以三个移动和三个转动自由度的空间直角坐标推导了空间弯曲和扭转形杆的一系列基本方程式,通过解决应变为常量和零时的位移与应变关系。建立了形杆的刚体和常应变模式.以位移为基本函数,形成了单元的有限元模型。分析了三个自由振动的例子,计算结果与实测值十分一致,证明了公式和单元矩阵的正确性。 A series of basic equations of spatial bending and torsion bar are deduced with three movements and three orthogonal coordinates of rotation degrees of freedom. By solving the relation between displacement and strain when the strain is constant and zero time. The rigid body and constant strain modes of the bar are established. The displacement is used as the basic function to form the finite element model of the unit. Three examples of free vibration are analyzed. The calculated results are in good agreement with the measured values. The correctness of the formula and the cell matrix is ​​proved.