带有全铰节点的三维杆系结构静力分析的回传波射矩阵法研究

Method of Reverberation-Ray Matrix for Static Analysis of 3D Bar-System Structures Containing Completely Hinged Joints

推导出含有全铰节点的三维杆系结构的回传波射矩阵表达式,完善了具有任意连接和约束的空间杆系结构静力分析的回传波矩阵法。基于节点平衡方程和协调方程,推导出表达杆件近端位移和远端位移关系的传递分配矩阵及载荷源向量,并通过由对偶坐标系下近端位移和远端位移的关系获得结构的总体相位矩阵,再引入转列矩阵,进而推导出结构的回传波射矩阵,在此基础上求解以杆端位移为基本未知量的线性方程组,最终得到精确确定所有杆件的杆端位移及杆端内力的矩阵列式。给出了空间杆系结构算例分析,与有限元结果比较,验证了回传波射矩阵法的计算精度。

The corresponding reverberation-ray matrix for space bar-system structures containing com- pletely hinged joints was developed to improve the method of reverberation-ray matrix （MRRM） for static analysis of such structures with arbitrary connections of members and constraint conditions. The carry-o- ver distribution matrix and source vector were obtained using the equilibrium equations and compatibility conditions for displacements and rotational angles at each end of members as unknown quantities. The phase matrix and permutation matrix of the structure can be gained based on the relation between the dis- placements of two ends of each member under the prescribed dual coordinates. Finally, the reverberation -ray matrix was established. All the displacements and rotational angles at the ends of each member thus can be measured by solving the resulting linear system of equations for them. As an example, a 3D framed structure was analyzed, and comparisons of internal forces and moments with the data from the finite element method indicate that the present method has high computational accuracy.