Wu Chih-Ping, Tan Tech-Fatt, Hsu Hao-Ting
Department of Civil Engineering, National Cheng Kung University, Tainan City 701, Taiwan.
Materials (Basel). 2023 Mar 15;16(6):2363. doi: 10.3390/ma16062363.
Within a framework of the consistent couple stress theory (CCST), a size-dependent finite element method (FEM) is developed. The three-dimensional (3D) free vibration characteristics of simply-supported, functionally graded (FG) graphene platelets (GPLs)-reinforced composite (GPLRC) cylindrical microshells are analyzed. In the formulation, the microshells are artificially divided into numerous finite microlayers. Fourier functions and Hermitian polynomials are used to interpolate the in-surface and out-of-surface variations in the displacement components induced in each microlayer. As a result, the second-order derivative continuity conditions for the displacement components at each nodal surface are satisfied. Five distribution patterns of GPLs varying in the thickness direction are considered, including uniform distribution (UD) and FG A-type, O-type, V-type, and X-type distributions. The accuracy and convergence of the CCST-based FEM are validated by comparing the solutions it produces with the exact and approximate 3D solutions for FG cylindrical macroshells reported in the literature, for which the material length scale parameter is set at zero. Numerical results show that by increasing the weight fraction of GPLs by 1%, the natural frequency of FG-GPLRC cylindrical microshells can be increased to more than twice that of the homogeneous cylindrical microshells. In addition, the effects of the material length scale parameter, the GPL distribution patterns, and the length-to-thickness ratio of GPLs on natural frequencies of the FG-GPLRC cylindrical microshells are significant.
在一致偶应力理论（CCST）框架内，开发了一种尺寸相关的有限元方法（FEM）。分析了简支功能梯度（FG）石墨烯片（GPLs）增强复合材料（GPLRC）圆柱微壳的三维（3D）自由振动特性。在公式推导中，微壳被人为地划分为许多有限微层。采用傅里叶函数和厄米多项式对每个微层中位移分量的面内和面外变化进行插值。结果，满足了每个节点表面位移分量的二阶导数连续性条件。考虑了GPLs在厚度方向上变化的五种分布模式，包括均匀分布（UD）和FG A型、O型、V型和X型分布。通过将基于CCST的有限元方法产生的解与文献中报道的FG圆柱宏壳的精确和近似3D解进行比较，验证了该方法的准确性和收敛性，其中材料长度尺度参数设为零。数值结果表明，将GPLs的重量分数增加1%，FG - GPLRC圆柱微壳的固有频率可提高到均质圆柱微壳固有频率的两倍以上。此外，材料长度尺度参数、GPL分布模式以及GPLs的长厚比对FG - GPLRC圆柱微壳固有频率的影响显著。
