一种等效的三边形杆件单元

An equivalent triangle plane bar element

基于有限元思想,根据三节点三角形单元与三角形平面杆件单元在受到同样荷载列向量的条件下位移等效原则,构造出一种更为简单适用的等效三角形杆件单元,使二维结构用一维单元进行分析.由于单元的推导不是根据微元体单元应力、应变等效,而是从节点位移等效的这一思路出发,使得本研究单元较以前的等效铰结桁架单元可以满足结构有限元划分单元时对矩形单元的要求.同时截面计算公式中包含了泊松比这一体现材料特性的参数,因而公式更加具有普遍意义.运用本研究方法对钢筋混凝土简支梁及悬臂梁进行计算分析,并将其计算结果与ANSYS计算结果进行比较.研究结果表明,本研究所推导的等效三边形杆件单元计算精度良好,计算结果可靠,可以满足工程应用需要.

Based on the inite element method, a new equivalent triangle element , which is according to the principle of equivalent displacement under the same load between bar ele- ment and shell unit with 3-node, is proposed in this paper. The two dimensional structures are analysed by using one-Dimension elements. Because the base theory is different with the principle of equivalent stress/strain between plane bar element（or space bar element） and micro unit, it is feasible to establish triangle element in analyzing plane stress problems by this new model. A concrete and RC simple beam and a RC cantilever beam models are ana- lyzed with this method and ANSYS. The calculation results of both methods are consistent too. The results showed that the proposed method has good analytical precition and reliable results, which can be used in engineering.