Efficient coupled polynomial interpolation scheme for out-of-plane free vibration analysis of curved beams

Ishaquddin, Md and Raveendranath, P and Reddy, JN (2016) Efficient coupled polynomial interpolation scheme for out-of-plane free vibration analysis of curved beams. In: FINITE ELEMENTS IN ANALYSIS AND DESIGN, 110 . pp. 58-66.

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Abstract

The performance of two curved beam finite element models based on coupled polynomial displacement fields is investigated for out-of-plane vibration of arches. These two-noded beam models employ curvilinear strain definitions and have three degrees of freedom per node namely, out-of-plane translation (v), out-of-plane bending rotation (theta(z)) and torsion rotation (theta(s)). The coupled polynomial interpolation fields are derived independently for Timoshenko and Euler-Bernoulli beam elements using the force-moment equilibrium equations. Numerical performance of these elements for constrained and unconstrained arches is compared with the conventional curved beam models which are based on independent polynomial fields. The formulation is shown to be free from any spurious constraints in the limit of `flexureless torsion' and `torsionless flexure' and hence devoid of flexure and torsion locking. The resulting stiffness and consistent mass matrices generated from the coupled displacement models show excellent convergence of natural frequencies in locking regimes. The accuracy of the shear flexibility added to the elements is also demonstrated. The coupled polynomial models are shown to perform consistently over a wide range of flexure-to-shear (EI/GA) and flexure-to-torsion (EI/GJ) stiffness ratios and are inherently devoid of flexure, torsion and shear locking phenomena. (C) 2015 Elsevier B.V. All rights reserved.

Item Type:	Journal Article
Publication:	FINITE ELEMENTS IN ANALYSIS AND DESIGN
Publisher:	ELSEVIER SCIENCE BV
Additional Information:	Copy right for this article belongs to the ELSEVIER SCIENCE BV, PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS
Keywords:	Finite element; Curved beam; Free vibration; Timoshenko beam; Euler-Bernoulli beam; Shear locking; Flexure locking; Torsion locking; Coupled polynomial field
Department/Centre:	Division of Mechanical Sciences > Aerospace Engineering(Formerly Aeronautical Engineering)
Date Deposited:	29 Jan 2016 07:36
Last Modified:	29 Jan 2016 07:36
URI:	http://eprints.iisc.ac.in/id/eprint/53190

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