基于蜂窝数值流形元的静弹性力学问题求解

Investigation of Elastostatic Problems by the Numerical Manifold Method on Honeycomb Elements

数值流形方法是一种求解固体力学问题的新颖高效数值方法,而n边形单元(n>4)则具有网格划分灵活、能高效进行材料分析等优点。本文利用数值流形方法中数学覆盖系统独立于物理域的优势,基于正六边形数学单元(蜂窝单元)求解二维静弹性力学问题。对典型问题的分析结果表明:在同等情况下,采用正六边形单元的求解精度与正四边形单元的相当,但明显高于正三角形单元上的精度。

The numerical manifold method（NMM） is widely applied to solve both continuous and discontinuous problems in solid mechanics with high efficiency.At the same time,the n-sided elements（n4） are also very attractive due to their greater flexibility in meshing and higher efficiency in materials modeling,compared with the frequently used triangular and quadrilateral elements.To take advantage of the special feature that the mathematical cover system is independent of the physical domain in the NMM,in the present paper,the NMM is applied to solve 2-D elastostatic problems based on regular hexagonal（honeycomb） elements.Our results show that the accuracy on hexagonal elements is very close to that on regular quadrilateral elements but much higher than that on regular triangular elements.