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CivilComp Proceedings
ISSN 17593433 CCP: 111
PROCEEDINGS OF THE FIFTH INTERNATIONAL CONFERENCE ON PARALLEL, DISTRIBUTED, GRID AND CLOUD COMPUTING FOR ENGINEERING Edited by:
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 , "A Hybrid Software Solution for the Harmonic Coupled
Finite Strip Method Characteristic Equations", in , (Editors), "Proceedings of the
Fifth International Conference
on
Parallel, Distributed, Grid and Cloud Computing
for Engineering", CivilComp Press, Stirlingshire, UK, Paper 31, 2017. doi:10.4203/ccp.111.31
Keywords: harmonic coupled finite strip method, numerical analysis, accuracy of
numerical evaluation, metaprogramming, 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 beam’s boundary conditions involve
hyperbolic sine and cosine functions, whose usage leads to exponential growth of rootfinding
errors as mode increases. Also, there isn’t a single rootfinding solver suitable
for all boundary conditions. We found solution in arbitraryprecision 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 precalculated 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. purchase the fulltext of this paper (price £22)
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