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

• Application study • Previous Articles     Next Articles

COMPOSITE IMPLICIT TIME INTEGRATION METHOD FOR DYNAMIC EQUATIONS WITH NONLINEAR DAMPING

  

  • Received:2009-09-03 Online:2010-08-08 Published:2010-08-20

Abstract: 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.