A novel weak form quadrature element for gradient elastic beam theories

摘要

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. (C) 2019 Elsevier Inc. All rights reserved.