# Introduction to Functionally Graded

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## Functionally Graded sentence examples within carbon nanotube reinforced

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In this paper, a first known study on the large deformation dynamic behavior of functionally graded carbon nanotube-reinforced (CNTR) nanocomposite cylinder considering the particle/matrix interphase property is presented.

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On the basis of that, an accurate and analytical method for investigation the dynamic instability of laminated functionally graded carbon nanotube reinforced composite (FG-CNTRC) conical shell surrounded by the elastic foundations is presented in this work based on the first-order shear deformation theory.

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## Functionally Graded sentence examples within finite element method

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OBJECTIVE: The aim of this work is to present the methodology for grading the Functionally Graded Material (FGM) using Level Set (LS) sign distance function around the multiple holes and parametrically analyse the maximum stresses for a pair of inclined unequal circular holes surrounded by the FGM layer in an infinite plate subjected to uniaxial tensile load using the Extended Finite Element Method (XFEM).

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In this paper, the free vibration of the functionally graded porous (FGP) non-uniform annular-nanoplates lying on Winkler foundation (WF) is studied by using the smoothed finite element method based on the first-order shear deformation theory (FSDT).

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## Functionally Graded sentence examples within higher order shear

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In this paper, a higher order shear deformation theory for bending analysis of functionally graded plates resting on Pasternak foundation and under various boundary conditions is exposed.

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This paper introduces a comprehensive investigation of bi-directional functionally graded sandwich plates using higher-order shear deformation theory and finite element method for the first time.

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## Functionally Graded sentence examples within first order shear

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Based on the geometrically exact beam theory, a first-order shear deformable curved beam element is developed for geometrically nonlinear analysis of functionally graded (FG) curved beams.

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This article proposes a general method to investigate the vibration characteristics of functionally graded corrugated plate structure (FGCPS) according to first-order shear deformation theory (FSDT) by adopting differential quadrature finite element method (DQFEM).

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## Functionally Graded sentence examples within nonlocal strain gradient

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The main goal of this research paper is to present the modeling and analysis of bi-directional functionally graded (BDFG) nanobeams within the framework of the Timoshenko beam theory and nonlocal strain gradient theory.

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A mathematical model for bi-directional functionally graded Euler-Bernoulli nanobeams has been developed based on nonlocal strain gradient theory intervened with Gurtin-Murdoch surface elasticity theory.

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## Functionally Graded sentence examples within graphene platelets reinforced

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In this study, the effect of nonlinear temperature gradient on the natural frequencies of functionally graded graphene platelets reinforced composite (FG-GPLRC) viscoelastic plate embedded in the v.

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The present work focuses on the size-dependent postbuckling characteristics of functionally graded (FG) graphene platelets reinforced composite (GPLRC) multilayer microtubes containing initial geometrical imperfection.

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## Functionally Graded sentence examples within shear deformation theory

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This work is the first exploration using the new shear deformation theory-type hyperbolic sine functions to carry out the free vibration analysis of the rotating functionally graded graphene beam resting on the elastic foundation taking into account the effects of both temperature and the initial geometrical imperfection.

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A new shear deformation theory is introduced to conduct free vibration analysis of the functionally graded plates with simply supported boundary conditions.

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## Functionally Graded sentence examples within magneto electro elastic

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The studied sandwich structure is consisted of a viscoelastic core that is located between the faces of functionally graded magneto-electro-elastic (FG-MEE).

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In the paper, a novel magneto electro elastic ( model of bi-directional ( 2 D) functionally graded material s (FGM s ) beam s is developed for investigating the nonlinear dynamics It is shown that the asymmetric modes induced by the 2D FGM s may significantly affect the nonlinear dynamic responses which is tremendously different from previous studies Taking into account the geometric nonlinearity, the nonlinear equation of motion and associated boundary conditions for the beam s are derived according to the Hamilton’s principle The linear frequencies and modes of the beam s are numerically calculated by the generalized differential quadrature method (GDQM) GDQM).

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## Functionally Graded sentence examples within high order shear

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The buckling behavior of functionally graded rectangular plates under mechanical and thermal loading is investigated using a four-node finite element based on a simple high-order shear deformation theory.

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In the present study, a simple four-node high-order shear deformation plate bending element based on modified first-order shear deformation theory has been developed to analyze functionally graded plates subjected to both sinusoidal or uniformly distributed transversal loads.

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## Functionally Graded sentence examples within finite element model

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In this research, a layerwise based finite element model is presented to obtain the transient responses for functionally graded material sandwich (FGM-SW) plates under blast load.

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In this study, an efficient nonlocal finite element model is developed to investigate the bending and buckling behavior of functionally graded (FG) nanobeams.

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## Functionally Graded sentence examples within directed energy deposition

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ABSTRACT Directed energy deposition (DED) shows outstanding advantages in manufacturing complex and functionally graded parts.

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An additive manufacturing (AM) functionally graded tungsten carbide using laser directed energy deposition (L-DED) is developed in an integrated numerically controlled multi-axis machining center with multi-material feeding capability.

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## Functionally Graded sentence examples within graphene platelet reinforced

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Presented herein is a novel numerical approach for the vibrational analysis of conical panels with arbitrary-shaped holes made of functionally graded graphene platelet-reinforced composite (FG-GPLRC) within the framework of higher-order shear deformation theory (HSDT).

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It is also assumed that the panel is made of functionally graded graphene platelet-reinforced composite with various patterns for the distribution of GPLs along the thickness direction whose effective properties are estimated using the modified Halpin–Tsai model in conjunction with the rule of mixture.

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## Functionally Graded sentence examples within nonlinear free vibration

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This paper investigates the nonlinear free vibration and nonlinear dynamic hygrothermal buckling behavior of imperfect functionally graded carbon nanotube-reinforced composite (FG-CNTRC) cylindrical panels under hygrothermal environment.

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The present study develops a size-dependent Euler–Bernoulli beam model to analyze the nonlinear free vibration of a bidirectional functionally graded (BFG) nanobeam with immovable ends, based on the nonlocal theory.

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## Functionally Graded sentence examples within carbon nanotubes reinforced

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This work studies the dynamic response of Bernoulli–Euler multilayered polymer functionally graded carbon nanotubes-reinforced composite nano-beams subjected to hygro-thermal environments.

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Also, the twisting deformation of torsion nanobeam can be tuned by functionally graded carbon nanotubes reinforced composites (FG-CNTRC).

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## Functionally Graded sentence examples within nonlocal elasticity theory

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In this article, we explore a three-dimensional solid isogeometric analysis (3D-IGA) approach based on a nonlocal elasticity theory to investigate size effects on natural frequency and critical buckling load for multi-directional functionally graded (FG) nanoshells.

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In this article, the bending analysis of flexoelectric functionally graded (FG) microbeams according to nonlocal elasticity theory is verified.

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## Functionally Graded sentence examples within free vibration behavior

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ABSTRACT Free vibration behaviors of a functionally graded (FG) disk-shaft rotor system reinforced with graphene nanoplatelet (GPL) resting on elastic supports are investigated in this paper.

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This work presents an investigation on the free vibration behavior of rotating pre-twisted functionally graded graphene platelets reinforced composite (FG-GPLRC) laminated blades/beams with an atta.

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## Functionally Graded sentence examples within refined plate theory

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In this paper, the size-dependent analysis of geometrically imperfect porous functionally graded (FG) nanoplates is studied by an isogeometric approach based on a new refined plate theory.

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In this study, static analysis of functionally graded (FG) sandwich plates is performed using the finite strip method based on the refined plate theory (RPT).

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## Functionally Graded sentence examples within size dependent nonlinear

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In the present paper, a continuous-based electromechanical model has been developed by the Kirchhoff plate's theory and the modified flexoelectric theory in order to study the size-dependent nonlinear free vibration of functionally graded flexoelectric nano-plate.

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This study presents the size-dependent nonlinear thermal postbuckling characteristics of a porous functionally graded material (PFGM) microplate with a central cutout with various shapes using isogeometric numerical technique incorporating non-uniform rational B-splines.

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## Functionally Graded sentence examples within boundary element method

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The paper describes the Field Boundary Element Method applied to the fracture analysis of a 2D rectangular plate made of Functionally Graded Material to calculate Mode I Stress Intensity Factor.

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A domain-boundary element method, based on modified couple stress theory, is developed for transient dynamic analysis of functionally graded micro-beams.

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## Functionally Graded sentence examples within scaled boundary finite

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In this research, free and forced vibrations of the functionally graded material (FGM) sandwich beams are investigated by using the scaled boundary finite element method (SBFEM).

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For the stability analysis of functionally graded material (FGM) sandwich plates, a semi-analytical scaled boundary finite element method (SBFEM) is established within the frame work of layerwise t.

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## Functionally Graded sentence examples within sandwich cylindrical shell

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The main objective of this research work is focused on acoustic radiation analysis of functionally graded material (FGM) sandwich cylindrical shell structure reinforced by periodically eccentrically ring stiffeners.

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The nonlinear forced vibrations of functionally graded material (FGM) sandwich cylindrical shells with porosities on an elastic substrate are studied.

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## Functionally Graded sentence examples within shape memory alloy

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A new model is developed for bending of functionally graded (FG) porous shape memory alloy (SMA)/poroelastic composite cantilever beams.

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This paper focuses on the size-dependent behaviors of functionally graded shape memory alloy (FG-SMA) microbeams based on the Bernoulli-Euler beam theory.

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## Functionally Graded sentence examples within rotor bearing system

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The present study aims to carry out finite element analysis to investigate the natural and whirl frequencies of a functionally graded (FG) rotor-bearing system modeled following the exponential law gradation.

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The present work aims to analyze the natural and whirl frequencies of a slant-cracked functionally graded rotor-bearing system using finite element analysis for the flexural vibrations.

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## Functionally Graded sentence examples within quasi three dimensional

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This work proposes a novel quasi three-dimensional (3D) approach for the bending analysis of moderately thick plates with a functionally graded material (FGM), in presence of porosities due to some incorrect manufacturing processes.

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In this work, the bending behavior of functionally graded (FG) porous plates connected with a layer made of piezoelectric fiber-reinforced composite (PFRC) on the upper surface is presented via a quasi-three dimensional (3D) refined shear and normal deformation theory.

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## Functionally Graded sentence examples within single walled carbon

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This analytical work deals with the dynamic analysis of the functionally graded composite plate reinforced with single walled carbon nanotubes is discussed in this article.

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This article presents continuous interlaminar shear stress analysis of laminated beams with functionally graded single-walled carbon nanotube reinforced composite (FG-CNTRC) layers based on an exte.

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## Functionally Graded sentence examples within higher shear deformation

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In this work a novel integral higher shear deformation theory (HSDT) which introducing the transverse shear effect is developed for thermoelastic bending analysis of Titanium/Zirconia power-law functionally graded (P-FG) sandwich plates.

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In this article, the mechanical buckling analysis of simply-supported functionally graded plates is carried out using a
higher shear deformation theory (HSDT) in conjunction with the stress function method.

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## Functionally Graded sentence examples within paper presents analytical

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This paper presents analytical studies on the dynamic instability of functionally graded material (FGM) sandwich conical shell subjected to time dependent periodic parametric axial and lateral load.

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This paper presents analytical investigations on the free vibration and static bending of functionally graded graphene-reinforced nanocomposite (FG-GPLRC) spherical shells.

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## Functionally Graded sentence examples within graphene reinforced composite

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In this numerical study, four different graphene sheets distributions, such as uniformly distributed (UD), functionally graded (FG-X), functionally graded (FG-O), and functionally graded (FG-V), are considered for the free vibration of graphene reinforced composite (GRC) stiffened plate.

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This paper investigates the buckling behaviors of edge-cracked functionally graded graphene reinforced composite (FG-GRC) beam with piezoelectric actuators.

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## Functionally Graded sentence examples within semi analytical method

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In this article, the free vibration characteristics and wave propagation analysis of functionally graded materials (FGM) cylindrical nanoshell is investigated by a semi-analytical method, wave-based method.

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In this paper, a semi-analytical method is presented for nonlinear vibration analysis of rotating stiffened truncated conical shells with functionally graded materials (FGM) in the thermal environm.

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## Functionally Graded sentence examples within finite difference method

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This paper presents an approach to the vibration analysis of axially functionally graded (AFG) non-prismatic Euler-Bernoulli beams using the finite difference method (FDM).

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