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International Journal for Multiscale Computational Engineering
Импакт фактор: 1.016 5-летний Импакт фактор: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN Печать: 1543-1649
ISSN Онлайн: 1940-4352

Выпуски:
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International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2015014055
pages 491-506

A SIZE-DEPENDENT FINITE-ELEMENT MODEL FOR A MICRO/NANOSCALE TIMOSHENKO BEAM

Long Zhang
Department of Engineering Mechanics, Chongqing University, Chongqing, 400044, P.R.China; Department of Theoretical and Applied Mechanics, Chongqing University of Science and Technology, Chongqing, 401331, P.R.China
Binglei Wang
School of Civil Engineering, Shandong University, Jinan, 250061, China; State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi'an Jiaotong University, Xi'an 710049, China
Binbin Liang
School of Civil Engineering, Shandong University, Jinan, 250061, China
Shenjie Zhou
School of Mechanical Engineering, Shandong University, Jinan, 250061, China
Yiguo Xue
School of Civil Engineering, Shandong University, Jinan, 250061, China

Краткое описание

A size-dependent finite-element model for a micro/nanoscale Timoshenko beam is developed based on the strain gradient elasticity theory. The newly developed element contains three material length scale parameters that capture the size effect. This element is a new, comprehensive Timoshenko beam element that can reduce to the modified couple stress Timoshenko beam element or the classical Timoshenko beam element if two (l0 and l1) or three (l0, l1, and l2) material length scale parameters are set to zero. The element satisfies C0 continuity and C1 weak continuity and has two nodes, with four degrees of freedom at each node considering only bending deformation. The deflection and cross-sectional rotation of the element are interpolated independently. The finite-element formulations and the stiffness and mass matrices are derived using the corresponding weak-form equations. To verify the reliability and accuracy of the proposed element, the problems of convergence and shear locking are studied. Using the newly developed element, the static bending and free vibration problems of the clamped and simply supported Timoshenko microbeam are investigated. The results for a simply supported Timoshenko microbeam predicted by the new element model agree well with results from the literature. Moreover, the results illustrate that the size effect on the Timoshenko microbeam can be effectively predicted by using the proposed element.