Three-dimensional polyhedral finite element method for the analysis of multi-directional functionally graded solid shells

Nguyen-Ngoc, Hau; Cuong-Le, Thanh; Nguyen, Khuong D.; Nguyen‐Xuan, H.; Abdel-Wahab, M.

doi:10.1016/j.compstruct.2022.116538

Cited by 15 publications

(4 citation statements)

References 42 publications

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“…The discrete system of linear equilibrium equation under small strain condition can be expressed as h Ku = F (11) where u h contains the normal displacements u and the enriched degrees of freedom a…”

Section: The Extended Consecutive-interpolation 4-node Quadrilateral ...mentioning

confidence: 99%

Fracture analysis in 2D plane strain problems for composite materials containing hard inclusions and voids using an extended consecutive-interpolation quadrilateral element

Hoang,

Lo,

Tran

et al. 2023

Vietnam J. Sci. Technol.

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This paper investigates fracture mechanics in particle-reinforced composites by using the extended finite element method enhanced by the consecutive-interpolation quadrilateral element. These composite materials have discontinuous boundaries such as cracks, voids, holes, and soft inclusions. And the extended consecutive-interpolation quadrilateral element (XCQ4) is employed to model these boundaries in two-dimensional linear elastic deformation problems. XCQ4 combines the enrichment functions in the traditional extended finite element method with the consecutive interpolation on a 4-node quadrilateral element. This element uses both nodal values and averaged nodal gradients as interpolated conditions. In fracture analysis, the stress intensity factors (SIFs) are important parameters that must be defined. In this study, the values of SIFs at the crack tips are evaluated with the help of the interaction integrals approach. The obtained numerical results are compared with other reliable results showing high accuracy and convergence rate of the XCQ4 element.

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Section: The Extended Consecutive-interpolation 4-node Quadrilateral ...mentioning

confidence: 99%

Fracture analysis in 2D plane strain problems for composite materials containing hard inclusions and voids using an extended consecutive-interpolation quadrilateral element

Hoang,

Lo,

Tran

et al. 2023

Vietnam J. Sci. Technol.

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“…Static and dynamic analyses of three-dimensional shells composed of multi-directional FG material (MD FGM) have been carried out using polyhedral finite element methods. That study explored the effects of shell thickness and slenderness on structural behavior [16]. The bending analysis of multilayer panels of FGMs was performed using a higher-order layer-wise model, with Young's modulus determined via the Halpin-Tsai method and Poisson's ratio via the rule of mixture [17].…”

Section: Introductionmentioning

confidence: 99%

Multi-Directional Functionally Graded Sandwich Plates: Buckling and Free Vibration Analysis with Refined Plate Models under Various Boundary Conditions

Hadji,

Plevris,

Madan

et al. 2024

Computation

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This study conducts buckling and free vibration analyses of multi-directional functionally graded sandwich plates subjected to various boundary conditions. Two scenarios are considered: a functionally graded (FG) skin with a homogeneous hard core, and an FG skin with a homogeneous soft core. Utilizing refined plate models, which incorporate a parabolic distribution of transverse shear stresses while ensuring zero shear stresses on both the upper and lower surfaces, equations of motion are derived using Hamilton’s principle. Analytical solutions for the buckling and free vibration analyses of multi-directional FG sandwich plates under diverse boundary conditions are developed and presented. The obtained results are validated against the existing literature for both the buckling and free vibration analyses. The composition of metal–ceramic-based FG materials varies longitudinally and transversely, following a power law. Various types of sandwich plates are considered, accounting for plate symmetry and layer thicknesses. This investigation explores the influence of several parameters on buckling and free vibration behaviors.

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“…Niknam et al [25] presented the model of architected multi-directional FGM cellular materials. Based on polyhedral finite elements, Nguyen-Ngoc et al [26] established a three-dimensional numerical model to explore the static bending and free vibration of multidirectional FGM shells. Asgari and Akhlaghi [27] investigated the free vibration behaviors of two-directional FGM hollow cylinder shells.…”

Section: Introductionmentioning

confidence: 99%

A Dynamic Analysis of Porous Coated Functionally Graded Nanoshells Rested on Viscoelastic Medium

et al. 2023

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Theoretical research has numerous challenges, particularly about modeling structures, unlike experimental analysis, which explores the mechanical behavior of complex structures. Therefore, this study suggests a new model for functionally graded shell structures called “Tri-coated FGM” using a spatial variation of material properties to investigate the free vibration response incorporating the porosities and microstructure-dependent effects. Two types of tri-coated FG shells are investigated, hardcore and softcore FG shells, and five distribution patterns are proposed. A novel modified field of displacement is proposed by reducing the number of variables from five to four by considering the shear deformation effect. The shell is rested on a viscoelastic Winkler/Pasternak foundation. An analytical solution based on the Galerkin approach is developed to solve the equations of motion derived by applying the principle of Hamilton. The proposed solution is addressed to study different boundary conditions. The current study conducts an extensive parametric analysis to investigate the influence of several factors, including coated FG nanoshell types and distribution patterns, gradient material distribution, porosities, length scale parameter (nonlocal), material scale parameter (gradient), nanoshell geometry, and elastic foundation variation on the fundamental frequencies. The provided results show the accuracy of the developed technique using different boundary conditions.

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Three-dimensional polyhedral finite element method for the analysis of multi-directional functionally graded solid shells

Cited by 15 publications

References 42 publications

Fracture analysis in 2D plane strain problems for composite materials containing hard inclusions and voids using an extended consecutive-interpolation quadrilateral element

Fracture analysis in 2D plane strain problems for composite materials containing hard inclusions and voids using an extended consecutive-interpolation quadrilateral element

Multi-Directional Functionally Graded Sandwich Plates: Buckling and Free Vibration Analysis with Refined Plate Models under Various Boundary Conditions

A Dynamic Analysis of Porous Coated Functionally Graded Nanoshells Rested on Viscoelastic Medium

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