Novel nonlinear elastic structural analysis with generalised transverse element loads using a refined finite element
Iu, C.K. & Bradford, M.A. (2015) Novel nonlinear elastic structural analysis with generalised transverse element loads using a refined finite element. Advanced Steel Construction, 11(2), pp. 223249.

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Abstract
In the finite element modelling of structural frames, external loads such as wind loads, dead loads and imposed loads usually act along the elements rather than at the nodes only. Conventionally, when an element is subjected to these general transverse element loads, they are usually converted to nodal forces acting at the ends of the elements by either lumping or consistent load approaches. In addition, it is especially important for an element subjected to the first and secondorder elastic behaviour, to which the steel structure is critically prone to; in particular the thinwalled steel structures, when the stocky element section may be generally critical to the inelastic behaviour. In this sense, the accurate first and secondorder elastic displacement solutions of element load effect along an element is vitally crucial, but cannot be simulated using neither numerical nodal nor consistent load methods alone, as long as no equilibrium condition is enforced in the finite element formulation, which can inevitably impair the structural safety of the steel structure particularly. It can be therefore regarded as a unique element load method to account for the element load nonlinearly. If accurate displacement solution is targeted for simulating the first and secondorder elastic behaviour on an element on the basis of sophisticated nonlinear element stiffness formulation, the numerous prescribed stiffness matrices must indispensably be used for the plethora of specific transverse element loading patterns encountered. In order to circumvent this shortcoming, the present paper proposes a numerical technique to include the transverse element loading in the nonlinear stiffness formulation without numerous prescribed stiffness matrices, and which is able to predict structural responses involving the effect of firstorder element loads as well as the secondorder coupling effect between the transverse load and axial force in the element. This paper shows that the principle of superposition can be applied to derive the generalized stiffness formulation for element load effect, so that the form of the stiffness matrix remains unchanged with respect to the specific loading patterns, but with only the magnitude of the loading (element load coefficients) being needed to be adjusted in the stiffness formulation, and subsequently the nonlinear effect on element loadings can be commensurate by updating the magnitude of element load coefficients through the nonlinear solution procedures. In principle, the element loading distribution is converted into a single loading magnitude at midspan in order to provide the initial perturbation for triggering the member bowing effect due to its transverse element loads. This approach in turn sacrifices the effect of element loading distribution except at midspan. Therefore, it can be foreseen that the loaddeflection behaviour may not be as accurate as those at midspan, but its discrepancy is still trivial as proved. This novelty allows for a very useful generalised stiffness formulation for a single higherorder element with arbitrary transverse loading patterns to be formulated. Moreover, another significance of this paper is placed on shifting the nodal response (system analysis) to both nodal and element response (sophisticated element formulation). For the conventional finite element method, such as the cubic element, all accurate solutions can be only found at node. It means no accurate and reliable structural safety can be ensured within an element, and as a result, it hinders the engineering applications. The results of the paper are verified using analytical stability function studies, as well as with numerical results reported by independent researchers on several simple frames.
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ID Code:  82861 

Item Type:  Journal Article 
Refereed:  Yes 
Additional URLs:  
Keywords:  Elastic instability, finite element; transverse element load effect, higherorder element formulation, nodal response, element response 
ISSN:  1816112X 
Subjects:  Australian and New Zealand Standard Research Classification > ENGINEERING (090000) > CIVIL ENGINEERING (090500) > Structural Engineering (090506) 
Divisions:  Current > Schools > School of Civil Engineering & Built Environment Current > QUT Faculties and Divisions > Science & Engineering Faculty 
Copyright Owner:  Copyright 2015 Please consult the authors. 
Deposited On:  26 Mar 2015 22:16 
Last Modified:  07 Oct 2015 11:09 
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