CAJ | 학술논문

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．
압만구건승수교대축력시，기표현출적명현적이계효응직접영향결구강도급동력특성，위계산계급이계효응적량주결구적순태향응，제출료일충전체구진방법．해방법채용Newmark-β법，대고필이계효응적Euler-Bernoulli량적동력편미분방정진행시역리산，장기변환위상미분방정，병이용상수변역법대미분방정진행구해，득도위이증량재련속공간내적해석해．결합전체구진법적기본원리，추도료리산시간순태분석적증량전체구진격식，급출료계급이계효응적량주결구순태향응적계산방법．산례계산결과표명，재계산정도상동적정황하，소제출적방법적계산효솔시ANSYS적3．57배，병가방편지대이동하재작용하결구적동력향응진행구해．
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.