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Quadrature element method for vibration analysis of functionally graded beams

Chunhua Jin (School of Architecture Engineering, Nantong University, Nantong, China and State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, China)
Xinwei Wang (State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, China)

Engineering Computations

ISSN: 0264-4401

Article publication date: 12 June 2017

Abstract

Purpose

The purpose of this paper is to present a general formulation of the quadrature element method (QEM). The method is then used to investigate the free vibration of functionally graded (FG) beams with general boundary conditions and different variations of material properties.

Design/methodology/approach

The quadrature elements with arbitrary number of nodes and nodal distributions are established on the basis of two types of FG Timoshenko beam theories. One called TBT-1 takes the cross-sectional rotation as the unknown function and the other called TBT-2 uses the transverse shear strain as the unknown function. Explicit formulas are provided via the help of the differential quadrature (DQ) rule and thus the elements can be implemented adaptively with ease.

Findings

The suitability and computational efficiency of the proposed quadrature elements for the vibration analysis of FG beams are demonstrated. The convergence rate of the proposed method is high. The elements are shear-locking free and can yield accurate solutions with a small number of nodes for both thin and moderately thick beams. The performance of the element based on TBT-1 is better than the one based on TBT-2.

Originality/value

The present QEM is different from the existing one which exclusively uses Gauss–Lobatto–Legendre (GLL) nodes and GLL quadrature and thus is more general. The element nodes can be either the same or different from the integration points, making the selection of element nodes more flexible. Presented data are accurate and may be a reference for other researchers to develop new numerical methods. The QEM may be also useful in multi-scale modeling and in the analysis of civil infrastructures.

Keywords

Acknowledgements

The project is partially supported by the Priority Academic Program Development of Jiangsu Higher Education Institutions.

Citation

Jin, C. and Wang, X. (2017), "Quadrature element method for vibration analysis of functionally graded beams", Engineering Computations, Vol. 34 No. 4, pp. 1293-1313. https://doi.org/10.1108/EC-07-2016-0271

Publisher

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Emerald Publishing Limited

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