Multiple shooting method in stability analysis of non-prismatic multi-segment columns
Ryszard Hołubowski
Institute of Civil Engineering; Faculty of Civil Engineering; Wrocław University of Technology (Poland)
https://orcid.org/0000-0002-2999-2758
Andrzej Merena
AQ7 Design Office (Poland)
Abstract
The application of multiple shooting method in stability analysis of non-prismatic multi-segment columns with pinned ends loaded with a concentrated force applied to the upper node has been presented. Numerical analyses were carried out for an exemplary three-segment column by solving the system of differential equations with variable coefficients and parameter. The results were compared with the solution obtained by using SOFiSTiK software based on the finite element method. The analyses show that considering the stiffness changes along the length can have a significant influence on the values of critical loads and thus change the resistance of the column. The advantage of the proposed method is its high efficiency and easy description of stiffness changes.
Keywords:
stability analysis, non-prismatic multi-segment columns, shooting methodReferences
] Pai P.F., Palazotto A.N. Large-deformation analysis of flexible beams. International Journal of Solids and Structures 33(9) (1996) 1335-1353.
DOI: https://doi.org/10.1016/0020-7683(95)00090-9
Google Scholar
Chen R.S. Evaluation of natural vibration frequency of a compression bar with varying cross-section by using the shooting method. Journal of Sound and Vibration 201(4) (1997) 520-527.
DOI: https://doi.org/10.1006/jsvi.1996.0807
Google Scholar
Li S.R., Zhou Y.H. Shooting method for non-linear vibration and thermal buckling of heated orthotropic circular plates. Journal of Sound and Vibration 248(2) (2001) 379-386.
DOI: https://doi.org/10.1006/jsvi.2001.3665
Google Scholar
Ribeiro P. Non-linear forced vibrations of thin/thick beams and plates by the finite element and shooting methods. Computers and Structures 82 (2004) 1413-1423.
DOI: https://doi.org/10.1016/j.compstruc.2004.03.037
Google Scholar
Ibrahim S.M., Patel B.P., Nath Y. Modified shooting approach to the non-linear periodic forced response of isotropic/composite curved beams. International Journal of Non-Linear Mechanics 44 (2009) 1073-1084.
Google Scholar
Glabisz W. Mathematica w zagadnieniach mechaniki konstrukcji. Oficyna Wydawnicza Politechniki Wrocławskiej, Wrocław 2003.
Google Scholar
Hołubowski R., Glabisz W. Analiza stateczności drewnianych niepryzmatycznych słupów o przekroju kołowym. Inżynieria i Budownictwo 10 (2012) 549-551.
Google Scholar
Życzkowski M. Stateczność prętów i ustrojów prętowych, w: Mechanika techniczna t. 9. Wytrzymałość elementów konstrukcyjnych. (red. Życzkowski M.) PWN, Warszawa 1988, s. 242-368.
Google Scholar
Zwillinger D. Handbook of Differential Equations. Academic Press, 1997.
Google Scholar
Stoer J., Bulirsch R. Introduction to Numerical Analysis. Springer-Verlag, New York 1993.
DOI: https://doi.org/10.1007/978-1-4757-2272-7
Google Scholar
PN-EN 1995-1-1:2010 Eurokod 5 – Projektowanie konstrukcji drewnianych – Część 1-1: Postanowienia ogólne – Reguły ogólne i reguły dotyczące budynków.
Google Scholar
PN-EN 338:2011 Drewno konstrukcyjne – Klasy wytrzymałości.
Google Scholar
Authors
Ryszard HołubowskiInstitute of Civil Engineering; Faculty of Civil Engineering; Wrocław University of Technology Poland
https://orcid.org/0000-0002-2999-2758
Authors
Andrzej MerenaAQ7 Design Office Poland
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