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A novel weak form quadrature element for gradient elastic beam theories

Ishaquddin, Md and Gopalakrishnan, S (2020) A novel weak form quadrature element for gradient elastic beam theories. In: APPLIED MATHEMATICAL MODELLING, 77 (1). pp. 1-16.

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Official URL: https://dx.doi.org/10.1016/j.apm.2019.07.014


A novel weak form quadrature element is proposed for non-classical strain gradient Euler-Bernoulli beam theories. The element is formulated with the aid of variational principles and has displacement as the only degree of freedom in the element domain and displacement, slope and curvature at the boundaries. All the classical and non-classical support conditions associated with the gradient beam theory are represented accurately. The Gauss-Lobatto-Legendre quadrature points are considered as element nodes and also used for numerical integration of the element matrices. Numerical examples on bending, free vibration and stability analysis of gradient beams are presented to demonstrate the efficiency and accuracy of the proposed element. To substantiate the generality of the element, beams with discontinuity in loading and geometry are examined.

Item Type: Journal Article
Additional Information: Copyright of this article belongs to ELSEVIER SCIENCE INC
Keywords: Quadrature element; Strain gradient Euler-Bernoulli beam theory; Weighting coefficients; Non-classical degrees of freedom; Hermite interpolation
Department/Centre: Division of Mechanical Sciences > Aerospace Engineering(Formerly Aeronautical Engineering)
Date Deposited: 16 Jan 2020 10:59
Last Modified: 16 Jan 2020 10:59
URI: http://eprints.iisc.ac.in/id/eprint/64317

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