基于双变量无单元法的欧拉梁动力特性计算与分析

DYNAMIC CHARACTERISTIC CALCULATION AND ANALYSIS OF EULER BEAM BASED ON ELEMENT-FREE GALERKIN DOUBLE-VARIABLE METHOD

以广义移动最小二乘法为理论基础,将同时考虑挠度和转角双变量的无单元法运用于欧拉梁的动力特性计算与分析。以罚函数法引入位移边界,建立欧拉梁无单元法质量矩阵和刚度矩阵的计算方法。运用双变量无单元法计算了四种不同边界条件欧拉梁的自振圆频率和振型,通过与理论解、有限元解、单变量无单元解的比较,表明该法较单变量无单元法具有更高的插值精度,在各种复杂边界条件下均能获得准确的计算结果。特别是在高阶振型中,计算精度明显优于有限元解。最后,通过试算法对多项式基的阶次进行了讨论,给定了在动力计算中的合理取值。

Based on the generalized moving least square method, a new Element-Free Galerkin （EFG） double-variable approximation is applied to dynamic characteristic calculation and analysis of Euler beam. In the development of the approximation, displacement boundary conditions are imposed with penalty method, and mass matrix and stiffness matrix are created catering for the implementation of EFG. Natural fi＇equencies and natural modes of four Euler beams with different boundary conditions are calculated by double-variable EFG. Comparing the proposed approximation with theoretical solution, finite element method （FEM） and single-variable EFG, it is concluded that the proposed approximation has higher interpolation precision and applicable to complicated boundary conditions. Especially, it is more accurate than FEM in higher modes. With trial method, the order of polynomial is discussed and then its reasonable value is given.