Journal of
Faculty of Civil Engineering

CONFERENCE PROCEEDINGS
6th INTERNATIONAL CONFERENCE
CONTEMPORARY ACHIEVEMENTS IN CIVIL ENGINEERING 2018 , 2018.y., pp. 133-142

	DOI: 10.14415/konferencijaGFS2018.011
	UDC: 624.072.042.3:519.6
	CC-BY-SA 4.0 license
	Author : Milašinović, Dragan D.; Marić, Petar; Živanov, Žarko; Hajduković, Miroslav
	Summary:
	It is well recognized that when using exact theory, as opposed to the more usual approximate finite element method, there exists a duality between buckling and natural vibration of an elastic structure, even though the former is a static problem whereas the latter is a dynamic one. The solution procedures for the both problems are analogous because both can be essentially represented by a transcendental eigenvalue problem, the eigenvalues being natural frequencies in vibration problems and load factors in buckling problems. Thus the elastic buckling of a structure is often regarded as the degenerated case of its natural vibration at zero frequency. In this paper duality is proved for the both elastic and viscoelastic (or damage) structure using semi-analytical finite strip method (FSM) and rheological-dynamical analogy (RDA). The governing dynamic RDA modulus has been derived in [1]. This paper presents an investigation of composite thin-walled wide-flange columns. Numerical examples showing the theoretical considerations are presented and agree with the experimental data. Two reference Open Source Software implementations are provided: for approximating the natural frequency from stress via physical duality (and vice versa) and for the visual analysis of the physical duality approximation effectiveness.
	Keywords:
	Duality, FSM, RDA, dynamic RDA modulus, Composite thin-walled wideflange column, numerical analysis, accuracy of numerical evaluation