The linear and nonlinear forced vibration response of axially functionally graded (AFG) cylindrical truncated conical and imperfect microbeam subjected to the dynamic harmonically load carried out in ...the presented research. Based on a couple of modified couple stress theory, the Euler-Bernoulli beam theory and von-Kármán theory, the linear and nonlinear governing equations and related boundary conditions for dynamic response of micro-size tubes are derived employing the Hamilton principle. We considered the uniform and nonuniform functions for the cross-section, in which the convex, linear and exponential functions are the nonuniform sections, and the porosity is regarded as an imperfection. The generalized differential quadrature method (GDQM) is used to prepare the initial conditions for homotopy perturbation (HP) techniques as the semi-analytical approach to calculate the linear and nonlinear results of dynamic responses. The obtained linear and nonlinear results of the free and forced vibration response show the negative and positive effects of some parameters such as the porosity parameter, the nonlinear amplitude, the small-scale parameter, AFG parameter, and different cross-section impact on the dynamic deflection and natural frequency of micro-scale tube and beams with both clamped and simply-supported boundary conditions.
In functionally graded materials (FGMs), the elemental composition, or structure, within a component varies gradually as a function of position, allowing for the gradual transition from one alloy to ...another, and the local tailoring of properties. One method for fabricating FGMs with varying elemental composition is through layer-by-layer directed energy deposition additive manufacturing. This work combines experimental characterization and computational analysis to investigate a material graded from Ti-6Al-4V to Invar 36 (64 wt% Fe, 36 wt% Ni). The microstructure, composition, phases, and microhardness were determined as a function of position within the FGM. During the fabrication process, detrimental phases associated with the compositional blending of the Ti-6Al-4V and Invar formed, leading to cracking in the final deposited part. Intermetallic phases (FeTi, Fe2Ti, Ni3Ti, and NiTi2) were experimentally identified to occur throughout the gradient region, and were considered as the reason that the FGM cracked during fabrication. CALPHAD (CALculation of PHase Diagrams) thermodynamic calculations were used concurrently to predict phases that would form during the manufacturing process and were compared to the experimental results. The experimental-computational approach described herein for characterizing FGMs can be used to improve the understanding and design of other FGMs.
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This paper investigates the eigenvalue buckling of functionally graded graphene platelets (GPLs) reinforced cylindrical shells consisting of multiple layers through finite element method (FEM). The ...mechanical properties of the composites, including Young’s modulus, mass density and Poisson’s ratio, are determined by modified Halpin-Tsai model and rule of mixture. Parametric study is conducted to investigate the effects of the weight fraction, geometry and distribution of GPLs, number of layers, shell dimensions and existence of cutout on the buckling. The results show that apart from concentration the GPL distribution in polymer matrix significantly influences the buckling behaviors of the cylindrical structures. Larger sized GPLs with fewer graphene layers have better reinforcing effects than their counterparts with smaller surface area and more graphene layers. The distribution of stresses along the thickness of the shells suggests the increase of the number of layers significantly decreases the stress gradient between two neighboring layers, which is beneficial to reduce the risk of delamination. Moreover, the effects of cutout imperfection on the buckling behaviors of the cylindrical shells are comprehensively investigated.
Over the 2010s technological improvements allowed metal additive manufacturing to graduate from a prototyping tool to a widespread, full-scale manufacturing process. Among the capabilities still ...under development, however, is the ability to locally tailor alloy composition and properties to fabricate bulk, complex geometry functionally graded materials (FGMs), eliminating the need for dissimilar-metal welds and joints. The challenge of compositional grading involves overcoming chemical, metallurgical, and thermal property differences to achieve a continuous structure between a wide range of selected combinations of alloys. In this review, examples are discussed of fabricating FGMs joining a variety of combinations of stainless, nickel, titanium and copper alloys, and FGMs joining metals to ceramics and metal-matrix composites. The change in design strategy enabled by practical FGMs may lead to effective use of biomimetic designs that are both much more efficient as well as aesthetically pleasing.
Residual stress greatly affects the mechanic performance of the functionally graded materials (FGM). The residual stress distributions in different Si3N4/SiC FGMs formed in the fabricating processes ...were investigated with X-ray diffraction method in this work. It's found that residual stresses in FGMs with different component gradients were the gradient function of the quadratic of the component content and mainly determined by gradual changes of thermal mismatch and elastic modulus caused by the component content gradient. And the maximum tensile strength of FGM was limited by the ultimate tensile strength or shearing strength of SiC. When the maximum tensile strength exceeded the ultimate tensile strength or shearing strength of SiC and the maximum residual stress was maintained within the ultimate limit and resulted in the newly balanced stress distribution due to the same gradient function, cracks were formed. These results obviously provide ideas for regulating the performance and designing the FGM gradient for some special applications.
This study presents the buckling response of functionally graded (FG) “sandwich plate” on a viscoelastic foundation and exposed to hygrothermal conditions. An accurate solution is developed using ...higher-order shear deformation theory (HSDT), with only four unknowns being placed to reach the solution. The displacement fields first utilize an indeterminate integral accompanied by a sinusoidal shape function to simulate the transverse shear deformation theory. The foundation’s mathematical model followed the two-Pasternak coefficient model, with one more term being added to represent the damping effect. The sandwich plate is essentially composed of three layers. This study presented three different FG sandwich plate geometric analytical solutions regarding layer orders and composition. The equations of motion were generated according to Hamilton’s principle. Thereafter, the analytical solution was based on Navier’s principle to solve the buckling temperature of a simply supported FG sandwich plate seated on a viscoelastic foundation. This paper shows a parametric study of the effect of the damping coefficient along with the aspect ratio, moisture condition, power-law index, and temperature variation over the buckling temperature of the FG “sandwich plate” on the viscoelastic foundation.
•Effect of visco-Pasternak foundation on buckling response of FG plate is studied.•An efficient analytical approach is developed for buckling analysis.•Original integral shear deformation model has been used.•Influences of geometry, hygrothermal conditions and damping coefficient are explored.
•An accurate buckling analysis of FG porous GPLRC cylindrical shells is proposed.•Pre-buckling deformations and in-plane boundary conditions are considered.•Unified governing equations are ...established based on Donnell's theory and HSDT.•Highly accurate critical buckling loads and buckling mode shapes are obtained.•Effects of the material properties on stability of shells are detailedly discussed.
By considering the pre-buckling effect and in-plane constraint, an accurate nonlinear buckling analysis of a functionally graded porous graphene platelet reinforced composite cylindrical shells under axial compressive load is performed. The stability equation is established according to a unified shell theory including the classical thin shell theory and the high-order shear deformation theory. Three types of porosity distributions and graphene platelet reinforced patterns are considered, and the modified Halpin–Tsai model and rule of mixtures are employed to determine their effective material properties. Explicit expressions of buckling equations for clamped or simply supported boundary conditions are obtained by the Galerkin's method. Highly accurate critical buckling loads and analytical buckling mode shapes are obtained simultaneously. A comparison between theoretical prediction and experiment is presented to verify the present method and very good agreement is reported. The influences of material properties on the buckling behaviors are also extensively investigated. It is recommended that the symmetric dispersion pattern is the optimal material distributions for both graphene platelets and porous, and the largest possible weight fraction, specific surface area and average thickness of graphene platelets could induce a better anti-buckling performance for the nanocomposite shell.
Display omitted An accurate nonlinear buckling analysis for functionally graded (FG) porous graphene platelet reinforced composite (GPLRC) cylindrical shells is performed by considering the pre-buckling effect and in-plane constraint. Highly accurate critical buckling loads and analytical buckling mode shapes are obtained by a unified shell theory.
In this study, an efficient nonlocal finite element model is developed to investigate the bending and buckling behavior of functionally graded (FG) nanobeams. New two-node beam element with eight ...degrees of freedom is formulated based on the recently refined higher order shear deformation theory proposed by the authors. The present theory can provide an accurate parabolic distribution of transverse shear stress through the thickness direction satisfying the traction free boundary conditions needless of any shear correction factor. In order to capture the small size effect, Eringen’s nonlocal elasticity theory is incorporated. The material properties of the FG nanobeams are assumed to vary continuously through the thickness direction according to the power-law form. The performance and reliability of the proposed model is demonstrated by comparing the author’s results with those available in the literature. The numerical results show that the present element model is free of shear locking and has a high accuracy and fast rate of convergence. Moreover, a detailed numerical study is carried out to examine the effects of several parameters such as boundary conditions, power-law index, nonlocal parameter and length-to-height ratio on the deflection and critical buckling load of the FG nanobeams. Many new results are also reported in the current study, which will serve as a benchmark for future research.
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Functionally graded materials have the potential to improve upon monolithic parts by locally tailoring compositions to surrounding environmental conditions. Difficulties arise when ...designing composition gradients as incompatible materials can result in detrimental phase formation and failure of the gradient joint. As many alloys are multi-component, designing a composition gradient free of detrimental phases is difficult due to the large composition space available to explore. A framework was developed that improves the path planning algorithm and surrogate models with adaptive sampling schemes specific to their problem definition. A cost function was created to minimize a property (such as cracking susceptibility) along a path. This framework was applied to the Mo-Nb-Ta-Ti system as a case study to showcase the efficiency in building the surrogate models and in iterating different optimal compositionally graded paths.
•Large amplitude vibration of FG-GPLRC annular plates is investigated.•A DQM-based iterative method is developed to obtain the nonlinear frequencies.•Dispersing more GPLs within outer layers ...decreases the nonlinear frequency ratio.•The GPL geometry has little influence on the nonlinear vibration behaviour.
This paper investigates the large amplitude vibration of functionally graded nanocomposite multilayer annular plates reinforced with graphene platelets (GPLs) in thermal environments. It is assumed that the GPL concentration varies from layer to layer across the plate thickness but remains constant in each individual GPL-reinforced composite (GPLRC) layer, whose elastic modulus is estimated by the modified Halpin-Tsai micromechanics model. Within the framework of first-order shear deformation theory and von Kármán geometric nonlinearity, the governing equations are derived by using the Hamilton’s principle and then solve by the differential quadrature method together with an iterative scheme. Numerical results are presented to show the influences of GPL geometry, distribution pattern and concentration, plate geometry, boundary conditions, as well as temperature rise on the nonlinear vibration behaviour of functionally graded GPLRC annular plates. It is found that dispersing more GPLs within the outer layers substantially decreases the nonlinear frequency ratio, while the effect of GPL geometry is insignificant.
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