基于数值流形方法的特殊孔缘单元构造及开孔板求解

采用有限元法对具有典型的开孔结构进行分析时,常常难以保证良好的单元形态,同时也难以兼顾计算效率和精度.本文采用具有两套覆盖系统的数值流形方法对此类结构开展分析,参考无限大板圆孔应力问题的理论解答,通过扩展局部逼近的基,构造了一种适用于平面圆孔问题的特殊流形单元,基于数值流形理论采用程序实现,并对不同载荷条件和几何尺寸下的平面圆孔问题进行了计算.结果 表明,相较于有限元法,本文方法在计算精度和收敛速度上均具有显著优势.上述结果也充分体现了数值流形方法在处理具有复杂几何构型的结构时的优越性,在工程结构领域具有的广阔应用前景.

A special hole edge element fitted to numerical manifold method for analyzing plates with holes

When analyzing typical structures with holes using the Finite Element Method(FEM), the inevitable reduction of mesh quality makes it difficult to achieve satisfying calculation precision and efficiency simultaneously.The Numerical Manifold Method (NMM) with two sets of cover systems was used for the analysis of such structures, where special hole-edge manifold elements were applied.These elements were constructed by extending the base of local approximation, referring to the theoretical solution of the benchmark circular hole stress concentration problem.Calculation results of numerical examples with different loads and geometrical characteristics suggest that NMM with the special hole-edge elements achieves higher accuracy and better convergence compared with the FEM, which indicates the advantages of the NMM when analyzing geometrically complex structures, as well as its broad application prospects in the relevant fields.