基于C0-HSDT的FG-GRC板大挠度弯曲分析

LARGE DEFLECTION BENDING ANALYSIS OF FUNCTIONALLY GRADED GRAPHENE REINFORCED COMPOSITE PLATES BASED ON C0-HIGHER ORDER SHEAR DEFORMATION THEORY

  • 摘要: 基于含7变量的C0-高阶剪切变形理论(C0-HSDT)框架下,选取了经典的三阶剪切变形理论(TSDT)、正弦剪切变形理论(SSDT)和指数剪切变形理论(ESDT),结合冯卡门大挠度理论,建立了求解功能梯度石墨烯增强复合材料(FG-GRC)板大挠度弯曲分析有限元模型。FG-GRC板等效杨氏模量和等效泊松比分别由修正Halpin-Tsai微观力学物理模型和混合律确定。该模型满足了板顶面和底面零牵引力条件,可规避有限元法中难以构造C1连续性单元的特性。为避免传统C0-HSDT中人工转动变量引入而产生的误差,采用罚函数法施加人工限制条件。通过超收敛小片修正(SPR)技术和应力-应变关系分别计算面内应力及横向剪切应力。该文将FG-GRC物性关系退化为各向异性板和层合板,并与现有文献结果进行对比,验证了该文方法的收敛性和准确性,同时研究了C0-TSDT、C0-SSDT和C0-ESDT及罚因子对数值结果的影响。在此基础上进一步讨论了石墨烯纳米片(GPLs)分布模式、重量分数gGPL、几何参数等对FG-GRC板大挠度弯曲的影响。

     

    Abstract: Within the C0-higher-order shear deformation theory (C0-HSDT) framework with seven variables, the classical third-order shear deformation theory (TSDT), sinusoidal shear deformation theory (SSDT) and exponential shear deformation theory (ESDT) are selected. Based on the von Karman theory of large deflection, a finite element model is established to analyze the large deflection bending behavior of functionally graded graphene-reinforced composite (FG-GRC) plates. The equivalent Young's modulus and equivalent Poisson's ratio of the FG-GRC plate are determined using the modified Halpin-Tsai micromechanical model and the mixing rule. The model satisfies the zero traction condition on the top and bottom surfaces of the plate, which avoids the difficulties in constructing C1-continuous elements in the finite element method (FEM). To overcome errors introduced by the artificial rotational variables in traditional C0-HSDT, a penalty function is used to enforce artificial constraints. Super-convergent patch recovery (SPR) technique and stress-strain relation are used to calculate the in-plane stresses and transverse shear stresses. The FG-GRC material properties are first simplified to isotropic plates and laminated plates, and the results are compared with existing literature to validate the convergence and accuracy of the proposed method. The influences of C0-TSDT, C0-SSDT, C0-ESDT, and the penalty factor on the numerical results are investigated. Furthermore, the effects of graphene nanoplatelets (GPLs) distribution patterns, weight fraction (gGPL), geometric parameters, etc., on the large deflection bending of FG-GRC plates are discussed.

     

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