The lateral-torsional buckling behavior of functionally graded (FG) non-local beams with a tapered I-section is here investigated using an innovative methodology. The material properties are supposed to vary continuously along the longitudinal direction according to a homogenization procedure, based on a power-law function, whereas the nanobeam is modeled within the framework of a Vlasov thin-walled beam theory. The flexural-torsional governing equations of the problem are derived based on the Eringen's nonlocal elasticity theory and the energy method. The system of lateral stability equations is, thus, reduced to a fourth-order differential equation in terms of the twist angle by uncoupling the equilibrium differential equations. The buckling loads are finally determined using the differential quadrature method (DQM), which is here applied as numerical tool to solve directly the differential equations of the problem in a strong form. A systematic investigation checks for the influence of some parameters such as the power-law index, tapering ratios, loading height parameter, boundary conditions and non-local parameter, on the lateral stability resistance of the tapered I-nanobeams. The numerical outcomes of this paper can be used as benchmarks for further studies on nanoscale tapered thin-walled beams.

本文使用一种创新的方法研究了具有渐变I型截面的功能梯度（FG）非局部梁的横向扭转屈曲行为。根据幂律函数，材料特性应根据均化程序沿纵向连续变化，而纳米束是在Vlasov薄壁梁理论的框架内建模的。基于Eringen的非局部弹性理论和能量方法，推导了该问题的弯曲扭转控制方程。因此，通过解耦平衡微分方程，将横向稳定性方程组的扭转角简化为四阶微分方程。最后使用微分求积法（DQM）确定屈曲载荷，它在这里用作数值工具，可以直接以强形式求解问题的微分方程。进行了系统的研究，以检查某些参数（例如幂律指数，锥度比，载荷高度参数，边界条件和非局部参数）对锥形I型纳米梁的横向稳定性的影响。本文的数值结果可以用作进一步研究纳米级锥形薄壁梁的基准。