标题：A SIZE-DEPENDENT FINITE-ELEMENT MODEL FOR A MICRO/NANOSCALE TIMOSHENKO BEAM
作者：Zhang, Long; Wang, Binglei; Liang, Binbin; Zhou, Shenjie; Xue, Yiguo
作者机构：[Zhang, Long; Wang, Binglei; Liang, Binbin; Xue, Yiguo] Shandong Univ, Sch Civil Engn, Jinan 250061, Peoples R China.; [Wang, Binglei] Xi An Jiao To 更多
通讯作者地址：[Wang, BL]Shandong Univ, Sch Civil Engn, Jinan 250061, Peoples R China.
来源：INTERNATIONAL JOURNAL FOR MULTISCALE COMPUTATIONAL ENGINEERING
关键词：microscale; Timoshenko beam element; strain gradient elasticity theory;; size effect
摘要：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 (l(0) and l(1)) or three (l(0), l(1), and l(2)) material length scale parameters are set to zero. The element satisfies C-0 continuity and C-1 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.