回传波矩阵法在杆系结构静力分析中的应用

Reverberation Matrix Method and Its Application to Static Analysis of Framed Structuress

回传波矩阵法最初是由Pao等人分析二维框架结构动力响应时提出的。对于三维杆系结构的静力分析, 为了确定结构的位移和内力,先要建立传递分配矩阵和载荷源向量,这可通过列出所有节点的静力平衡方程和位移协调方程来实现。同时,通过分析每根杆近端位移和远端位移的关系,建立结构的回传波矩阵(重分配矩阵)。在此基础上求解线性方程组,就可以得到结构的位移和内力。本文推导了空间杆系结构的有关矩阵方程式,并给出了一固定梁的两端弯矩求解算例。

Reverberation matrix method （RMM） was developed by Pao et al. for the dynamic analysis of two dimensional framed structures. For the static analysis of 3D framed structures, the calculations of displacements and internal forces of static structures was first attributed to the determination of a carry-over and distribution matrix and a source vectors resulting from the equilibrium equations and compatibility conditions for displacements of each joint. Meanwhile, a reverberation matrix can be constructed based on the relation between the displacements of two ends of each beam. All the displacements and internal forces can be then derived by solving the linear set of equations for the near- and far-end displacements. Some corressponding formulae for 3D framed structures were presented. A procedure for the solution of bending moments at the ends of a beam was given to illustrate the RMM.