双锥型圆钢管的单元刚度矩阵及修正系数

Element stiffness matrix and modified coefficients for circular steel tubes with tapered ends

本文采用传递矩阵法推导了双锥型圆钢管单元的空间弹性刚度矩阵。首先简略阐述了传递矩阵法的基本原理,推导了等截面圆钢管和锥型圆钢管的传递矩阵;然后利用传递矩阵关系原理推导出双锥型圆钢管单元的空间弹性刚度矩阵,并运用实例进行公式验证与误差分析,结果表明本文所推导的刚度矩阵具有足够精度,可用于工程分析,也可用于有限元程序的编制;最后在单元刚度矩阵的基础上提出了双锥型圆钢管的刚度修正系数,当进行稳定计算时,可将双锥型圆钢管等效成等截面圆钢管分析。文末给出常用双锥型圆钢管的刚度修正系数表,以供广大设计人员参考。

Element stiffness matrix of circular steel tubes with tapered ends has been formulated in the paper. Firstly, transfer matrix method is introduced, and transfer matrices for the uniform cross-section circular steel tube and tapered circular steel tube are derived. Then the dement stiffness matrix for circular tubes with tapered ends is obtained on the basis of the relationship principle of transfer matrices. Some typical examples are given to verify the dement stiffness matrix, which prove that the presented stiffness matrix is sufficiently accurate for engineering analysis and FE programming. And the stiffness matrix for circular tubes with tapered ends can be treated as a modification of the stiffness matrix for uniform cross-section tubes. Stiffness modified coefficients are introduced to represent the modification, by which the tubes with tapered ends can be replaced by uniform cross-section tubes in stability analysis. The stiffness modified coefficients for frequently used tubes are listed in table and given at the end of the paper.