Abstract
The paper presents the extension of an edge-based smoothed finite element method using three-node triangular elements for dynamic analysis of the functionally graded porous (FGP) plates subjected to moving loads resting on the elastic foundation taking into mass (EFTIM). In this study, the edge-based smoothed technique is integrated with the mixed interpolation of the tensorial component technique for the three-node triangular element (MITC3) to give so-called ES-MITC3, which helps improve significantly the accuracy for the standard MITC3 element. The EFTIM model is formed by adding a mass parameter of foundation into the Winkler–Pasternak foundation model. Two parameters of the FGP materials, the power-law index (k) and the maximum porosity distributions (Ω), take forms of cosine functions. Some numerical results of the proposed method are compared with those of published works to verify the accuracy and reliability. Furthermore, the effects of geometric parameters and materials on forced vibration of the FGP plates resting on the EFTIM are also studied in detail.
Highlights
E paper presents the extension of an edge-based smoothed finite element method using three-node triangular elements for dynamic analysis of the functionally graded porous (FGP) plates subjected to moving loads resting on the elastic foundation taking into mass (EFTIM)
Nguyen et al developed the polygonal finite element method (PFEM) combined with HSDT to calculate the free vibration of FGP plates reinforced by the graphene platelet reinforcement (GPL) [34] and active-controlled vibration of the FGP plate reinforced by the GPL [35]
We examine the effects of porosity distributions on the dynamic response of the SSSS rectangular FGP plate with three different cases of porosity distributions: case 1, case 2, and case 3
Summary
Where w is the vertical displacement of the FGP plate; k1 and k2 are the Winkler foundation stiffness and shear layer stiffness of the Pasternak foundation, respectively; mf βμFρ in which the parameter β(kg− 1) is the influence level of the foundation mass on the free vibration response of the structures, which is determined by experiments; and μF is the density ratio of the foundation to the plate material (ρF/ρ). From equation (3), it can be seen that the investigation of the EFTIM model and Winkler–Pasternak foundation model on the static analysis is similar. These two models become complex in the dynamic response problems. If the influence of the foundation mass parameter is ignored, the EFTIM model will be equivalent to the Winkler–Pasternak foundation model, and the EFTIM model will be close to the EF model in practice
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