Strain gradient differential quadrature beam finite elements

被引:27
|
作者
Zhang, Bo [1 ,2 ]
Li, Heng [1 ]
Kong, Liulin [3 ]
Wang, Jizhen [4 ]
Shen, Huoming [2 ]
机构
[1] Hong Kong Polytech Univ, Dept Bldg & Real Estate, Hong Kong, Peoples R China
[2] Southwest Jiaotong Univ, Sch Mech & Engn, Chengdu, Sichuan, Peoples R China
[3] Huazhong Univ Sci & Technol, Sch Civil Engn & Mech, Wuhan, Hubei, Peoples R China
[4] PowerChina Turbine Technol Co Ltd, Chengdu, Sichuan, Peoples R China
基金
中国国家自然科学基金;
关键词
Finite element method; Differential quadrature method; Beam elements; Strain gradient; FREE-VIBRATION ANALYSIS; SIZE-DEPENDENT ANALYSIS; COUPLE STRESS THEORY; HIGHER-ORDER SHEAR; ISOGEOMETRIC ANALYSIS; ELASTICITY; MODEL; FORMULATION; PLATES;
D O I
10.1016/j.compstruc.2019.01.008
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
In this paper, the superiorities of finite element method (FEM) and differential quadrature method (DQM) are blended to construct two types of beam elements corresponding to modified strain gradient Bernoulli and Timoshenko beam models respectively. The two elements, being independent of shape functions and introducing three kinds of strain gradient effects, possess 3-DOFs (degrees of freedom) and 4-DOFs separately at each node. The Lagrange interpolation formula is employed to establish the trial functions of deflection and or rotation at Gauss-Lobatto quadrature points. To realize the inner-element compatibility condition, displacement parameters of quadrature points are converted into those of element nodes through a DQ-based mapping strategy. Total potential energy functional for each beam model is discretized in terms of nodal displacement parameters. The associated differential quadrature finite element formulations are derived by the minimum total potential energy principle. Specific expressions of element stiffness and mass matrices and nodal vector are provided. Numerical examples concerning with static bending, free vibration and buckling of macro/micro-beams are presented to demonstrate the availability of the proposed elements. (C) 2019 Elsevier Ltd. All rights reserved.
引用
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页码:170 / 189
页数:20
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