Nano-sized batteries composed of nanostructured electrode materials stand as one of the most promising candidates for next-generation rechargeable charging devices which have been widely used in the energy storage systems for advanced power applications. Buckling analysis of nanobeam under non-uniform concentration is significantly important for the design of nano-sized batteries under the rapid charging mode. In this work, such issue is investigated in the framework of the size-dependent mechanical–diffusion model, and size effect of mass transfer on buckling property is considered for the first time. By using the eigenvalue method, the critical buckling loads of Euler–Bernoulli nanobeam under the conditions of clamped–clamped, clamped–free, simply supported–simply supported and clamped–simply supported are analytically obtained. The derived results are compared with those of non-gradient nonlocal elastic stress theory, classical elasticity theory and classical theory of mass transfer. It is also found that the value of critical buckling load will be reduced if diffusive nonlocal parameter becomes larger.

中文翻译：

---

非均匀浓度下Euler–Bernoulli纳米束的尺寸依赖性屈曲分析

由纳米结构电极材料组成的纳米尺寸电池是下一代可再充电设备的最有希望的候选者之一，该设备已被广泛用于先进电力应用的储能系统中。纳米束在不均匀浓度下的屈曲分析对于快速充电模式下纳米尺寸电池的设计非常重要。在这项工作中，在与尺寸有关的机械扩散模型的框架内研究了这个问题，并且首次考虑了传质对屈曲特性的尺寸影响。通过使用特征值方法，可以得到在夹钳，夹钳，无夹钳，简单支撑，简单支撑和简单支撑的条件下，Euler–Bernoulli纳米束的临界屈曲载荷。将得出的结果与非梯度非局部弹性应力理论，经典弹性理论和经典传质理论的结果进行比较。还发现，如果非局部扩散参数变大，临界屈曲载荷的值将减小。