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- 2015
非均质复合材料力学性能的确定性多尺度计算方法
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Abstract:
针对具有多尺度特性的非均质复合材料进行结构强度分析,提出了一种确定性多尺度计算方法――有限细胞法(FCM)。该方法通过矩阵凝聚和插值近似得到粗网格的刚度矩阵,在计算得到粗网格解后,通过回代技术可获得全域细网格解。为验证FCM的计算精度和计算效率,构造了多个数值算例,并与理论和有限元(FEM)结果进行了对比,结果发现:相对于FEM,FCM可显著扩大计算规模,提高计算速度,且易于并行;相对于其他多尺度计算方法,FCM在构造粗网格刚度矩阵过程中无需引入微观边界条件,计算精度高,易于降尺度计算。因此,FCM是分析复合材料结构强度的一种有效的多尺度算法,同时该方法易于推广至多尺度的非线性结构分析、热分析、地下水渗流分析等领域。
For the strength analysis of heterogeneous materials in elasticity, a deterministic multiscale calculation method, finite cell method (FCM), is presented. The condensation and interpolation technique are adopted to obtain the coarse element stiffness matrix, then the original problem can be solved in coarse？？scale, and the fine？？scale solution can be sought out by back substitution. The comparison with analytic method and finite element method (FEM) on several numerical examples indicates that FCM enables to significantly expand computational scale and greatly improve computing rate. In FCM, the artificial boundary conditions are unnecessary for constructing macroscopic meshes, and the downscaled computing can be easily performed. FCM is also feasible for non？？linear multiscale structure analysis, thermal analysis and porous flow analysis
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