高阶剪切变形板理论下FG-GRC板的屈曲和弯曲分析

基于三阶剪切变形板理论(TSDPT)和正弦剪切变形板理论(SSDPT)，研究了功能梯度石墨烯增强复合材料(FG-GRC)板的屈曲和弯曲行为，并通过与一阶剪切变形板理论(FSDPT)计算结果的比较，分析了TSDPT、SSDPT与FSDPT在FG-GRC板屈曲和弯曲力学行为研究过程中的差异。材料的有效杨氏模量通过修正的Halpin-Tsai微观力学模型估算，有效泊松比通过混合律确定。利用最小势能原理推导出了包含五个未知量的控制方程，并获得了简支FG-GRC矩形板弯曲挠度和临界屈曲载荷Navier形式的解析解。数值结果表明：与TSDPT和SSDPT相比，FSDPT明显高估了FG-X型FG-GRC板的临界屈曲载荷而明显低估了其弯曲挠度，且略微低估了FG-O型FG-GRC板的临界屈曲载荷而略微高估了其弯曲挠度，而UD型和FG-A型FG-GRC板在三种理论下的计算结果几乎完全一致；TSDPT和SSDPT在计算FG-GRC板的弯曲挠度和临界屈曲载荷时结果十分相近；当板的总层数NL小于10层～15层时，弯曲载荷比率和临界屈曲载荷比率的变化非常显著，当总层数NL超过10层～15层时，弯曲载荷比率和临界屈...

BUCKLING AND BENDING ANALYSIS OF FG-GRC PLATES USING HIGH-ORDER SHEAR DEFORMATION PLATE THEORIES

Based on the third-order shear deformation plate theory (TSDPT) and sinusoidal shear deformation plate theory (SSDPT), the buckling and bending behaviors of functionally graded graphene-reinforced composite (FG-GRC) plates were investigated. By comparing the calculated results with the first-order shear deformation plate theory (FSDPT), the differences among TSDPT, SSDPT and FSDPT in the buckling and bending mechanical behaviors of FG-GRC plates were analyzed. The effective Young's modulus is estimated using the modified Halpin-Tsai model, and the effective Poisson's ratio is determined using the rule of mixtures. The governing equations containing five unknown quantities are derived using the principle of minimum potential energy, and the analytical solutions in Navier form for the bending deflection and critical buckling load of simply supported FG-GRC rectangular plates are obtained. Numerical results show that: Compared with TSDPT and SSDPT, FSDPT significantly overestimates the critical buckling load and significantly underestimates the bending deflection of FG-X type FG-GRC plate, and slightly underestimates the critical buckling load and slightly overestimates the bending deflection of FG-O type FG-GRC plate, while the calculated results of UD type and FG-A type FG-GRC plate are almost identical using the three theories; The results of TSDPT and SSDPT are very similar in calculating the bending deflection and critical buckling load of FG-GRC plates; When the total number of layers N_L of the plate is less than 10~15, the variation of the ratio of bending load and the ratio of critical buckling load is significant. When N_L exceeds 10~15, The variation of these two ratios become small; Due to the extremely high modulus of elasticity of graphene nanoplatelets (GPLs), the weight fraction f_G of GPLs in FG-GRC plates is positively correlated with the capability of the plates to resist bending and buckling.