Mechanics in Engineering ›› 2010, Vol. 32 ›› Issue (4): 66-70.DOI: 10.6052/1000-0879-lxysj2009-348
• Application study •
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.
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