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

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Journal of Vibration and Shock ›› 2024, Vol. 43 ›› Issue (2) : 79-87.

YANG Lijun1，CHEN Kong2，CHEN Wei3

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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.

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improved Reddy type third-order shear deformation theory / functionally graded graphene-reinforced composite plate / stabilized moving least-square approximation / linear bending / natural frequency

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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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