This paper investigates the nonlinear bending behaviours of functionally graded trapezoidal nanocomposite plates reinforced with graphene platelets (GPLs) under thermo-mechanical loading by employing finite element method. The modified Halpin–Tsai model and rule of mixtures are adopted to determine the Young’s modulus, Poisson’s ratio and the thermal expansion coefficient of the nanocomposites. The influences of a number of factors, including the distribution pattern, concentration and size of GPLs, plate geometry and temperature, on the nonlinear bending of the nanocomposite plates are comprehensively investigated. Numerical results demonstrate that dispersing a small amount of GPLs into nanocomposites can significantly enhance the nonlinear bending performance of the trapezoidal plates. The trapezoidal plates with more GPLs dispersing close to the top and bottom surfaces has the minimum bending deflection and are less sensitive to the temperature increases. GPLs with fewer layers and larger surface area are better reinforcing fillers than their counterparts. Moreover, the plates with bigger bottom angles are found to have better bending performances. However, when the bottom angles are greater than 75°, the variation of the bottom angles will have limited effects on the bending behaviours of the trapezoidal plates.

本文采用有限元方法研究了功能梯度梯形纳米复合材料增强石墨烯薄片（GPLs）在热力作用下的非线性弯曲行为。采用改进的Halpin-Tsai模型和混合物规则确定纳米复合材料的杨氏模量，泊松比和热膨胀系数。全面研究了GPL的分布方式，浓度和大小，板的几何形状和温度等因素对纳米复合板非线性弯曲的影响。数值结果表明，将少量的GPL分散到纳米复合材料中可以显着增强梯形板的非线性弯曲性能。GPL较多的梯形板分散在顶面和底面附近，具有最小的弯曲挠度，并且对温度升高不敏感。层数较少且表面积较大的GPL是比同类产品更好的补强填料。此外，发现具有较大底角的板具有更好的弯曲性能。然而，当底角大于75°时，底角的变化将对梯形板的弯曲行为具有有限的影响。