改进Reddy型三阶剪切变形理论下FG-GRC板弯曲和模态分析的无网格法

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振动与冲击 ›› 2024, Vol. 43 ›› Issue (2) : 79-87.

论文

杨立军1，陈孔2，陈卫3

作者信息 +

Meshless method for the bending and modal analysis of FG-GRC plates based on the improved Reddy type third order shear deformation theory

YANG Lijun1，CHEN Kong2，CHEN Wei3

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文章历史 +

摘要

基于含7个自由度变量的改进Reddy型三阶剪切变形理论（TSDT）假设，采用稳定移动最小二乘近似（SMLS）的无网格法研究了功能梯度石墨烯增强复合材料（functionally graded graphene-reinforced composite ,FG-GRC）板结构的静态线性弯曲和自振模态。通过Halpin-Tsai模型来估算材料的有效杨氏模量，有效质量密度和泊松比由混合定律确定。利用最小势能原理和Hamition原理分别推导了FG-GRC板的线性弯曲和自振频率无网格控制方程。由于基于SMLS构造的形函数不满足克罗内克条件，故采用完全转换法处理本质边界条件。文中首先介绍了基于TSDT下FG-GRC板的SMLS离散模型。随后通过与已有成果进行比较，检验了本文方法的收敛性及准确性。最后数值分析了石墨烯片（GPLs）分布模式，重量分数、几何参数、总层数及边界条件等对FG-GRC板结构弯曲和模态的影响。

Abstract

Based on the assumption of the improved Reddy type third-order deformation theory (TSDT) with seven degrees of freedom variables, the static linear bending and natural vibration modes of functionally graded graphene-reinforced composite (FG-GRC) plate structures are studied by using the meshless method of stabilized moving least-square approximation (SMLS). The effective Young's modulus of the material is estimated by Halpin-Tsai model, and the effective mass density and Poisson's ratio are determined by the rule of mixture. The meshless governing equations of linear bending and natural frequency of FG-GRC plates are derived by using the principle of minimum potential energy and Hamilton principle, respectively. Since the shape function based on SMLS does not satisfy the Kronecker condition, the complete transformation method is used to deal with the essential boundary conditions. Firstly, the SMLS discrete model of FG-GRC plate based on TSDT is introduced. Then, the convergence and accuracy of this method are tested by comparing with the existing results. Finally, the effects of the distribution mode of graphene sheets (GPLs), weight fraction, geometric parameters, total number of layers and boundary conditions on the bending and mode of FG-GRC plate structure are numerically analyzed.

导出引用

杨立军1，陈孔2，陈卫3. 改进Reddy型三阶剪切变形理论下FG-GRC板弯曲和模态分析的无网格法[J]. 振动与冲击, 2024, 43(2): 79-87

YANG Lijun1，CHEN Kong2，CHEN Wei3. Meshless method for the bending and modal analysis of FG-GRC plates based on the improved Reddy type third order shear deformation theory[J]. Journal of Vibration and Shock, 2024, 43(2): 79-87

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