complex geometry. The outperformance of the current method shows competitive potentials in homogenization for the real 3D composites.

中文翻译：

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基于等几何边界元法的单向纤维增强复合材料有效参数的渐近均质化


本文提出了基于边界元法 （BEM） 的渐近均质法公式，用于估计二维平面应变情况下单向纤维增强复合材料的有效参数。根据等几何分析的特点，通过非均匀有理 B 样条曲线 （NURBS） 的形状函数对边界进行离散化，并建立了相关的等几何边界元方法。边界积分方程中的强奇异积分和弱奇异积分在直接方案中精确计算。将现有方法获得的有效参数与常规边界元法和有限元法 （FEM） 获得的有效参数进行了综合比较。研究发现，目前工作中的估计比传统边界元法的估计更准确，控制点较少，并且对于具有更复杂几何形状的纤维，也比有限元法的估计更准确。当前方法的优异性能显示了真实 3D 复合材料的均质化方面的竞争潜力。