杆的加模态式有限单元法

为了提高杆单元精度和降低自由度，将静态有限单元线性特征值问题和动态有限单元高精度的优点有机的结合起来形成一种高精度的动力有限单元法，将杆元固有振动方程分解为满足单元边界条件的平衡方程和固支边界条件的振动方程两部分，前者的解即静态元的位移函数，后者的解为为本方法添加部分，由此得出的有限单元法只对静态元刚度阵和质量阵做添加式修改，求解过程不变，理论和算例均表明其有效性。

Adding Mode Finite Element Method for Bars

In order to improve the precision and to decrease the degree of freedom, the free vibration differential equation of the bar element is decomposed to two. One is that of equilibrium satisfying the boundary of the element and solution of which is the displacement function of the static method. The other is that of free vibration of the fixed support element and the solution of which is the adding part of the new method. Consequently, the procedure of the new method, the adding mode finite element method for bars, is the same as the static one and its advantages includes both the linear eigenproblem of the static method and the precision of the dynamic method. So it is a simple, convenient finite element method with high precision.