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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 111
PROCEEDINGS OF THE FIFTH INTERNATIONAL CONFERENCE ON PARALLEL, DISTRIBUTED, GRID AND CLOUD COMPUTING FOR ENGINEERING
Edited by: P. Iványi, B.H.V. Topping and G. Várady
Paper 31

A Hybrid Software Solution for the Harmonic Coupled Finite Strip Method Characteristic Equations

P. Marić, D.D. Milašinović, D. Goleš, Ž. Živanov and M. Hajduković

University of Novi Sad, Faculty of Technical Sciences, Novi Sad, Serbia 2 University of Novi Sad, Faculty of Civil Engineering, Subotica, Serbia

Full Bibliographic Reference for this paper
P. Maric, D.D. Mila¬šinovic, D. Gole¬š, ¬é. ¬éivanov, M. Hajdukovic , "A Hybrid Software Solution for the Harmonic Coupled Finite Strip Method Characteristic Equations", in P. Iványi, B.H.V. Topping, G. Várady, (Editors), "Proceedings of the Fifth International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering", Civil-Comp Press, Stirlingshire, UK, Paper 31, 2017. doi:10.4203/ccp.111.31
Keywords: harmonic coupled finite strip method, numerical analysis, accuracy of numerical evaluation, meta-programming, multithreading, parallelization, basic functions, roots of characteristic equations.

Summary
This paper presents the hybrid software solution for solving the characteristic equations of the basic functions, used in harmonic coupled finite strip method (HCFSM). Functions are defined by the equation for the normal modes of a uniform beam under transverse free vibration. Some variants of beamís boundary conditions involve hyperbolic sine and cosine functions, whose usage leads to exponential growth of rootfinding errors as mode increases. Also, there isnít a single root-finding solver suitable for all boundary conditions. We found solution in arbitrary-precision floating point arithmetic, in framework for selecting best solver for any given boundary condition and in extensive parallelisation.

The obtained roots of characteristic equations are then used for solving the problem of free vibration, which requires calculating definite integrals over basic functions, as defined by HCFSM. The lengths (upper limit) of these definite integrals can be normalised due to their integrand formulation, so it is practical to create a table of pre-calculated normalised integrals. Generating this table is computationally and time expensive, and parallelisation is used on this stage too.

Every aspect of the software implementation is covered by tests, over 4400 in total, which help us assure the correctness of the hybrid method and its reference implementation.

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