Buckling analysis of functionally graded (FG) nanobeams is examined using doublet mechanics theory. The material properties of FG nanobeams change with the thickness coordinate. A periodic nanostructure model is considered in FG nanobeams which has a simple crystal square lattice type and Euler–Bernoulli beam theory is used in the formulation. Softening or hardening material behaviour has been observed by changing chiral angle of the considered FG periodic nanobeams in the present doublet mechanics theory. Unlike other size dependent theories such as nonlocal stress gradient elasticity theory, couple stress theory, strain gradient theory, this mechanical response (softening or hardening) is seen for the first time in doublet mechanics theory. Mechanical material responses are directly affected by the atomic structure of the considered material in the doublet mechanics theory. Firstly, micro-stress and micro-strain relations are obtained for the considered nanostructure model in doublet mechanics theory. Then, these microequations are transformed to macroequations in the present doublet mechanics theory. Thus, more physical and accurate mechanical results can be obtained in nanostructures using the doublet mechanics theory. After developing the mathematical formulations of FG periodic nanobeams, Ritz method is applied to obtain the critical buckling loads for different boundary conditions. Comparison of example studies with the present doublet mechanics model is presented for verification, and effects of chiral angle on stability response of periodic FG nanobeams are discussed.

使用双峰力学理论对功能梯度（FG）纳米束的屈曲分析进行了研究。FG纳米束的材料特性随厚度坐标而变化。在FG纳米束中考虑了周期性的纳米结构模型，该模型具有简单的晶体方格类型，并且在配方中使用了Euler–Bernoulli束理论。在当前的双峰力学理论中，通过改变所考虑的FG周期纳米束的手征角，可以观察到材料的软化或硬化行为。与其他依赖大小的理论（例如非局部应力梯度弹性理论，耦合应力理论，应变梯度理论）不同，这种机械响应（软化或硬化）是首次在双重力学理论中看到的。在双峰力学理论中，机械材料的响应直接受到所考虑材料的原子结构的影响。首先，在双峰力学理论中为所考虑的纳米结构模型获得了微应力和微应变关系。然后，在当前的双峰力学理论中，这些微方程被转换为宏观方程。因此，使用双峰力学理论可以在纳米结构中获得更多的物理和精确的机械结果。在发展了FG周期纳米束的数学公式之后，应用Ritz方法获得了不同边界条件下的临界屈曲载荷。实例研究与目前的双峰力学模型进行了比较，以进行验证，并讨论了手性角对周期性FG纳米束稳定性响应的影响。