Functionally graded materials

This study addresses free vibration analysis of rotating Functionally Graded Material (FGM) beams lying on elastic foundations using the Homotopy Perturbation Method (HPM). The HPM, a semi-analytical technique combining Homotopy from topology with perturbation methods to solve complex nonlinear equations, is employed to solve the resulting nonlinear eigenvalue problem. Its key advantages include effectively handling system inhomogeneity and nonlinearity while yielding insightful semianalytical expressions. The resulting governing equations, based on Euler-Bernoulli beam theory and Hamilton's principle, are nondimensionalized to capture centrifugal stiffening, foundation interaction, and material gradation. The HPM is used to solve the obtained nonlinear eigenvalue problem, and the dimensionless natural frequencies and mode shapes are obtained for clamped-clamped (C-C), clamped-simply supported (C-S), and clamped-free (C-F) boundary conditions. Validation against Finite Element Method (FEM) and Lagrange-based solutions confirms the high accuracy of HPM, with relative errors consistently less than 2%. Parametric studies show that dimensionless natural frequencies increase as η and λ increase, whereas the increase of the gradient index of FGM (n) leads to lower frequency values due to the severity degradation (ceramic to metal control). Importantly, CC boundaries display a 4-5 times higher frequency than C-F configurations, emphasizing boundaries as key limiting factors for design. This study fills a significant void in rotating FGM beam dynamics and demonstrates HPM's capability for complex systems, providing valuable semianalytical tools for engineering design applications such as turbine blades, robotic arms, and rotating machines in extreme environments.

Functionally Graded Materials (FGMs) represent a notable advancement in materials research as they enable the smooth incorporation of distinct characteristics from various materials. This study examines the vibrational characteristics of functionally graded ceramic-metal composite beams via the use of Finite Element Analysis (FEA) in MATLAB. To capture and study the dynamic response of the replicas. The focus of this investigation is on ceramic and metallic materials that are represented by power-law distribution along their length. In order to include material variation in the global mass and stiffness matrices, the beam segments have been divided into many sections. In this regard, the objective was to calculate natural frequencies and mode shapes of these beams using eigenvalue problems. Results obtained reveal that MATLAB is a reliable tool for investigating dynamic properties of Functionally Graded Materials (FGMs) because it has proven to be user-friendly as well. The present work shows how to use functionally graded indices and porosity on vibration characteristics of composite beams.

The present study deals with buckling, free vibration, and bending analysis of Functionally Graded (FG) and porous FG beams based on various beam theories. Equation of motion and boundary conditions are derived from Hamilton's principle, and the finite element method is adopted to solve problems numerically. The FG beams are graded through the thickness direction, and the material distribution is controlled by power-law volume fraction. The effects of the different values of the power-law index, porosity exponent, and different boundary conditions on bending, natural frequencies and buckling characteristics are also studied. A new function is introduced to approximate the transverse shear strain in higher-order shear deformation theory. Furthermore, shifting the position of the neutral axis is taken into account. The results obtained numerically are validated with results obtained from ANSYS and those available in the previous work. The results of this study specify the crucial role of slenderness ratio, material distribution, and porosity condition on the characteristic of FG beams. The deflection results obtained by the proposed function have a maximum of six percent difference when the results are compared with ANSYS. It also has better results in comparison with the Reddy formulae, especially when the beam becomes slender.

Functionally gradient materials are one of the most widely used materials. The objective of this research work is to perform a thermo-mechanical analysis of functionally gradient material square laminated plate made of Aluminum / Zirconia and compare with pure metal and ceramic. The plates are assumed to have isotropic, two-constituent material distribution through the thickness, and the modulus of elasticity of the plate is assumed to vary according to a power-law distribution in terms of the volume fractions of the constituents. To achieve this objective, we shall use first shear deformation theory of plates and numerical analysis will be accomplished using finite element model prepared in ANSYS software. The laminated Functionally Gradient Material plate is divided in to layers and their associated properties are then layered together to establish the through-the-thickness variation of material properties. The displacement fields for functionally gradient material plate structures under mechanical, thermal and thermo mechanical loads are analyzed under simply supported boundary condition

An analytical thermoelasticity solution for a disc made of functionally graded materials (FGMs) is presented. Infinitesimal deformation theory of elasticity and power law distribution for functional gradation are used in the solution procedure. Some relative results for the stress and displacement components along the radius are presented due to internal pressure, external pressure, centrifugal force and steady state temperature. From the results, it is found that the grading indexes play an important role in determining the thermomechanical responses of FG disc and in optimal design of these structures.

Additive manufacturing (AM) has revolutionised the fabrication of architected lattice structures, enabling tunable mechanical properties, enhanced fatigue resistance, and biointegration, making them suitable for biomedical, aerospace, and high-performance structural applications. Among these, triply periodic minimal surface (TPMS) lattices and stochastic porous networks have demonstrated superior stress shielding mitigation, fatigue behaviour, and osseointegration potential compared to conventional strut-based designs. Functionally graded TPMS scaffolds improve fatigue life by up to 30% compared to uniform designs, whereas biomimetic gyroid and primitive lattices enhance bone ingrowth and vascularisation, closely mimicking native bone morphology. Despite these advantages, understanding their behaviour under multiaxial fatigue remains limited, posing challenges for practical applications. Post-processing effects and pore size optimisation for tissue integration remain critical challenges that require further investigation. This review evaluates AM lattice structures' mechanical behaviour, fatigue performance, and osseointegration potential. Functionally graded TPMS scaffolds improve fatigue life by up to 30%, whereas biomimetic gyroid and primitive lattices enhance bone ingrowth and vascularisation, closely mimicking native bone morphology. Post-processing strategies, such as hot isostatic pressing and electropolishing, significantly affect the fatigue life, surface roughness, and mechanical properties. Research is needed to optimise pore size distribution and multidirectional porosity gradients to enhance biomechanical adaptation and long-term implant stability.

A three-dimensional (3D) finite-element-method (FEM) formulation is developed to investigate the response of functionally graded material (FGM) multiferroic composites under different types of loads. Numerical examples are carried out for the threelayered piezoelectric (PE)/piezomagnetic (PM) composite with its top and bottom layers being FGMs and the middle layer homogenous PE material. For the FGM layer, two cases of material grading along the thickness direction of the composite are considered: one is the PM material with the properties varying as an exponential function (E-FGM) and the other is the PE/PM composite material with the volume ratios varying as a power-law function (P-FGM). The effect of different material grading functions on the mechanical, electric and magnetic responses is clearly showed by both E-FGM and P-FGM grading cases, which could be useful to the future design of FGM multiferroic devices.

This study considers Timoshenko beam theory and the isogeometric analysis method to investigate the free vibration and buckling of axially functionally graded (AFG) tapered beams. The governing equations are obtained from the kinematic assumptions of Timoshenko beam theory and Hamilton's principle. The isogeometric analysis approach is implemented to solve the motion equations. One-dimensional B-spline basis functions are used to estimate the displacement field, describe the geometry, and illustrate the deformed shapes of the beam. Due to suffering the isogeometric approach from the shear locking phenomenon, the selectively reduced integration is applied. It is shown that this method can mitigate the effect of shear locking. In this attempt, the effect of material non-homogeneity parameters, mass density, Young's modulus, and taper ratio on the critical buckling loads and natural frequencies are considered for various boundary conditions. Several numerical examples show the accuracy and reliability of this method. The obtained results are in accord with the ones in the related articles and can be adopted as future reference solutions.

Functionally graded WC-Co materials can be manufactured by controlling liquid phase migration or liquid redistribution during liquid phase sintering. The driving force of liquid phase migration is liquid migration pressure P m which depends on the solid particle size d and the liquid phase volume fraction u. In this study, the effect of d on P m has been studied experimentally for WC-Co system. The results show that P m is proportional to 1/d 0.4 which is different from previous postulation that P m is proportional to 1/d. The reason for this difference is that the previous postulation was based on the assumption that all the solid particles in a composite are mono-sized and isometric-shaped, while in real WC-Co composites WC particles usually have non-isometric shape and there is a wide particle size distribution. The dependence of P m on both d and u has been quantitatively established, enabling the prediction of final Co composition gradient in liquid-phase-sintered WC-Co composites.

This study investigates the 3D motion of a rigid body (RB) rotating around a fixed point, focusing on Lagrange's case while considering the effects of a gyrostatic moment (GM) and a Newtonian force field (NFF). It is notably that the center of mass is displaced very much from the principal dynamic symmetry axis. Utilizing the fundamental principle of angular momentum, the equations of motion (EOM) are formulated and solved applying the large parameter approach (LPA) to determine approximate solutions (AS) for the irrational frequencies' case. Euler's angles, which define the body's orientation at any moment, are explicitly calculated. Additionally, to assess the impact of applied moments on motion stability, we utilize advanced computational tools to generate graphical representations of the achieved solutions and the related Euler's angles. This work enhances the understanding of RB dynamics in complex motion scenarios, emphasizing the interaction between external forces and GMs in shaping stability and behavior. The study is poised to greatly influence the aerospace industry by advancing our understanding of rotational motion and the dynamics of celestial bodies, with direct applications in the design and operation of spaceships, spacecraft, and satellites.

The goal of the present paper is the analysis of the effect of geometric imperfections in circular cylindrical shells. Perfect circular shells are characterized by the presence of double shell-like modes, i.e., modes having the same frequency with modal shape shifted of a quarter of wavelength in the circumferential direction. In presence of geometric imperfections, the double natural frequencies split into a pair of distinct frequencies, the splitting is proportional to the level of imperfection. In some cases, the imperfections cause an interesting phenomenon on the modal shapes, which present a strong localization in the circumferential direction. This study is carried out by means of a semi-analytical approach compared with standard finite element analyses. brought to you by CORE View metadata, citation and similar papers at core.ac.uk provided by Archivio istituzionale della ricerca -

The nonlinear dynamics o f circular cylindrical shells under combined axial static and periodic forces are experimentally investigated. The goal is to study the dynamic scenario and to analyze non-linear regimes. The linear behavior under static preload is analyzed by means o f the usual modal testing techniques. The complex dynamics arising when a periodic axial load excites the first axisymmetric mode are analyzed by means o f amplitude frequency diagrams, waterfall spectrum diagrams, bifurcation diagrams o f Poincare maps, time histories, spectra, phase portraits.

In this paper, the effect of the boundary conditions on the nonlinear vibrations of functionally graded (FGM) cylindrical shells is analyzed. The Sanders-Koiter theory is applied to model the nonlinear dynamics of the system in the case of finite amplitude of vibration. The shell deformation is described in terms of longitudinal, circumferential and radial displacement fields. Simply supported, clamped and free boundary conditions are considered. The displacement fields are expanded by means of a double mixed series based on Chebyshev polynomials for the longitudinal variable and harmonic functions for the circumferential variable. Numerical analyses are carried out in order to characterize the nonlinear response when the cylindrical shell is subjected to a harmonic external load; a convergence analysis is carried out by considering a different number of axisymmetric and asymmetric modes. The analysis is focused on determining the nonlinear character of the response as the boundary ...

In the present paper linear and nonlinear vibrations of circular cylindrical shells having different boundary conditions are analyzed by means of the Sanders-Koiter theory. Displacement fields are expanded in a mixed double series based on harmonic functions and Chebyshev polynomials. Simply supported and clamped-clamped boundary conditions are analyzed, as well as connection with rigid bodies; in the latter case experiments are carried out. Comparisons with experiments and finite element analyses show that the technique is computationally efficient and accurate in modelling linear vibrations of shells with different boundary conditions. An application to large amplitude of vibration shows that the technique is effective also in the case of nonlinear vibration: comparisons with the literature confirm the accuracy of the approach. The continuous growing of the commercial use of Space facilities lead to the development of new and more efficient aerospace vehicles; therefore, new and accurate studies on light-weight, thin-walled structures are needed. A wide part of the technical literature in the past century was focalized on the analysis of thin-walled structures and tried to investigate their behaviour in many different operating conditions, i.e. under static or dynamic loads, either in presence or absence of fluid-structure interaction. Both linear and nonlinear models have been developed to forecast the response of such structures. Many studies were concerned with cylindrical shells that constitute main parts of aircrafts, rockets, missiles and generally aerospace structures. The literature about vibration of shells is extremely wide and the reader can refer to Leissa [1] or more recently to Amabili and Païdoussis [2] for a comprehensive review of models and results present in literature. In the following some studies, strictly related to the present paper, are described. Liew et al. [3] analyzed linear vibrations of shallow conical shells using two-dimensional orthogonal polynomials and the Ritz procedure, for obtaining frequencies and modes of vibration: the approach was mesh-free, but able to handle complex geometries and boundary conditions. Bhaskar and Dumir [4] analyzed the dynamics of rectangular orthotropic plates, resting on a nonlinear elastic foundation: they used a discretization approach based on polynomials and orthogonal point collocation method, obtained from zeros of Legendre polynomials. The nonlinear dynamics was analyzed by means of the averaging method and backbone curves were obtained. Liew et al. analyzed conical shells by means of a mesh free approach based on the Ritz method and a mixed Fourier and polynomial expansion. They considered both simply supported and clamped boundary conditions. The same authors used the same approach for analyzing laminated cylindrical panels . Zhou et al. [7] developed an approach based on Chebyshev polynomials and Ritz method for evaluating natural frequencies of solid and hollow cylinders. Soldatos and Messina [8] used orthogonal polynomials for analyzing laminated circular cylinders. Nayfeh and Arafat [9] analyzed nonlinear axisymmetric vibrations of spherical shells, by means of Legendre polynomials for spatial discretizations, and multiple scale method for the dynamic scenario. A special comment deserves the work of Trotsenko and Trotsenko [10], who studied vibrations of circular cylindrical shells with attached rigid bodies, by means of an approach quite close to the present theory. In Ref. the authors used a mixed expansion based on trigonometric functions and Legendre polynomials; they considered only linear vibrations. One of these authors published recently a paper on the same subject , in which results and theory present in Ref. are reprinted (such work is reported for completeness). In the present paper, linear and nonlinear vibrations of circular cylindrical shells are analyzed. Sanders-Koiter theory is considered for shell modelling; in this theory, the shell deformation is described in terms of three displacements fields (longitudinal, circumferential and radial). Displacement fields are expanded by means of a double mixed series: harmonic functions for the circumferential variable; Chebyshev polynomials for the longitudinal variable. Then Lagrange equations are considered to obtain an ordinary differential equation system, from potential and kinetic energies and the virtual work of external forces.

In this work, we investigate the transient thermal analysis of two-dimensional cylindrical anisotropic medium subjected to a prescribed temperature at the two end sections and to a heat flux over the whole lateral surface. Due to the complexity of analytically solving the anisotropic heat conduction equation, a numerical solution has been developed. It is based on a coordinate transformation that reduces the anisotropic cylinder heat conduction problem to an equivalent isotropic one, without complicating the boundary conditions but with a more complicated geometry. The equation of heat conduction for this virtual medium is solved by the alternating directions method. The inverse transformation makes it possible to determine the thermal behavior of the anisotropic medium as a function of study parameters: diagonal and cross thermal conductivities, heat flux.

Functionally Graded Materials (FGM) parts are heterogeneous objects with material composition and microstructure that change gradually into the parts. The distinctive feature of FGM structure gives the possibility of selecting the distribution of properties to achieve the desired functions. Today, multimaterial parts manufactured with additive manufacturing processes are not functional. To move from these samples to functional and complex parts, it is necessary to have an overall process control. This global approach requires a control of process parameters and an optimal manufacturing strategy. This paper presents a process modeling and a system control to manufacture FGM parts with a direct laser deposition system. This works enable to choose an adapted manufacturing strategy and control process parameters to obtain the required material distribution and the required geometry.

This article provides a new finite-element procedure based on Reddy's third-order shear deformation plate theory (TSDT) to establish the motion equation of functionally graded porous (FGP) sandwich plates resting on Kerr foundation (KF). Although Reddy's TSDT is attractive, it cannot be exploited as expected in finite-element analysis due to the difficulties in satisfying the zero shear stress boundary condition. In this study, the proposed element has four nodes, each with seven degrees of freedom (DOF). The performance of this element is confirmed by conducting various examples, showing its accuracy and range of applications. Then, some studies are performed to present the effects of input parameters on the vibration of FGP sandwich plates resting on KF.

In this paper, free vibration analysis of the functionally graded porous (FGP) plates on the elastic foundation taking into mass (EFTIM) is presented. The fundamental equations of the FGP plate are derived using Hamilton’s principle. The mixed interpolation of the tensorial components (MITC) approach and the edge-based smoothed finite element method (ES-FEM) is employed to avoid the shear locking as well as to improve the accuracy for the triangular element. The EFTIM is a foundation model based on the two-parameter Winkler–Pasternak model but added a mass parameter of foundation. Materials of the plate are FGP with a power-law distribution and maximum porosity distributions in the forms of cosine functions. Some numerical examples are examined to demonstrate the accuracy and reliability of the proposed method in comparison with those available in the literature.

This study investigates the application of centrifugal force for the compaction of metal powder. Previous studies using the centrifugal force for manufacturing the green bodies were focused on fine powders with narrow particle size distribution or binary mixtures. This study explores the particle packing of multi-sized powder. Aluminum alloy powder with a particle size less than 100 μm and polymer binder were admixed and compacted in the centrifugal casting with ranging magnitudes of centripetal acceleration. Three different centrifugal forces were tested: 700, 1800, and 3700 G. The microstructure of the green bodies was then observed on the SEM micrographs. The obtained green bodies had high packing densities ranging from 62 to 69%. The packing density and median particle size increase at the positions further away from the center of rotation of the centrifuge with an increase of centrifugal force. The effect of centrifugal force on the segregation of particles was investigated through the quasi-binary segregation index. The segregation phenomena was not observed at 700 G, but clear particle segregation was found at higher centrifugal forces. The increase of the centrifugal force resulted in higher segregation with finer particles moving to the inner part of the spinning mold, with a significant change in the size of particles located closer to the center of rotation. Overall, the centrifugal process was found to produce highly compacted green bodies while yielding a segregation effect due to wide particle size distribution.

Vibroacoustic performance of the doubly curved thick shell is explored based on the three dimensional sound propagation approach as well as state space solution. In fact, the main aim is particularly focused on inspecting the influence of using three-dimensional theory through sound transmission loss (STL) of the structure which includes more reliable and accurate results especially for relatively thick and thick shells even in high frequency domain in comparison with other theories. In order to achieve this end, firstly stress and strain components are developed to present the governing equations of thick shell. This procedure is carried out by dividing the shell into slayers. Then, a solution technique is provided on the basis of state vector methodology wherein approximate layer model along with local transfer matrix are performed. Moreover, this method is followed by global transfer matrix method for the all layers of structure. As an outcome, in results section, not only the accuracy of the offered results is proved but also the importance of employing the current theory in high frequencies is revealed. Another remarkable achievement of this work is related to nominate the dip points of STL diagram. On contrary to panels, doubly curved shells contain two dips, because of their both radii of curvatures. In this work, the first dip is nominated as curvature frequency. The second dip is similar to that of panels at high frequency zone. Thus, it is called as coincidence frequency. Finally, the behavior of the transmitted pressure and the effect of curvatures on the position of curvature frequency are discussed. c

The selective laser melting (SLM) process is a metal-based 3D printing technology which is capable of fabricating cellular structures for various engineering applications. This study aims to investigate the compressive mechanical performance and energy absorption capability of uniform and functionally graded lattice structures fabricated using this process. A solution heat treatment was carried out to explore its effect on the mechanical properties of the printed Al-Si12 lattice structures. The as-built condition of SLM lattice structures underwent brittle failure and demonstrated nonideal energy absorption behaviours, while heat treatment was found to significantly improve deformation and energy absorption performance. The deformation behaviour of the heat-treated lattice structure exhibited distinct responses with typical stress strain curves, providing ideal compressive regions. Calculation of energy absorption showed that the gradually denser lattice structure absorbed higher levels of energy than the uniform lattice structure.

Functionally graded materials (FGMs) represent a cutting-edge approach for enhancing thermal shock resistance in ceramic systems exposed to extreme thermal environments. This study focuses on the development and characterization of alumina–zirconia-based FGMs tailored for structural applications at high temperatures. Alumina provides high hardness and thermal stability, while zirconia offers superior fracture toughness due to its transformation toughening mechanism. A graded composition was designed to optimize the distribution of mechanical and thermal properties across the ceramic body, significantly improving resistance to thermal shock and reducing crack propagation under extreme conditions. The paper outlines the synthesis techniques, microstructural design, and thermal testing results. It concludes with an evaluation of the developed material’s suitability for aerospace and energy-sector components.

This study aimed to compare the biomechanical behaviour of functionally graded structured posts (FGSPs) and homogenous-type posts in simulated models of a maxillary central incisor. Two models of FGSPs consisting of a multilayer xTi-yHA composite design, where zirconia and alumina was added as the first layer for models A and B respectively were compared to homogenous zirconia post (model C) and a titanium post (model D). The amount of Ti and HA in the FGSP models was varied in gradations. 3D-FEA was performed on all models and stress distributions were investigated along the dental post. In addition, interface stresses between the posts and their surrounding structures were investigated under vertical, oblique, and horizontal loadings. Strain distribution along the post-dentine interface was also investigated. The results showed that FGSPs models, A and B demonstrated better stress distribution than models C and D, indicating that dental posts with multilayered structure dissipate localized and interfacial stress and strain more efficiently than homogenous-type posts.

The low-velocity impact response of fully clamped slender metal foam core sandwich beams with geometrically asymmetric cross-section struck by a heavy mass at midspan is investigated. The exact and approximate yield criteria for metal sandwich cross-section are presented considering the effect of core strength. Using the yield criteria, the analytical solutions for large deflection of the fully clamped slender sandwich beams, including dynamic and quasi-static solutions, are derived respectively. Also, finite element (FE) calculations are carried out to validate the analytical model. Moreover, the effects of material elasticity and strain hardening of face sheets are considered in FE analysis. Comparisons of the FE results and analytical solutions reveal that the present analytical model enables the acceptable predictions of the low-velocity impact response of fully clamped asymmetric slender sandwich beams. Material elasticity and strain hardening of face sheets have minor effects on dynamic response.

The present study investigated the nonlinear harmonic vibration of functionally graded multilayer graphene nanoplatelet (GPL)-reinforced nanocomposite beams on the basis of the third-order shear deformation theory. The GPL volume fraction shows a layer-wise change, while in each individual layer GPLs are uniformly dispersed in the matrix. The effective Young's moduli of the GPLreinforced nanocomposite (GPLRC) beams were estimated through the Halpin-Tsai micromechanics model. The mass densities as well as the effective Poisson's ratios of the GPLRC beams were predicted by the rule of mixture. The nonlinear partial differential equations of motion were discretized by means of the Galerkin procedure. A parametric study was carried out by using the multiple scales method to examine the effects of GPL distribution pattern, weight fraction, geometry, and size on the nonlinear response of the primary, secondary, and combination resonances. Results show that an addition of a very low weight fraction of GPL

This study investigates the linear free vibration and elastic buckling behaviors of functionally graded (FG) multilayer graphene platelet (GPL)-reinforced composite beams containing a single edge crack and resting on a Pasternak-type elastic foundation. GPLs are randomly oriented, and their concentration varies layer-wisely through the beam thickness. A modified Halpin-Tsai model is employed to estimate Young's modulus of the GPL-reinforced composite (GPLRC). The first-order shear deformation beam theory is applied in structural modeling. The bending stiffness of the cracked section is assumed to be equivalent to that of a massless rotational spring, which is related to the stress intensity factor (SIF) at the crack tip. SIFs of the cracked FG multilayer GPLRC beams are calculated by the finite element method. The differential quadrature method is used to discretize the equations of motion of the cracked beams. A parametric study is performed after a validation study for the present approach to illustrate the effects of crack location, crack length, boundary condition, GPL weight fraction, GPL distribution pattern, GPL size and geometry, and foundation stiffnesses on the fundamental frequencies and critical buckling loads.

The present study investigated the nonlinear harmonic vibration of functionally graded multilayer graphene nanoplatelet (GPL)-reinforced nanocomposite beams on the basis of the third-order shear deformation theory. The GPL volume fraction shows a layer-wise change, while in each individual layer GPLs are uniformly dispersed in the matrix. The effective Young's moduli of the GPLreinforced nanocomposite (GPLRC) beams were estimated through the Halpin-Tsai micromechanics model. The mass densities as well as the effective Poisson's ratios of the GPLRC beams were predicted by the rule of mixture. The nonlinear partial differential equations of motion were discretized by means of the Galerkin procedure. A parametric study was carried out by using the multiple scales method to examine the effects of GPL distribution pattern, weight fraction, geometry, and size on the nonlinear response of the primary, secondary, and combination resonances. Results show that an addition of a very low weight fraction of GPL

This study investigates the linear free vibration and elastic buckling behaviors of functionally graded (FG) multilayer graphene platelet (GPL)-reinforced composite beams containing a single edge crack and resting on a Pasternak-type elastic foundation. GPLs are randomly oriented, and their concentration varies layer-wisely through the beam thickness. A modified Halpin-Tsai model is employed to estimate Young's modulus of the GPL-reinforced composite (GPLRC). The first-order shear deformation beam theory is applied in structural modeling. The bending stiffness of the cracked section is assumed to be equivalent to that of a massless rotational spring, which is related to the stress intensity factor (SIF) at the crack tip. SIFs of the cracked FG multilayer GPLRC beams are calculated by the finite element method. The differential quadrature method is used to discretize the equations of motion of the cracked beams. A parametric study is performed after a validation study for the present approach to illustrate the effects of crack location, crack length, boundary condition, GPL weight fraction, GPL distribution pattern, GPL size and geometry, and foundation stiffnesses on the fundamental frequencies and critical buckling loads.

In this study, functionally graded zirconia-based ceramic composites were synthesized and characterized with the aim of enhancing their performance as thermal barrier coatings (TBCs) in gas turbine engines. The work focuses on controlling microstructural gradation to achieve a balance between low thermal conductivity and high fracture toughness—two key requirements for next-generation TBC systems. Using a powder metallurgy route followed by spark plasma sintering, a series of layered composite specimens were fabricated with varying compositions of YSZ (Yttria-Stabilized Zirconia), alumina (Al₂O₃), and silicon carbide (SiC). Microstructural, thermal, and mechanical analyses confirmed a spatial gradient in properties, indicating the successful development of a functionally graded architecture. The results show significant improvement in damage tolerance and thermal insulation capacity compared to homogeneous ceramic coatings

The main purpose of this paper is to define the notion of neutrosophic based normal and regular spaces. This study investigates and open new class and conception of generalization of classical regular and normal spaces. The hereditary and topological properties of neutrosophic based normal and regular spaces have been analyzed and investigated. It also examines neutrosophic topological subspaces, providing insights into their characteristics. Furthermore, the paper investigates neutrosophic regular spaces and demonstrates their hereditary nature, specifically focusing on 𝑅 1 , 𝑅 2 , 𝑅 3 and 𝑅 4. Additionally, we explain some example of a neutrosophic-regular based space X which is a neutrosophic based normal-space but it is not necessary to neutrosophic-𝑇 1 spaces. Eventually, it is shown that under certain conditions that the images are preserved in neutrosophic based normal and regular spaces.

This paper presents the effect of twist and rotational speeds on free vibration characteristics of functionally graded conical shells employing finite element method. The objective is to study the natural frequencies, the influence of constituent volume fractions and the effects of configuration of constituent materials on the frequencies. The equation of dynamic equilibrium is derived from Lagrange's equation neglecting the Coriolis effect for moderate rotational speeds. The properties of the conical shell materials are presumed to vary continuously through their thickness with power-law distribution of the volume fractions of their constituents. The QR iteration algorithm is used for solution of standard eigenvalue problem. Computer codes developed are employed to obtain the numerical results concerning the combined effects of twist angle and rotational speed on the natural frequencies of functionally graded conical shells. The mode shapes for typical shells are also depicted. Numerical results obtained are the first known non-dimensional frequencies for the type of analyses carried out here.

In the manufacturing industry the term Process Planning (PP) is concerned with determining the sequence of individual manufacturing operations needed to produce a given part or product with a certain machine. In this technical report we propose a preliminary analysis of scientific literature on the topic of process planning for Additive Manufacturing (AM) technologies (i.e. 3D printing). We observe that the process planning for additive manufacturing processes consists of a small set of standard operations (repairing, orientation, supports, slicing and toolpath generation). We analyze each of them in order to emphasize the most critical aspects of the current pipeline as well as highlight the future challenges for this emerging manufacturing technology.

The case of molecular diffusion is investigated and a method is proposed to predict the effective diffusion properties of transversely isotropic composite materials. This paper is the second one of a set of two consecutive papers published in this volume. The general modelling strategy was devised in the first paper and applied to the biphasic case in this one. Closed-form analytical expressions are given to investigate fibre packing effects on the effective transverse diffusivity of any unidirectional composite. The specific case of insulated fibres embedded in a diffusive matrix is studied and a clear procedure is then described to determine the model parameters. It is worth noting that only a very simple cross-section image analysis of the unidirectional composite medium is required to provide the two morphological parameters needed to predict the overall diffusivity tensor. Finally, an application on a real microstructure is provided to demonstrate the efficiency of the suggested turnkey method. Very simple analytical calculations make possible parametric studies less expensive than numerical or experimental characterizations.

The designing of ballistic resistance armors, which can efficiently withstand and dissipate the enormous energy of high-velocity projectiles or bullets without sacrificing protection, is a very critical task. Armor must resist penetration and control the transmission of kinetic energy to minimize blunt force injuries during impact, all the while preserving structural integrity and avoiding becoming excessively bulky or heavy. Advanced materials are essential for resolving these problems. In the current era, functionally graded material (FGM) is replacing conventional and composite materials very rapidly due to its advanced characteristics. Lightweight FGMs can significantly improve the efficacy of armor against ballistic impact by progressively changing the material compositions and porosities over thickness without sacrificing flexibility or durability. With this gradation, FGMs may combine the energy-absorbing properties and toughness of metals, polymers, ceramics, composites, or their combinations to resist penetration against ballistic impacts. However, this paper summarized the in-depth classifications of FGMs, ammunition used for ballistic impacts, and FGMs ballistic performance. A critical correlation between the various standards of ballistics tests is developed in this article. Methods of ballistic testing with shoot spacing patterns for different standards are well described. The ballistic performance of conventional, composite, and hybrid FGMs used as plate and sandwich structures is also compared in terms of their failure modes, ballistic limit, and energy absorption capabilities. By strategically stacking different materials in the armor, the danger of catastrophic failure can be effectively reduced. This article also provides an insight into key future challenges and scopes of the FGM armors.

This study offers a comprehensive review of the research related to the Composite Tjoint for the combination of materials-Glass fiber, Epoxy Resin and PVC foam. Data were obtained from numerous articles between the years of 1976 to 2018 in journals. The content of the study is distinguished based upon the study of composite materials, study of composite Tjoint, study of FEA analysis of composite structures, study of delamination composite sandwich core. The preeminent defect that occurs in composite t-joint is the undefined failure at the joint which is the only complex part in composite structure. Many researchers have done most of the study to analyze how actually the t-joint fails and the failure conditions. Many attempts have been made to overcome this problem by CFD or by Finite Element Analysis approach composite structure, but there is ample scope for modelling of composite t-joint and use of composite materials.

A non-classical plate theory based on the direct approach is introduced and applied to plates composed of functionally graded materials (FGM). The governing two-dimensional equations are formulated for a deformable surface, the viscoelastic stiffness parameters are identified assuming linear-viscoelastic material behavior. In addition, the material properties are changing in the thickness direction. Solving some problems of the global structural analysis it can be shown that in some cases the results based on the presented theory significantly differ from the results based on the Kirchhofftype theory.

Inverse problem for spring-mass systems called shear structures is presented in this paper. Shear structure is a system with spring and mass after each other and there is a spring between two masses. Damping effects are neglected here. The aim is determining the mass and stiffness of the system with pre assigned frequencies. There is a method for solving such a problem that is presented here. Some examples are discussed. Such a problem can be used for several important problems.

In order to obtain accurate results from displacement-based Finite Element Method (FEM), it is crucial to introduce accurate shape functions that interpolate the displacement field within an element. This paper attempts to provide such a new component by using Finite Element method using Basic Displacement Function (BDFs) for the free vibration analysis of plates with in-plane Functionally Graded Material (FGM). The first step is to introduce displacement functions and compute them using the energy method. Later, new shape functions are developed based on stiffness and force methods used to model the mechanical behavior of the element, wherein the shape functions benefit from the generality and accuracy of the stiffness and force methods. Last, the plate is analyzed using Finite Element method to derive the structural matrices from new shape functions. Several numerical examples demonstrate the accuracy and efficiency of the method, and a special material graded index named Ns is introduced.

With the development of new industries and modern processes, many structures serve in thermal environments, resulting in a new class of composite materials called functionally graded materials (FGMs). FGMs were initially designed as thermal barrier materials for aerospace structural applications and fusion reactors. They are

In the present paper, electrical energy harvesting from random vibrations of an Euler-Bernoulli nano-beam with two piezoelectric layers is investigated. The beam is composed of an aluminum layer together with two piezoelectric ceramic layers (PZT 5A) serving as energy harvesting sensors. In the proposed method, the equations governing the bimorph nano-beam will be analytically derived using classical beam theory with corresponding modification coefficients to the nano-structure applied. Then, the derived system of equations will be solved following Kantorovich method. Assumed boundary conditions for the nano-beam are as follows: a clamped end with the mass concentrated at the free end of the beam. Further, the input activation function of the system for energy harvesting was taken as being random. Since the objective of this research is to investigate the amount of harvested energy, the section on the results provides associated voltage and maximum output power curves with the bimor...

The objective of this review was to investigate dental literature for attempts including graded, layered or multimaterial Additive Manufacturing of dental ceramics, with a goal to improve zirconia dental restorations, limitations related to decreased translucency and weak adhesion to tooth structure of zirconia materials may be noticed in routine dental practice. Additive Manufacturing (AM) is gaining interest as a manufacturing method that may replace Subtractive Manufacturing (SM). Functionally Graded Additive Manufacturing (FGAM) can produce a functionally graded material in 3D printing techniques; it allows for adjusting the material chemical structure and phase across its section, innovation of new composite materials and modifications of the design using a single construction step. The need for veneering and lamination of zirconia restorations inspired the authors to investigate FGAM technologies for a solution. An extensive search was conducted on experiments regarding AM to construct multi-material or graded designs, main findings were listed in a try to achieve a favorable material manufacturing technique for application in restorative dentistry.

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This paper presents the time history response of a sandwich beam with a porous core subjected to two moving harmonic loads with opposite directions. In the modelling, the beam is combined of two isotropic face sheets and a porous core with symmetric porosity distribution. The quasi-3D shear deformation beam theory in conjunction with Hamilton's variational principle is utilized to set up the governing equations of motion. The Navier solution is used to obtain the displacement field. The accuracy of the study is validated by comparing with existing results in the literature for specific cases. Effects of the velocity and excitation frequency of the moving loads on the deflection-time history are investigated and discussed. Numerical results reveal that in the case of the doublemoving harmonic loads in the antiphase, the resonance phenomenon cannot occur when the excitation frequency approaches the natural frequency of the beam.

The present article deals with the buckling response of functionally graded multilayer graphene platelet-reinforced composite (FG-GPL RC) rectangular plates with circular/elliptical cutouts resting on a Winkler-type elastic foundation under uniaxial and biaxial normal and shear loads. Rule of mixtures and the Halpin-Tsai approach are applied to obtain the effective Poisson's ratio, mass density, and elastic modulus of the reinforced composite. The governing equations are developed by applying the third-order shear deformation plate theory. Then, the finite element procedure is used to solve the problem. Four different types of graphene platelet distributions, namely, UD, FG-X, FG-V, and FG-O, are considered. A broad range of factors such as plate aspect ratio, plate slenderness ratio, applying uniaxial and biaxial normal and shear loads to the plate, several Winkler elastic foundation stiffness parameters, different displacement boundary conditions, the effect of size of the circular cutout and orientation of the elliptical cutout, and the influence of GPL weight fraction are discussed in several tabular and graphical data in detail.

A non-classical plate theory based on the direct approach is introduced and applied to plates composed of functionally graded materials (FGM). The governing two-dimensional equations are formulated for a deformable surface, the viscoelastic stiffness parameters are identified assuming linear-viscoelastic material behavior. In addition, the material properties are changing in the thickness direction. Solving some problems of the global structural analysis it can be shown that in some cases the results based on the presented theory significantly differ from the results based on the Kirchhofftype theory.

Within the framework of the direct approach to the plate theory we consider natural oscillations of plates made of functionally graded materials taking into account both the rotatory inertia and the transverse shear stiffness. It is shown that in some cases the results based on the direct approach differ significantly from the classical estimates. The reason for this is the non-classical computation of the transverse shear stiffness.

In this work, an analytical solution of the thermal stresses for a fiber embedded in a matrix is presented based on the idea of the boundary layer and under some simplifying assumptions. These assumptions include: the properties of both materials, fiber and matrix, remain constant; both materials remain in the elastic range so no plastic-deformation are considered; there exists a perfect bonding between the fiber and matrix so the condition of no-opening holds over the entire interface; and the composite is subjected to an uniform change of temperature. The analytical solution to the problem is found for the case when the length of the embedded bar (fiber) is much greater than its radius, and the Young's modulus of the matrix is much less than that of the fiber. The problem is also solved numerically by means of finite element analysis using a commercial package. Both results are compared and it is shown that both approaches coincide very close qualitatively and quantitatively although significant discrepancies may appear at specific points for specific cases.

nia in dentistry. However, some fabrication procedures such as grinding, polishing, sandblasting, heat treatment, and veneering of the fine-grained metastable zirconia microstructures may affect the long-term stability and success of the material by influencing its aging sensitivity. The purpose of this review is to address the evolution of zirconia as a biomaterial; to explore the material's physical, chemical, biological, and optical properties; to describe strengthening procedures; and finally to examine aging, processing, and core/veneer interfacial effects.