A new isogeometric Timoshenko beam model incorporating microstructures and surface energy effects
A new isogeometric Timoshenko beam model incorporating microstructures and surface energy effects
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结合微观结构和表面能效应的新等几何 Timoshenko 梁模型
DOI：
10.1177/1081286520917998
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发表时间：
2020
影响因子：
2.6
通讯作者：
Gu Shuitao
中科院分区：
文献类型：
--
作者：
Yin Shuohui;Deng Yang;Zhang Gongye;Yu Tiantang;Gu Shuitao
使用修正偶应力理论 (MCST) 和表面弹性理论开发了一种新的等几何 Timoshenko 梁模型。 MCST 广泛用于捕获仅包含一个材料长度尺度参数的微观结构效应，而包含三个表面弹性常数的 Gurtin-Murdoch 表面弹性理论用于近似表面能效应的本质。针对当前非经典Timoshenko梁模型，基于非均匀有理B样条高阶连续基函数的等几何分析，提出了一种新的有效计算方法，有效满足了MCST较高的连续性要求。为了验证新方法并定量说明微观结构和表面能效应，将开发的梁静态偏转和固有频率方法获得的数值结果与文献中的分析结果进行了比较。数值结果表明，在非常薄的梁中应考虑微观结构效应和表面能效应，这也解释了尺寸相关的行为。
A new isogeometric Timoshenko beam model is developed using a modified couple stress theory (MCST) and a surface elasticity theory. The MCST is wildly used to capture microstructure effects that includes only one material length scale parameter, while the Gurtin–Murdoch surface elasticity theory containing three surface elasticity constants is employed to approximate the nature of surface energy effects. A new effective computational approach is presented for the current nonclassical Timoshenko beam model based on isogeometric analysis with high-order continuity basis functions of non-uniform rational B-splines, which effectively fulfills the higher continuity requirements in MCST. To validate the new approach and quantitatively illustrate both the microstructure and surface energy effects, the numerical results obtained from the developed approach for static deflection and natural frequencies of beams are compared with the analytical results available in the literature. Numerical results reveal that both the microstructure effect and surface energy effect should be considered in very thin beams, which also explains the size-dependent behavior.