A lateral buckling analysis of simply supported web- and/or flange-tapered I-beams made of axially functionally graded materials and subjected to a uniformly distributed load is performed. The properties of beam material vary continuously along the beam axis, depending on the volume fraction of constituent materials, according to an exponential or power law. Considering the coupling between the lateral displacement and twist angle, equilibrium equations are derived via the energy method in association with the Vlasov thin-walled beam theory. For simply supported beams with free warping, the system of equilibrium equations is transformed into a differential equation in the twist angle. The differential quadrature method is then used to numerically solve the resulting fourth-order differential equation with variable coefficients and to determine the lateral buckling loads. A numerical example is finally considered to study the influence of different parameters — the axial variation of material properties, tapering ratios, and load eccentricities — on the lateral stability of the beams considered. The numerical results of this paper can be used as benchmarks for future studies on axially functionally graded nonprismatic I-beams with pinned-pinned end conditions.

中文翻译：

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具有锥形 I 形截面的简支轴向功能梯度梁的横向扭转稳定性分析

对由轴向功能梯度材料制成并承受均匀分布载荷的简支腹板和/或翼缘锥形工字梁进行横向屈曲分析。根据指数或幂律，梁材料的属性沿梁轴连续变化，这取决于组成材料的体积分数。考虑横向位移和扭转角之间的耦合，结合Vlasov薄壁梁理论，通过能量法推导出平衡方程。对于自由翘曲的简支梁，将平衡方程组转化为扭转角的微分方程。然后使用微分正交法对所得的具有可变系数的四阶微分方程进行数值求解，并确定横向屈曲载荷。最后考虑一个数值例子来研究不同参数——材料特性的轴向变化、锥度比和载荷偏心——对所考虑梁的横向稳定性的影响。本文的数值结果可用作未来研究具有销钉端部条件的轴向功能梯度非棱柱工字梁的基准。