考虑二阶效应梁柱瞬态分析的传递矩阵法

压弯构件承受较大轴力时，其表现出的明显的二阶效应直接影响结构刚度及动力特性，为计算计及二阶效应的梁柱结构的瞬态响应，提出了一种传递矩阵方法.该方法采用Newmark-β法，对考虑二阶效应的Euler-Bernoulli梁的动力偏微分方程进行时域离散，将其变换为常微分方程，并利用常数变易法对微分方程进行求解，得到位移增量在连续空间内的解析解.结合传递矩阵法的基本原理，推导了离散时间瞬态分析的增量传递矩阵格式，给出了计及二阶效应的梁柱结构瞬态响应的计算方法.算例计算结果表明，在计算精度相同的情况下，所提出的方法的计算效率是ANSYS的3.57倍，并可方便地对移动荷载作用下结构的动力响应进行求解. 

Transfer Matrix Method of Beam-Column Transient Analysis Considering Second-Order Effect

Second-order effect of a compression-bending member under a high axial force will influence the stiffness and dynamic characteristics of a structure, so a transfer matrix method was proposed to calculate the transient response of beam-column with considering the second-order effect. With this method, the dynamic partial differential equations for Euler-Bernoulli beam are discretized in time domain with the Newmark-β method and transformed into an ordinary differential equation; the differential equation is solved with the variation of constants method to obtain the analytical solution of displacement increment in continuous space domain. Based on the principle of the transfer matrix method, an incremental transfer matrix for discrete-time transient analysis is derived, and a corresponding algorithm was proposed for the transient analysis considering the second-order effect. The numerical results indicate that under the same calculation accuracy, computational efficiency of the proposed method is 3.57 times that of finite element software ANSYS, and the dynamic responses of a structure subjected to a moving load can be obtained easily.