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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 approximation space based on unit decomposition generalized finite element method is composed of unit decomposition function and local coverage function. The traditional finite element shape function is used as unit decomposition function. The definition of local coverage function does not depend on the finite element mesh. The hexagonal isoparametric hexagonal unit function is taken as the unit decomposition function, and a 16-node hexahedron generalized unit is established by using the first-order polynomial local coverage function. Based on this, the characteristics of anisotropic approximation space can be flexibly constructed by using the generalized finite element method. According to the deformation characteristics of the shell, the first-order and zero-order polynomial local coverage functions are applied to the shell normal deflection and tangential displacement respectively. The physical shell generalized unit. The calculation results show that the generalized hexagonal hexahedron and solid shell generalized elements have higher convergence rate and higher efficiency than the corresponding conventional solid elements when used in plate and shell structure analysis. Point-hexahedron generalized unit has higher solution efficiency.