非线性阻尼动力方程的复合积分法

非线性动力方程直接积分法的基础是构造$t$时刻与t+\Delta t时刻状态量间的关系, 由此形成基本量的非线性方程组, 再在每个时间步内采用 Newton-Raphson或BFGS等迭代方法求解. 该文基于Bathe复合积分法(composite implicit time integration), 提出了非线性阻尼系统基于速度变量的复合时间 积分迭代格式. 以非线性黏滞阻尼Sdof系统为例, 按上述方法以及基于BFGS迭代 的Newmark-\beta法编制Fortran程序, 结果与Adina软件对比, 验证了该文方法的有效性.

COMPOSITE IMPLICIT TIME INTEGRATION METHOD FOR DYNAMIC EQUATIONS WITH NONLINEAR DAMPING

The direct time integration methods for nonlinear dynamic equations are based on a relationship of state variables between the time of $t$ and $t+\Delta t$, and the nonlinear dynamic equations can be converted into a set of nonlinear algebraic equations, to be solved with Newton-Raphson or BFGS iterations during each time increment. The composite implicit time integration method proposed by K. J. Bathe is deduced for dynamic equations including nonlinear damping, in which the velocity is taken as the basic variable in this paper. Sdof system with fluid viscous dampers is taken as an example, and Fortran programs are developed according to above iteration procedure and Newmar $k$-$\beta $ algorithm based on BFGS iteration for the Sdof system. Results are compared with that of Adina, and the accuracy is valieated.