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.

中文翻译：

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一种新的等几何 Timoshenko 梁模型，结合了微观结构和表面能效应

使用修正的耦合应力理论 (MCST) 和表面弹性理论开发了一种新的等几何 Timoshenko 梁模型。MCST 被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 表面弹性理论被用来近似表面能效应的性质。基于非均匀有理B样条的高阶连续性基函数等几何分析，针对当前非经典Timoshenko梁模型提出了一种新的有效计算方法，有效地满足了MCST中更高的连续性要求。为了验证新方法并定量说明微观结构和表面能效应，从所开发的梁的静态挠度和自然频率方法中获得的数值结果与文献中可用的分析结果进行了比较。数值结果表明，在非常薄的梁中应同时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。