2节点6自由度直梁单元

利用构造形函数的方法,得到了2节点6自由度直梁单元形函数表达式,运用变分原理,对梁单元的总势能进行变分导出梁单元的刚度矩阵和节点荷载列阵.以集中荷载作用下的Winkler基础梁为例,分别用2节点4自由度和2节点6自由度梁单元的有限元法计算了梁中点的位移和截面弯矩,计算结果表明:在相同精度的条件下,用2节点6自由度梁单元的有限元法有利于提高计算效率.图4,表1,参12.

A straight beam element of two-node with six degrees of freedom

The formulations of the shape functions of a straight beam element of two-node with six degrees of freedom are presented by using constructing function method.The stiffness matrix and load column vector of the beam element are derived from the first variation of the total potential energy of the beam element by means of variational principle.Winkler foundation beam under a concentrated force are taken as an example,the displacement and bending moment of cross-section at mid-point of beam are obtained by the finite element method using two-node beam element with four degrees of freedom and with six degrees of freedom,respectively.The results of the numerical example show,under the condition of the same precision,that the calculation efficiency can be increased by the finite element method using two-node beam element with six degrees of freedom.4figs.,1tab.,12refs.