Keywords: harmonic coupled finite-strip method, geometric nonlinear analysis, MPI, OpenMP.

Applying the full Green-Lagrange strains the harmonic coupled finite-strip method (HCFSM) has been derived in [1]. Depending on the particular problem of continuum mechanics under consideration, the nonlinear contributions in a manner consistent with the usual von Karman assumptions may be safely ignored.

However, in the HCFSM formulation the coupling of all series terms dramatically increases the calculation time in an existing finite-strip sequential program when a large number of series terms are used. The HCFSM algorithm requires geometric stiffness matrix calculation. Calculations of stiffness matrix for different strips are independent and can be carried out in parallel on a cluster with suitable number of nodes. Therefore it is natural to use parallel programming libraries, such as MPI to obtain the parallel calculation of the stiffness matrix for different strips [2]. Such an approach allows substantial speedup as the calculation of each stiffness matrix requires a large number of arithmetic operations to be conducted on a relatively small set of input data. Further speedup is possible if each cluster node contains a multi-core processor offering different cores to conduct simultaneous independent calculation of different stiffness matrices elements. This is natural ambient for the OpenMP approach.

The examples provided demonstrate a critical need for the proposed improvements in the FSM. The method only touches a small academic community, though has contributed a great deal to the understanding of many important problems.

1

D.D. Milašinovic, "The Finite Strip Method in Computational Mechanics", Faculties of Civil Engineering: University of Novi Sad, Technical University of Budapest and University of Belgrade, Subotica, Budapest, Belgrade, 1997.

2

P. Rakic, D.D. Milašinovic, Z. Zivanov, M. Hajdukovic, "MPI-CUDA Parallelisation of the Finite Strip Method for Geometrically Nonlinear Analysis", in B.H.V. Topping, P. Iványi, (Editors), "Proceedings of the First International Conference on Parallel, Distributed and Grid Computing for Engineering", Civil-Comp Press, Stirlingshire, UK, Paper 33, 2009. doi:10.4203/ccp.90.33

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