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A novel weak form quadrature element for gradient elastic beam theories

机译：梯度弹性梁理论的新型弱形式正交元

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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.
机译：针对非经典应变梯度Euler-Bernoulli梁理论，提出了一种新型的弱形式正交单元。单元是根据变分原理制定的，其位移是单元域中的唯一自由度，位移是边界处的位移，斜率和曲率。与梯度梁理论相关的所有经典和非经典支撑条件都可以精确表示。 Gauss-Lobatto-Legendre正交点被视为元素节点，还用于元素矩阵的数值积分。给出了关于梯度梁弯曲，自由振动和稳定性分析的数值例子，以证明所提出元件的效率和准确性。为了证实元素的通用性，研究了荷载和几何形状不连续的梁。 （C）2019 Elsevier Inc.保留所有权利。

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