The main objective of this study is to further extend the mixed integration smoothed quadrilateral element with 20 unknowns of displacement (MISQ20) to investigate the nonlinear dynamic responses of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates with four types of carbon nanotube distributions. The smooth finite element method is used to enhance the accuracy of the Q4 element and avoid shear locking without using any shear correction factors. This method yields accurate results even if the element exhibits a concave quadrilateral shape and reduces the error when the element meshing is rough. Additionally, the element stiffness matrix is established by integrating the boundary of the smoothing domains. The motion equation of the FG-CNTRC plates is solved by adapting the Newmark method combined with the Newton–Raphson algorithm. Subsequently, the calculation program is coded in the MATLAB software and verified by comparing it with other published solutions. Finally, the effects of the input parameters on the nonlinear vibration of the plates are investigated.

本研究的主要目的是进一步扩展具有 20 个位移未知数的混合积分平滑四边形单元 (MISQ20)，以研究具有四种类型碳纳米管的功能梯度碳纳米管增强复合材料 (FG-CNTRC) 板的非线性动态响应分布。采用光滑有限元方法，提高Q4单元的精度，在不使用任何剪切修正系数的情况下避免剪切锁定。即使单元呈现凹四边形形状，该方法也能产生准确的结果，并在单元网格划分粗糙时减少误差。此外，单元刚度矩阵是通过积分平滑域的边界来建立的。FG-CNTRC 板的运动方程采用 Newmark 方法结合 Newton-Raphson 算法求解。随后，将计算程序编码在MATLAB软件中，并通过与其他已发布的解决方案进行比较来验证。最后，研究了输入参数对板非线性振动的影响。