Keywords: sub-domain decomposition method, finite element code, non-matching time scales, transient non-linear dynamic problems, external code coupling.

The GC method has been proposed by Gravouil and Combescure for Newmark time schemes in linear dynamics [1] and, then, extended to non linear dynamics [2]. Batti et al. [3] have proposed a sub-domain decomposition method called GC+ and also the GC+ external code coupler which is energy conserving; which permits parallel computation of free and link problems and which was limited to transient linear dynamic problems.

In this paper, we have presented the key equations of the GC+ sub-domain decomposition method in the case of a same time step used for all the sub-domains composing the structure. Then, we have described a linear external code coupler using the GC+ method in the case of multi-time scales. The extension of the GC+ method and of the GC+ external code coupling to the non-linear cases is proposed. The non-linear GC+ external code coupler manages to couple a macro non-linear implicit FE code with a micro non-linear explicit FE code. We have seen with an industrial numerical example, that the non-linear GC+ external code coupler is well used (with appropriate choice of the definition of the two macro implicit and micro explicit sub-domains of the global structure; and appropriate choice of values of macro and micro time steps imposed in each sub-domain during the analysis computation) and permits us to obtain good results in terms of maximal displacements and velocities of the structure considered, ensuring continuity of velocities at the interface between the two chosen sub-domains, ensures a weak energy dissipation at the interface, and needs very less CPU time than classical mono-domain solving.

1

A. Combescure, A. Gravouil, "A numerical scheme to couple subdomains with different time-steps for predominantly linear transient analysis", Computer methods in applied mechanics and engineering, 191, 1129-1157, 2002. doi:10.1016/S0045-7825(01)00190-6

2

A. Gravouil, A. Combescure, "A multi-time-step explicit-implicit method for non-linear structural dynamics", International Journal for Numerical Methods in Engineering, 50, 199-225, 2001. doi:10.1002/1097-0207(20010110)50:1<199::AID-NME132>3.0.CO;2-A

3

A. Batti, M. Brun, A. Gravouil, A. Combescure, "An external code coupler based on an improved sub-domain decomposition method", Computers & Structures, submitted, 2010.

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £85 +P&P)