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一引言用有限元法计算梁的固有振动问题,已发表了许多文献。文献[1]从变分原理出发分析了位移法有限元必须满足的连续条件和边界条件,给出了带有内节点的斜削梁高阶协调元族刚阵和质阵表达式,比较了六种算例协调元和过协调元计算结果,指出高阶协调元可提高斜削梁固有特性的计算精度。本文在此基础上提出一种高阶协调梁元族的改进方案。改进的梁元族利用多项式的待定系数作为广义内自由度参数,使得单元之间既满足c~1连续条件又不必设内节点。同时,基于这种有限元族推导了传递矩阵法公式。
INTRODUCTION Finite element method to calculate the inherent vibration of the beam, has published a lot of literature. Based on the principle of variational principle, literature [1] analyzed the continuous conditions and boundary conditions that the finite element method must satisfy for the displacement method, and presented the rigid matrix and the matrix expression of the higher-order coordination elements of the bevelled beam with internal nodes. An example is given to illustrate the computational results of the coordination element and the over-coordination element. It is pointed out that the high-order coordination element can improve the calculation accuracy of the inherent characteristics of the bevel beam. Based on this, an improved scheme of higher-order coordination beam elements is proposed. The improved beam element uses the coefficient to be determined of polynomials as the parameter of generalized internal freedom, which makes the elements not only satisfy the c ~ 1 continuous condition but also do not need to set the inner nodes. At the same time, the transfer matrix method is derived based on this finite element family.