基于单位分解法的实体壳广义单元模型

A SOLID-SHELL ELEMENT OF PARTITION OF UNITY-BASED GENERALIZED FEM

基于单位分解的广义有限元法的逼近空间由单位分解函数和局部覆盖函数构成,采用传统有限元形函数作为单位分解函数,其局部覆盖函数的定义不依赖于有限元网格。以十六结点六面体等参单元形函数作为单位分解函数,采用一阶多项式局部覆盖函数建立了十六结点六面体广义单元。在此基础上利用广义有限元法可以灵活构造各向异性逼近空间的特点,根据薄壳的变形特性,对壳体法向挠度和切向位移分别采用一阶和零阶多项式局部覆盖函数,构造了实体薄壳广义单元。计算结果表明:十六结点六面体广义单元和实体薄壳广义单元用于板壳结构分析时具有比相应的常规实体单元更高的收敛性和求解效率,且实体薄壳广义单元比十六结点六面体广义单元具有更高的求解效率。

The approximate space of partition of unity based finite element method was composed of the partition of unity function and local cover function. The shape function of traditional finite element method was used as the partition of unity and a mesh independent local cover function was constructed. Based on the partition unity of traditional sixteen-node hexahedron isoparametric element shape function and local cover function of the first order polynomial, a generalized sixteen-node hexahedron element is developed. By utilizing the potential of construction anisotropic approximate space of generalized finite element method, a generalized solid-thin shell element is devised. Based on the anisotropic deformation characteristic of thin shell, first and zeroth order polynomial local cover function are applied to capture normal and tangent displacement respectively. Examples show that the generalized sixteen-node hexahedron element and the generalized solid-thin shell element perform better than traditional element in terms of convergence and efficiency and the generalized solid-thin shell element is more efficient than the generalized sixteen-node hexahedron element.