张氏积分法在非线性动力分析中的应用

Application of Chang explicit method to nonlinear dynamic analysis

一个理想的积分法希望同时具有内隐式积分法的无条件稳定与外显式积分法的计算简单的优点,张氏积分法即是为了此目的而发展出来的积分法,虽然已有完整的理论推导与简单的数值验证,但其在实务上的应用仍有待进一步的探究。为了验证张氏积分法的实用性与优异的计算效率,特别将张氏积分法加入Open Sees分析软件中,并针对各式各样不同类型的结构系统来进行动态历时分析。除了张氏积分法以外,也利用等平均加速度积分法与Newmark外显式积分法来进行动态历时分析,并经由分析结果的比较,除了可以验证张氏积分法的数值特性之外,也可以证实张氏积分法能广泛地应用于线性及非线性动力分析。最后则利用每次动力分析所使用的CPU时间比较,来进一步证实此积分法的优异计算效率。

Since Chang explicit method can simultaneously integrate with unconditional stability and explicit formulation together,it is very computationally efficient for solving inertial problems,where the total response is dominated by low frequency modes while the high frequency responses are of no interest. In order to confirm the numerical properties and computational efficiency of this integration method,its solution procedure was implemented into a finite element software,Open Sees. Subsequently,it is applied to solve a variety of nonlinear structural dynamics problems,where material nonlinearity and / or geometric nonlinearity are considered. All computed results are compared to those obtained from the constant average acceleration method. Thus,it is confirmed that Chang explicit method can generally have unconditional stability and comparable accuracy when compared to the constant average acceleration method. In addition,it is evident from the comparison of CPU time for each dynamic analysis that Chang explicit method is very computationally efficient in the solution of an inertial problem in contrast to the constant average acceleration method.