An Efficient Beam Element Based on Quasi-3D Theory for Static Bending Analysis of Functionally Graded Beams

Nguyen, Hoang-Nam; Hong, Tran Thi; Vinh, Pham Van; Thom, Do Van

doi:10.3390/ma12132198

Cited by 32 publications

(13 citation statements)

References 45 publications

(60 reference statements)

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“…at is the reason why numerous researchers focus on investigating the dynamic as well as static behaviors of the FGM structures, for example, beams [5][6][7][8][9][10], plates [11][12][13][14][15][16][17][18], shells [19][20][21], and other structures [22,23]. Many plate theories have been established and/or applied to investigate these structures, for example, classical plate theory (CPT), first-order shear deformation (FSDT), higherorder shear deformation theory (HSDT), and quasi-3D shear deformation theory.…”

Section: Introductionmentioning

confidence: 99%

Formulation of a New Mixed Four-Node Quadrilateral Element for Static Bending Analysis of Variable Thickness Functionally Graded Material Plates

Vinh

2021

Mathematical Problems in Engineering

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A new mixed four-node quadrilateral element (MiQ4) is established in this paper to investigate functionally graded material (FGM) plates with variable thickness. The proposed element is developed based on the first-order shear deformation and mixed finite element technique, so the new element does not need any selective or reduced numerical integration. Numerous basic tests have been carried out to demonstrate the accuracy and convergence of the proposed element. Besides, the numerical examples show that the present element is free of shear locking and is insensitive to the mesh distortion, especially for the case of very thin plates. The present element can be applied to analyze plates with arbitrary geometries; it leads to reducing the computation cost. Several parameter studies are performed to show the roles of some parameters such as the power-law index, side-to-thickness ratio, boundary conditions (BCs), and variation of the plate thickness on the static bending behavior of the FGM plates.

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Section: Introductionmentioning

confidence: 99%

Formulation of a New Mixed Four-Node Quadrilateral Element for Static Bending Analysis of Variable Thickness Functionally Graded Material Plates

Vinh

2021

Mathematical Problems in Engineering

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“…In the last decades of the twentieth century, functionally graded materials (FGMs) have been become the most innovative composite materials and applied in many fields of engineering. [1][2][3][4][5] Because of their exotic properties, the application and investigation of FGM beams, plates and shells are increasing rapidly. Therefore, enormous beam, plate and shell theories were established and applied to scrutinize FGM structures, especially FGM plates.…”

Section: Introductionmentioning

confidence: 99%

Bending and free vibration analyses of functionally graded material nanoplates via a novel nonlocal single variable shear deformation plate theory

Hoa

Vinh

Duc

et al. 2020

Proceedings of the Institution of Mechanical Engineers, Part C:

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A novel nonlocal shear deformation theory is established to investigate functionally graded nanoplates. The significant benefit of this theory is that it consists of only one unknown variable in its displacement formula and governing differential equation, but it can take into account both the quadratic distribution of the shear strains and stresses through the plate thickness as well as the small-scale effects on nanostructures. The numerical solutions of simply supported rectangular functionally graded material nanoplates are carried out by applying the Navier procedure. To indicate the accuracy and convergence of this theory, the present solutions have been compared with other published results. Furthermore, a deep parameter study is also carried out to exhibit the influence of some parameters on the response of the functionally graded material nanoplates.

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“…In order to study the static bending of FG beams under different boundary conditions, Nguyen et al 55 developed an effective twonoded beam element with five DOFs per node based on Quasi-3D HSDT. Recently, Koutoati et al 56 used three finite element models based on CPT, FSDT and HSDT to study the static and free vibration behaviors of FGM sandwich beams. They concluded that the axial bending and shear coupling affect the behavior of the FGM sandwich beams in both statics and dynamics.…”

Section: Introductionmentioning

confidence: 99%

Finite element bending analysis of symmetric and non-symmetric functionally graded sandwich beams using a novel parabolic shear deformation theory

Belarbi

Khechai

Bessaim

et al. 2021

Proceedings of the Institution of Mechanical Engineers, Part L:

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In this paper, the bending behavior of functionally graded single-layered, symmetric and non-symmetric sandwich beams is investigated according to a new higher order shear deformation theory. Based on this theory, a novel parabolic shear deformation function is developed and applied to investigate the bending response of sandwich beams with homogeneous hardcore and softcore. The present theory provides an accurate parabolic distribution of transverse shear stress across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the functionally graded sandwich beam without using any shear correction factors. The governing equations derived herein are solved by employing the finite element method using a two-node beam element, developed for this purpose. The material properties of functionally graded sandwich beams are graded through the thickness according to the power-law distribution. The predictive capability of the proposed finite element model is demonstrated through illustrative examples. Four types of beam support, i.e. simply-simply, clamped-free, clamped–clamped, and clamped-simply, are used to study how the beam deflection and both axial and transverse shear stresses are affected by the variation of volume fraction index and beam length-to-height ratio. Results of the numerical analysis have been reported and compared with those available in the open literature to evaluate the accuracy and robustness of the proposed finite element model. The comparisons with other higher order shear deformation theories verify that the proposed beam element is accurate, presents fast rate of convergence to the reference results and it is also valid for both thin and thick functionally graded sandwich beams. Further, some new results are reported in the current study, which will serve as a benchmark for future research.

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An Efficient Beam Element Based on Quasi-3D Theory for Static Bending Analysis of Functionally Graded Beams

Cited by 32 publications

References 45 publications

Formulation of a New Mixed Four-Node Quadrilateral Element for Static Bending Analysis of Variable Thickness Functionally Graded Material Plates

Formulation of a New Mixed Four-Node Quadrilateral Element for Static Bending Analysis of Variable Thickness Functionally Graded Material Plates

Bending and free vibration analyses of functionally graded material nanoplates via a novel nonlocal single variable shear deformation plate theory

Finite element bending analysis of symmetric and non-symmetric functionally graded sandwich beams using a novel parabolic shear deformation theory

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