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This analysis explores natural leading modes represented by logarithmic functions, achieved by imposing four boundary constraints at the ends of an elastic inhomogeneous beam. The beam possessing constant material inertia, is assumed to be uniformly loaded, and is composed of material with variable stiffness. It is sought analytical expressions for beam deflections in terms of logarithmic functions. Our findings demonstrate that such formulae can be derived for a beam under axially uniform load and with spatially distributed flexural rigidity. Subsequently, the beam shapes and material properties for four specific scenarios are identified: free-free logarithmic beam, cantilevered logarithmic beam, simply-supported logarithmic beam, and simply-supported sliding logarithmic beam. Explicit logarithmic beam responses, governed by a limited number of shape parameters, are illustrated graphically using normalized deflections with respect to the maximum deflection. Highly deflected elastic logarithmic modes emerge as a consequence of high flexural rigidity influenced by the uniformly applied transverse load. These elucidated logarithmic beam modes offer potential practical applications in the structural design of functionally graded materials. They also serve as valuable testing platforms for numerical techniques employed in the analysis of more complex beam problems. [ABSTRACT FROM AUTHOR]

The early shrinkage-deformation and mechanical property evolution of gradient-structured composites in extreme environments are still insufficient. The paper prepared ordinary Portland cement-alkali-activated slag (OPC-AAS) and ordinary Portland cement-alkali-activated metakaolin (OPC-AAMK) gradient-structured composite by stacking cement and alkali-activated materials together. The effects of temperature difference cycling and wetdry cycling extremes on the early shrinkage strain and splitting strength of OPC-AAS and OPC-AAMK composites, as well as the structure of the bond interface and the micromorphology of the hydration products, were comparatively analyzed. The results demonstrated that the temperature difference cycling affected the early deformation and bond strength of the gradient-structured composite interfaces more significantly than the dry-wet cycling. The maximum expansion strains of OPC-AAS and OPC-AAMK were 1,130.88 μm and 1,399.25 μm, respectively, under the effect of temperature difference cycling; the splitting strengths of OPC-AAS and OPC-AAMK after three cycles of temperature difference cycling were reduced by 26.37% and 31.32%, respectively, compared with that after three cycles of wet-dry cycling. In addition, the OPC-AAS composites showed better interfacial bonding properties after extreme environmental cycling compared to the OPC-AAMK composites. The early splitting strengths under the two extreme environmental effects increased and then decreased, and the maximum splitting strengths of OPCAAS were 2.66 MPa and 3.65 MPa under the temperature difference cycling and dry-wet cycling, respectively, which were 5.14% and 35.69% higher than those of OPC-AAMK, respectively. Scanning electron microscopy (SEM) characterization analysis showed that the temperature difference cycling resulted in more severe product decomposition of the AAMK cementitious material, and obvious cracks and holes appeared at the bonding interface of OPC-AAMK. This study provides some references for the optimal design of the early shrinkage-deformation properties and mechanical properties of gradient-structured composites under extreme environments as well as the assessment of service life. [ABSTRACT FROM AUTHOR]

With the increasing emphasis on biocompatibility and aesthetic considerations, all-ceramic dental restorations have gradually supplanted traditional metal-ceramic restorations. Among commonly used all-ceramic dentures, glass-ceramic (GC) dentures offer excellent aesthetics but have limited load-bearing capacity, while zirconia dentures exhibit outstanding mechanical properties but lack aesthetics and cause excessive wear on opposing teeth. Additionally, GC-zirconia bilayer dentures are prone to interface fractures, which compromise their long-term durability. Therefore, this study proposes a design and preparation method for a GC/zirconia stabilized with 5 mol% yttria (5Y-PSZ) composites functionally gradient ceramic denture. The objective of this study was to enhance the similarity between dentures and natural teeth, ensuring high strength while minimizing wear on the opposing dentition. First, the influence of PSZ content on the microstructure, mechanical and tribological properties of the GC/PSZ composites was investigated by incorporating 5Y-PSZ particles (0-15 wt%) into self-prepared fluorapatite GCs. Secondly, based on the performance of the composites and the actual requirements of dentures, a gradient ceramic was designed with an increasing PSZ content from top to bottom. Finally, gradient ceramic specimens were fabricated using vat photopolymerization 3D printing technology, and their mechanical properties were thoroughly evaluated. The results indicated that the gradient ceramic material effectively combines superior strength and fracture toughness with aesthetic appeal, while also can minimize wear on the antagonistic natural teeth. This study presents a novel strategy for designing and manufacturing high-performance all-ceramic dentures. [ABSTRACT FROM AUTHOR]

AbstractThis article investigates the influence of self-weight on the buckling and post-buckling behavior of a cantilever column made of axially functionally graded materials (AFGMs) with properties that vary according to a power-law distribution. The column rests on a spring-hinged support and is subjected to a tip load. Using Voigt’s rule of mixtures, two different power-law functions are considered. Three loading scenarios are discussed: tip load, self-weight, and combined loads. For buckling behavior, the Rayleigh–Ritz method is employed, in which the polynomial degree can be adjusted. The shooting method examines the post-buckling behavior of the AFGM column by solving the governing differential equations with boundary conditions. The results indicate that the Rayleigh–Ritz method achieves high accuracy when using a 15th-order polynomial. Increasing the degree of fixity at the support enhances the stiffness until the support is completely fixed. The buckling load varies with the material index, exhibiting different trends with and without self-weight. The study captures limited points of self-weight and combined loads. In the post-buckling state, the AFGM column shows stable behavior. Moreover, equilibrium shapes, support rotation, and hardening/softening behavior are highlighted. [ABSTRACT FROM AUTHOR]

Advancements in technology have revolutionized healthcare, with notable impacts on auditory health. This study introduces a novel approach aimed at optimizing materials for middle ear prostheses to enhance auditory performance. We developed a finite element (FE) model of the ear incorporating a pure titanium TORP prosthesis, validated against experimental data. Subsequently, we applied Functionally Graded Materials (FGM) methodology, utilizing linear, exponential, and logarithmic degradation functions to modify prosthesis materials. Biocompatible materials suitable for auditory prostheses, including Stainless Steel, titanium, and Hydroxyapatite, were investigated. Our findings indicate that combinations such as Stainless Steel with titanium and Hydroxyapatite offer improved outcomes compared to pure titanium and Hydroxyapatite ceramic, in terms of both displacement and stress. Additionally, personalized prostheses tailored to individual patient needs are feasible, underscoring the potential for further advancements in auditory healthcare. [ABSTRACT FROM AUTHOR]

In this article, a simple refined shear deformation theory that eliminates the use of a shear correction factor was presented for buckling analysis of in-plane bi-directional functionally graded (IBFG) porous plates under various boundary conditions. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. Material properties of IBFG are assumed to vary continuously along with two different directions simultaneously, that is, the longitudinal and transversal ones, respectively. Governing equations and boundary conditions are derived. Analytical solutions were obtained for buckling analysis of (IBFG) porous plates. Several numerical examples are presented to demonstrate the performance and effectiveness of the proposed theory. The effects of material gradations, aspect ratios, and porosity on IBFG plate responses are examined in detail as well. [ABSTRACT FROM AUTHOR]

In this research work, an axially functionally graded (AFG) Nano-composite beam is modeled to observe the free vibration behavior beamfor non-uniform geometry. The beam is mathematically modeled as an Euler-Bernoulli beam using MATLAB code. Where the graphene Nanoplatelets (GPL) are axially reinforced with A and V type functions. The geometry nonuniformity in the beam is introduced with an exponential function, where the exponent of the equation governs the cross-section of the geometry. The material modulus and other properties at each section along the beam axis are modeled as particulate fiber randomly oriented composite with the help of Halpin Tsai theory and rule of mixture. The finite element method (FEM) is used for the solution and analysis of the model. The model is first validated for uniform geometry results then the non-dimensional fundamental frequency of the AFG beam is obtained for various parameter combinations. The results for various combinations are plotted and it is noted that the free vibration characteristic of the model is strongly dependent on non-uniformity in geometry, end-support constraints,and slenderness ratios (L/h0) combination of the model. This research contributes significantly to the understanding of advanced composite structures and offers potential benefits for the design and optimization of these materials in various engineering applications. The study reveals significant variations in natural frequencies depending on the A type & V type GPL distribution pattern and geometric parameters, which are crucial for the structural integrity and performance of nano composite beams. [ABSTRACT FROM AUTHOR]

This study investigates functionally graded materials (FGMs) as reinforcement for notched plates prone to crack propagation. Using a novel meshing technique and the Gurson-Tvergaard-Needleman damage model within ABAQUS-Explicit, we explore how various gradation parameters affect material damage under stress. The model, incorporating Von Mises stress theory and Voce hardening law, simulates plastic flow and progressive damage from void dynamics. Validated against experimental data, our findings reveal that local gradation parameters significantly influence void damage and structural performance of notched components. This research provides crucial insights into FGMs' potential to enhance structural integrity in engineering applications involving notched structures. [ABSTRACT FROM AUTHOR]

This article presents a novel investigation of the free vibration behavior of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates under hygrothermal environments. It explores both uniform and non-uniform (functionally graded) distributions of CNTs across the plate thickness for the first time. The effective material properties of the CNTRC, considering temperature and moisture dependence, are determined using the extended rule of mixture. First-order shear deformation theory (FSDT) is employed to derive the governing equations incorporating hygro-elastic and thermo-elastic relations. These equations are solved using the finite element method. A validation study verifies the accuracy of the employed approaches. Subsequently, a comprehensive parametric study investigates the influence of plate geometry (length-to-width and width-to-thickness ratios), CNTs volume fraction, boundary conditions, linear and non-linear CNTs distributions, and hygrothermal environments on the free vibration behavior of polymeric nanocomposite plates reinforced with CNTs fillers is conducted. The results reveal that the increase in temperature and moisture leads to a decrease in the effective stiffness of the FG-CNTRC plates. [ABSTRACT FROM AUTHOR]

This study addresses wave propagation in beams made of bidirectional functionally graded materials (BDFG) and having nonuniform cross section by using a quasi-3D analytical solution. For the first time, this aspect will be studied. The mechanical characteristics of the beams are supposed to be variable in both axial and transvers direction according to a specific law depending on the porosity. The mathematical formulation used is based on a displacement field containing indeterminate terms and requiring a few variables to be determined. The thickness and width of the beams are assumed to be linearly variable in the longitudinal direction. The equations governing the simply supported beams are obtained by applying the principle of virtual work and are then analytically solved to obtain the phase velocities and wave frequencies. In addition, the validation results reveal excellent concordance of the proposed theory with those given in the literature. Then, a detailed parametric study is carried out to investigate the influence of the several geometrical and material parameters on the wave propagation in BDFG tapered beams. It is observed that these parameters have significant impact on the wave propagation in BDFG tapered porous beams. These results can be used as benchmark solutions for future studies. [ABSTRACT FROM AUTHOR]

This paper presents a three-dimensional (3D) analysis of the post-buckling behavior of functionally graded (FG) plates for the first time using an elastoplasticity-based meshfree formulation. A novel 3D Tchebychev-radial point interpolation approach, which combines radial basis functions with Tchebychev polynomials, is developed to solve the nonlinear post-buckling problem. The incremental plastic deformation is modeled by the Prandtl–Reuss flow rule along the isotropic hardening von Mises criterion. The governing equations are derived using the principle of virtual work by considering the 3D full Green–Lagrange strain components. The Newton–Raphson technique along with the arc-length method is used to determine post-buckling equilibrium paths of FG plates. The effective elastoplastic properties of the functionally graded material are assessed by exploiting the homogenization method, named Tamura–Tomota–Ozawa (TTO) model. It has been demonstrated that the accuracy of the solution is improved by incorporating Tchebychev polynomials into the radial point interpolation method (RPIM) shape function, and the stability and robustness of the results are independent of variations in the shape parameter. Furthermore, it is confirmed that TRPIM, with a slightly higher CPU time compared to RPIM, exhibits a higher convergence rate. The excellent agreement of the results with those existing in the literature shows that the proposed meshfree method can be used as a robust and accurate numerical tool to predict the elastoplastic post-buckling behavior of FG plates. Further numerical assessments indicate that post-buckling paths are significantly affected by factors such as geometric parameters, material gradient, loading ratio, and boundary conditions (BCs). [ABSTRACT FROM AUTHOR]

The buckling-like mechanical behavior of functionally graded graphene platelet-reinforced composite (FG-GPLRC) structures is increasingly attracting research attention. However, buckling behavior has previously been studied separately as thermal buckling and mechanical buckling. In this context, this study investigates the buckling behavior of FG-GPLRC plates under combined thermal and mechanical loads. The coupled buckling problem is formulated according to the minimum potential energy theorem using first-order shear deformation theory (FSDT). In addition, the problem is approximated by the 2-D natural element method (NEM), and the resulting coupled eigen matrix equations are derived to compute the critical buckling temperature rise (CBTR) and the mechanical buckling load. The developed numerical method can solve thermal, mechanical, and coupled thermo-mechanical buckling problems, and its reliability is examined through convergence and benchmark tests. Using the developed numerical method, the buckling behavior of FG-GPLRC plates under thermal and mechanical buckling loads is examined in depth with respect to the key parameters. In addition, a comparison with functionally graded CNT-reinforced composite (FG-CNTRC) plates is also presented. [ABSTRACT FROM AUTHOR]

This paper presents an effective nonlocal finite element method (FEM) for investigating the free vibration behavior of sigmoid functionally graded material (S-FGM) nanoshells using nonlocal elasticity theory. The effective nonlocal parameters via third-order shear deformation theory (TSDT) are varied along the thickness of the nanoshells following the sigmoid function. In this study, two different sigmoid functions FGM (S1-FGM and S2-FGM) are considered for the ceramic volume fraction. For S1-FGM, the top and bottom surfaces are ceramic and metal, respectively, whereas the middle surface has the average properties of its constituent materials. In order to increase the stiffness of S1-FGM, ceramic and metal are used at the bottom and midplane surfaces, respectively, to form S2-FGM, which is used to investigate and compare with S1-FGM. The governing equation of the S-FGM nanoshells is formulated based on Hamilton's principle. The numerical results are obtained by finite element method (FEM) with a nine-node quadrilateral (Q9) Lagrangian element and are in close agreement with the published results. The numerical investigation indicates that the frequency parameter decreases with increasing nonlocal parameters. The frequency parameters of S1-FGM nanoshells decrease slowly when the sigmoid material index increases, whereas the frequency parameters of the S2-FGM shells increase quickly (0 ≤ n ≤ 1). then slowly as the sigmoid material index increases. Finally, the effects of the geometrical parameters of the S-FGM nanoshells accounting for the effective nonlocal parameters on the non-dimensional frequency parameter are investigated. [ABSTRACT FROM AUTHOR]

Since the initial observation of carbon nanotubes (CNTs) and graphene platelets (GPLs) in the 1990 and 2000s, the demand for high-performance structural applications and multifunctional materials has driven significant interest in composite structures reinforced with GPLs and CNTs. Incorporating these nanofillers into matrix materials markedly enhances the mechanical properties of the structures. To further improve efficiency and functionality, functionally graded (FG) distributions of CNTs and GPLs have been proposed. This study presents an extensive review of computational approaches developed to predict the global behavior of composite structural components enhanced with CNT and GPL nanofillers. The analysis focuses on key structural elements, such as plate-type configurations, cylindrical and curved shells, and beams, emphasizing the computational techniques utilized to simulate their mechanical behavior. The utilization of three-dimensional elasticity theories and equivalent single-layer (ESL) frameworks, which are widely employed in the modeling and analysis of these composites, is comprehensively discussed. Additionally, the paper examines various mechanical performance aspects, including static, buckling, post-buckling, vibrational, and dynamic responses for the mentioned structures. The unique features of hybrid nanocomposites, combining CNTs and GPLs, are also analyzed. Furthermore, the study delves into the fabrication and processing techniques of these materials, with a particular focus on strategies to mitigate nanofiller agglomeration. The review extends to cover thermal and electrical properties, durability under environmental exposure, fatigue resistance, and vibration-damping characteristics. In conclusion, the paper underscores the necessity for ongoing advancements in computational modeling to facilitate improved design, analysis, and optimization of nanocomposite structures. Future research opportunities in this rapidly advancing domain are also outlined. [ABSTRACT FROM AUTHOR]

AbstractFunctionally graded piezoelectric/piezomagnetic (FGPEPM) materials in a hygrothermal environment exhibit complex multi-physical field coupling effects when subjected to various loads such as mechanical, electric, magnetic, temperature, and moisture concentration. In this paper, a theoretical analysis of the electro-magneto-elasto-hygrothermal (EMEHT) coupling effects for a rotating FGPEPM hollow sphere is presented. By assuming that the properties of hygrothermo, electro-magneto-elastic, hygrothermal expansion, and density of the FGPEPM sphere obey different power laws along the thickness direction, the distributions of temperature, moisture, magnetic potential, radial displacement, electric potential, and stresses within the rotating FGPEPM sphere are determined. The present theoretical solutions are verified with existing analytical solutions for some related simplified problems. The FGPEPM hollow sphere exhibits complex multi-physical field coupling effects, containing positive/inverse piezoelectric, positive/inverse piezomagnetic, positive/inverse magnetoelectric, thermal/moist stress, pyroelectric/pyromagnetic, and hydroelectric/hydromagnetic effects under a hygrothermal environment. The influence of gradient parameters and other material properties on these EMEHT coupling effects is also investigated for FGPEPM hollow spheres under various types of loads. This theoretical research provides some reference for the optimal design for this type of functionally gradient multifield coupling material. [ABSTRACT FROM AUTHOR]

AbstractThis study examines the free vibration and nonlinear transient response of functionally graded graphene origami-enabled auxetic metamaterial (GOEAM) cylindrical shells under thermal conditions. The multilayered shells feature GOri distributions across their thickness, introducing distinct auxetic and thermal properties. Material properties are modeled using micromechanical models optimized via genetic programming. Employing Reddy’s third-order shear deformation theory and von Kármán’s nonlinear geometric assumptions, nonlinear kinematic relationships are formulated and solved using Galerkin method. A novel contribution is the analysis of Winkler-Pasternak elastic foundations in two configurations: centrally distributed along the shell length and concentrated at both ends. Foundation effects are quantified by integrating stiffness coefficients across contact areas, offering insights into foundation-shell interactions. Artificial Neural Networks (ANNs) are developed to predict natural frequencies with high accuracy. Trained using the Levenberg-Marquardt algorithm and tan-sigmoid transfer function, these models demonstrate robust performance through metrics like validation performance plots, regression analysis, and error histograms. Validation against literature confirms the reliability of both ANN and analytical approaches. Key findings reveal that increased GOri folding enhances the negative Poisson’s ratio but reduces Young’s modulus, decreasing shell stiffness, natural frequencies, and increasing vibration amplitudes. Additionally, centrally concentrated elastic foundations yield higher natural frequencies and smaller vibration amplitudes compared to foundations distributed at the shell ends. By integrating advanced analytical techniques with state-of-the-art ANN modeling, this study not only provides a comprehensive understanding of the dynamic behavior of FG-GOEAM cylindrical shells but also offers valuable insights for the design, optimization, and application of auxetic metamaterial structures in thermal environments. [ABSTRACT FROM AUTHOR]

AbstractStiffened functionally graded (FG) folded plates are being widely used these days in aeronautical, automotive, and naval applications which are often exposed to extreme environmental conditions characterized by high temperature and moisture concentrations. However, a numerical model to estimate the dynamic response of such structures in hygrothermal environment is almost non-existent. It is from this perspective that, a MATLAB-based finite element (FE) model is developed to assess the free vibration characteristics of stiffened FG folded panels in hygrothermal environment and is presented for the first time in this article. The governing equation is derived following the first order shear deformation theory including hygro-elastic and thermo-elastic relations. Temperature and moisture concentrations are assumed to vary both linearly and uniformly through the plate’s thickness to numerically simulate hygrothermal environment. Non-linear strains are incorporated in the present FE model to consider the hygrothermal effect. Another FE model is also developed in COMSOL Multiphysics software for these structures and is compared with the MATLAB-based model. Numerical simulations reveal that the free vibration characteristics of stiffened FG folded plates are significantly affected by hygrothermal environment. The present FE models can be effectively utilized by engineers and researchers to analyze and optimize the dynamic behavior of stiffened FG folded plates. The results are also expected to serve as a benchmark for future research works. [ABSTRACT FROM AUTHOR]

The purpose of this study is to analyze the large deflection problem of bimodular functionally graded truncated thin conical shells under the transverse mechanical load and non-uniform thermal load, in which two different boundary constraints of the truncated shell with two ends simply supported and fully fixed are considered. It is assumed that the temperature distribution along the thickness direction satisfies the Fourier law of heat transfer, and the material properties change exponentially along the thickness direction while different properties in tension and compression are considered. The geometric equation of the conical shell is established based on the equivalent method of curvature correction of von-Kármán deformation theory, and the analytical solution of the problem is obtained by Ritz method. Numerical simulation of bimodular functionally graded conical shells under the thermal and mechanical loads is carried out by Abaqus, and the numerical solution agrees with the theoretical solution. The results show that the introduction of bimodular functionally graded material will affect the maximum displacement and this effect has different rules under the mechanical load and thermal load. In addition, factors such as the cone apex angle and the truncated distance have a great influence on the maximum displacement and its location of the conical shell. [ABSTRACT FROM AUTHOR]

This paper investigates the free vibration, buckling and dynamic stability of spinning bi-directional functional gradient materials (BDFGMs) conical shells. The material properties vary along the thickness and axial direction. The dynamics model is established based on the first-order shear deformation theory and the governing equations and boundary conditions of the conical shell are derived employing Hamilton's principle. Subsequently, the differential quadrature (DQ) method is employed to discretize the governing equations into an algebraic system of equations for solving and analyzing the free vibration characteristics of the conical shell. The theoretical model's accuracy and the solution method's reliability are rigorously verified. The effects of temperature, functional gradient index, and rotation on the vibration characteristics, traveling wave vibration and critical speed of the conical shell in a thermal environment are systematically explored through numerical analysis. The results indicate that both the material gradient index and temperature increase lead to a decrease in the shell's natural frequency. For the spinning BDFGMs shell, elevated temperature causes the occurrence of trailing wave vibration to advance to the critical speed. Centrifugal force emerges as the primary factor influencing the critical buckling load and unstable region variation of the spinning shell. [ABSTRACT FROM AUTHOR]

Process-induced microstructure modification was investigated for the strengthening mechanism of laser powder bed fusion fabricated (LPBF) Ti-6Al-4 V material. An innovative approach by mimicking the fiber structure of the composite materials was studied. Different cylindrical reinforcement diameters were selected in the LPBF-fabricated Ti-6Al-4 V samples to replicate the function of the carbon fibers in composite materials, providing stiffness and reinforcement in the matrix. The corresponding regions of the assigned reinforcement shape at each layer were exposed to a secondary laser scan through the sample during the fabrication. Multi-scan laser scanning strategies, involving a combination of laser power and scan speed, were employed after the melting laser scan to maximize the relative density of the material. The optimized post-heating laser scan enhanced the relative density (> 99.95%), recrystallized the α and α′ phases' lath morphology, modified the lattice structure, transformed the initial microstrain mode, and enhanced the inherent grain texture of the PBF fabricated Ti-6Al-4 V. The tailored microstructure achieved a 46.5% higher yield strength (YS) accompanied by a 99.3% higher elongation. [ABSTRACT FROM AUTHOR]

In the present study, a discrete layer model was established to explore the vibration performance of Functionally Graded Carbon Nanotube‐Reinforced Composite (FG‐CNTRC) open cylindrical shells with damping film embedded based on the first‐order shell theory. There are four configurations of stacking arrangements considered for FG‐CNTRC open cylindrical shells with damping film embedded. The equivalent structural parameters of the top and bottom FG‐CNTRC panels are generated by implementing the extended mixing rule. Governing equations are derived based on the Hamilton principle and solved with the Naiver solution. Subsequently, after verifying the validity of this paper's solution by comparing it with the published literature, a parametric elaborated investigation discloses the variation patterns of vibration performance of four FG‐CNTRC open cylindrical shells with damping film embedded. The conclusions of the study can be used as a useful guide about open cylindrical composite shell structures with the design of high strength and damping. Highlights: Discrete layer vibration model was bulit based on first‐order shell theory.Vbration performance of FG‐CNTRC open sandwich shells was studied.Variation patterns of frequency and loss factor was disclosed. [ABSTRACT FROM AUTHOR]

AbstractIn this article, the dynamic behavior of nanoplates under time-dependent load is investigated, focusing on functionally graded viscoelastic materials and nanoscale effects. Eringen’s nonlocal elasticity theory is utilized to examine mechanical response of the nanoplate. Hamilton’s principle is utilized to derive the equations of motion, taking into account both kinetic and potential energy aspects. The obtained complex partial differential equations are then solved employing Navier method and provides an efficient way to obtain analytical solutions. The study initially performed a free vibration analysis for functionally graded nanoplate, comparing the obtained results with those available in the literature to validate the developed method. Following this validation, a parametric analysis was conducted to examine the influence of both nonlocal parameter, which accounts for nanoscale effects, and power law exponent governing material gradation on free vibration behavior of functionally graded nanoplate. Finally, as the original contribution of this study, a damped forced vibration analysis was carried out within the scope of the parametric study, investigating the effects of power law exponents, viscoelastic parameters, nonlocal parameters, and various geometric properties on functionally graded viscoelastic nanoplates’ the displacement-time relationship and maximum displacements. [ABSTRACT FROM AUTHOR]

The primary aim of this work is to investigate the heat transfer behavior in a thick-walled functionally graded cylindrical shell subjected to internal pressure and thermal gradients, specifically focusing on how different material grading profiles (linear, exponential, and power-law) affect thermal performance. This study examines the influence of material gradation on the temperature distribution by considering variations in Young's modulus, thermal conductivity, expansion coefficient, and yield stress as functions of the shell's radial position, based on the Erdogan model. Finite element analysis (FEA) utilizing ABAQUS software was used to conduct the steady-state and transient heat transport calculations in an aluminum metal/alumina ceramic shell. For a pure aluminum shell, it is about 15% of the temperature difference between the inner and outer surfaces for the inner temperature of 115 °C and the outer one of 136 °C. By contrast, the ceramic shell thermal insulation reduces the outer wall temperature by 85%: the inner surface temperature is 149 °C and the outer surface 28 °C. Besides, the analysis of several grading profiles evidenced that quite different heat transfer features occur across the component: more steep temperature gradients and higher thermal insulation result when exponential grading is used instead of a linear one. These findings highlight the role of FGM and the optimization of grading profiles in improving high-temperature thermal management applications. [ABSTRACT FROM AUTHOR]

This study focuses on the multi-field coupling phenomena in a rotating functionally graded piezoelectric/piezomagnetic (FGPEPM) hollow cylinder under magneto-electro-elasto-hygrothermal loading. The cylinder is assumed to be infinitely long and on a Winkler elastic foundation. The hygrothermo parameter, magneto-electro-elastic properties, hygrothermal expansion, and density within the FGPEPM cylinder follow power laws with different gradient indexes along its thickness. Analytical solutions for the distributions of radial displacement, stresses, electric potential, magnetic potential, temperature, and moisture are derived by solving magneto-electro-elasto-hygrothermal coupling differential equations with appropriate boundary conditions. Validation against the existing analytical results for simplified models confirms the effectiveness of the present analytical solution. Numerical analyses further explore the effects of gradient indexes, rotational velocity, and elastic foundation stiffness on the multi-field coupling behavior of the FGPEPM cylinder. The findings provide valuable insights for designing multi-field coupling characteristics for FGPEPM materials. [ABSTRACT FROM AUTHOR]

This article presents an analytical approach leveraging a novel quasi-three-dimensional shear deformation theory to analyze the free vibration response of functionally graded graphene platelet-reinforced composite (FG-GPLRC) plates in a liquid medium. The study meticulously determines material properties using the Halpin-Tsai micromechanical model, offering a thorough characterization of these advanced nanocomposite structures. Differential motion equations, incorporating transverse shear and normal stresses, are derived via Hamilton's principle. The natural frequencies of the nanocomposite plates are computed using Galerkin's method and validated against published results, affirming their accuracy and reliability. The key innovation of this research is introducing a new trigonometric shape function, which exhibits superior precision compared to previously proposed shape functions and existing theories. Furthermore, an artificial neural network (ANN) model is developed to train the computed results, enabling precise prediction of the natural frequencies without further computational runs. The Bayesian Regularization algorithm, implemented in Matlab, is utilized for this purpose. Across different GPLs patterns and varying input parameters, the error percentage between the ANN model predictions and the results from the Galerkin's method is consistently low, often below 0.1%. The ANN model demonstrates robust generalization by effectively predicting outcomes with input data beyond its training range. Additionally, it provides immediate computational results, eliminating the delays of traditional methods. The article also examines the effects of various factors, including material characteristics, geometric parameters, and the fluid medium, on the free vibration behavior of FG-GPLRC plates. [ABSTRACT FROM AUTHOR]

The main objectif of this work is to examine the thermal environment's effect of on the free vibration of double curvature shells made of functionally graded materials. A new mathematical model based on higher order shear deformation theory, is developed to incorporate the influence of dependent and independent thermal stresses, which can be uniform, linear, nonlinear, or sinusoidal on the mechanical properties of the double curvature shell. Two material couples, (S i 3 N 4 / SUS 304 , ZrO 2 /Ti‐6Al‐4V) , are considered as progressive materials, accounting for temperature-dependent and temperature-independent heat conduction and material properties in the thickness direction. The temperature field is assumed to be uniform across the shell surface but varies only in the thickness direction. The accuracy of the analytical results is validated by comparing them with existing literature results for functionally graded material (FGM) shells with infinite radii under dependent and independent temperature conditions. The study aims to demonstrate the thermal effects on material composition, as well as various specific geometric shapes such as plates, cylinders, spheres and ellipses and how different temperature laws influence the frequencies of vibrating double curvature FGM shells. Both existing theories accurately predict temperature-independent and temperature-dependent vibration responses of the shells. By verifying and comparing the results with the literature, a better agreement is achieved, thereby paving the way for further research in this field. [ABSTRACT FROM AUTHOR]

This study focuses on free vibration analysis of functionally graded material (FGM) plates supported by Winkler–Pasternak elastic foundation in thermal environment using element-free Galerkin (EFG) meshless method. Plate kinematics depend on first-order shear deformation theory. Uniform, linear, and nonlinear temperature variations through the thickness direction are considered, along with the temperature-dependent material properties. The numerical outcomes obtained from EFG method are compared with those available in the published literature to validate the proposed method's accuracy. An artificial neural network (ANN) model that can easily predict the natural frequencies of the plate is constructed from the EFG method outcomes. Further, the effect of foundation parameters, power law index, thickness ratio, temperature variations, and different boundary conditions are investigated; results show that these significantly influence the vibration response of FGM plates supported by the elastic foundation. Increasing the temperature of FGM plates supported by the Winkler–Pasternack foundation causes a decrease in the dimensionless fundamental natural frequency, and the uniform temperature influence is greater than that of linear and nonlinear temperature variation. The proposed EFG-ANN prediction model saves approximately 98.80% computation time when predicting the natural frequency with an accuracy of approximately 98.76% compared to that by EFG meshless method alone. [ABSTRACT FROM AUTHOR]

Functionally graded materials (FGMs) are advanced composite materials with spatially varying properties, and their porosity distribution further enhances their complexity. The distribution pattern of porosity within a porous material plays a crucial role in determining the mechanical response of these structures. Therefore, the main objective of this study is to analyze the bending, free vibration, and buckling characteristics of porous FG plates by considering different porosity distributions and their effects on the overall behavior. To achieve this goal, a new finite element model is developed in the framework of an improved first-order shear deformation theory (IFSDT). In contrast to the conventional Mindlin–Reissner theory, the present IFSDT incorporates an improved mathematical formulation and provides a more realistic parabolic depiction of shear strain throughout the plate's thickness without using any shear correction factors. In the present study, five types of porosity distribution functions are considered for the analysis. The material characteristics of the FGM porous plate change gradually in the thickness direction based on a power-law function. The governing equations are derived here using Hamilton's principle, and a finite element method is employed for numerical analysis. Comparative analyses with previously published literature underscore the precision and simplicity of our developed finite element model. Moreover, the effects of various types of loads, porosity parameters, power-law index, side-to-thickness ratio, aspect ratio, porosity distributions and boundary conditions on the deflections, natural frequencies, and critical buckling loads are thoroughly analyzed in detail. Finally, the findings of this research contribute to the understanding of the mechanical behavior of FGMs and pave the way for designing and optimizing novel porous functionally graded structures. [ABSTRACT FROM AUTHOR]

This study presents the buckling and lateral torsional buckling behaviors of thin-walled laminated composite or functionally graded sandwich I-beams. A refined beam model (RBT) based on the 3D Saint-Venant (SV) solution is used in this study to formulate the problem. This model allows for a realistic analysis of beams with arbitrary cross-sections and is free from the limitations of classical beam theories. The displacement models establish a consistent 1D beam theory that accurately captures the essence of the cross-section's nature. The governing models consider cross-section deformations, including in and out of plane warpings and distortions derived from the 3D SV solution associated with the cross-section vibrational behavior. Furthermore, a user-friendly numerical tool called CSB (cross-section and beam analysis) is used to facilitate the implementation of this method. The numerical results are examined in detail and compared with previous works to investigate the influence of boundary conditions, angle-ply, shear effects, span-to-height ratio, and material distribution on the critical buckling loads of thin-walled I-beams. The results demonstrate that the RBT models accurately and efficiently analyze thin-walled I-beams under different loads and boundary conditions. Furthermore, some of the new results are presented as reference values for the future. [ABSTRACT FROM AUTHOR]

Aluminum alloys are widely used in industry due to their light weight. These alloys are generally exposed to abrasive wear, which diminishes their effective lifespan. The wear resistance of these alloys is enhanced by adding various reinforcements, however, this enhancement comes at the cost of reduced fracture toughness. This paradox of increased wear resistance versus decreased fracture toughness in aluminum alloys can be resolved by using functionally graded materials (FGMs). This study focuses on the abrasive wear behavior of functional graded aluminum matrix composites reinforced with Al3Ti particles. The wear properties of the composites were investigated by considering the characteristics of the composite such as matrix type and various composite zones, as well as the wear parameters such as abrasive particle diameter, load, sliding speed and distance. Taguchi method was used in the abrasive wear tests in order to get more reliable results in a timeefficient manner. Experiment recipes were created based on the L27(36) orthogonal series. As a result of the study, it is observed that the wear resistance of the composites increases with an increase in Al3Ti reinforcement content and hardness of the matrix. In addition, the size of abrasive particles and the applied load are significant factors affecting abrasive wear. [ABSTRACT FROM AUTHOR]

This study introduces a novel analytical framework for investigating the vibration characteristics of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) elliptical cylindrical shells under arbitrary boundary conditions. Unlike previous studies that focused on simplified geometries or specific boundary conditions, this work combines the least-squares weighted residual method (LSWRM) with an adapted variational principle, addressing high-order vibration errors and ensuring continuity across structural segments. The material properties are modeled using an extended rule of mixtures, capturing the effects of carbon nanotube volume fractions and distribution types on structural dynamics. Additionally, virtual boundary techniques are employed to generalize elastic boundary conditions, enabling the analysis of complex boundary-constrained structures. Numerical validation against existing methods confirms the high accuracy of the proposed framework. Furthermore, the influence of geometric parameters, material characteristics, and boundary stiffness on vibration behavior is comprehensively explored, offering a robust and versatile tool for designing advanced FG-CNTRC structures. This innovative approach provides significant insights into the optimization of nanoscale reinforced composites, making it a valuable reference for engineers and researchers in aerospace, marine, and construction industries. [ABSTRACT FROM AUTHOR]

In the present study, the vibration characteristics of a cylindrical shell (CS) made up of four layers are investigated. The ring is placed in the axial direction of a four-layered functionally graded material (FGM) cylindrical shell. The layers are made of functionally graded material (FGM). The materials used are stainless steel, aluminum, zirconia, and nickel. The frequency equations are derived by employing Sander's shell theory and the Rayleigh–Ritz (RR) mathematical technique. Vibration characteristics of functionally graded materials have been investigated using polynomial volume fraction law for all FGM layers. The characteristic beam functions have been used to determine the axial model dependency. The natural frequencies are obtained with simply supported boundary conditions by using MATLAB software. Several analogical assessments of shell frequencies have also been conducted to confirm the accuracy and dependability of the current technique. [ABSTRACT FROM AUTHOR]

The ability to control process parameters over time and build space in electron beam powder bed fusion (PBF-EB) opens up unprecedented opportunities to tailor the process and use materials of a different nature in the same build. The present investigation explored the various methods used to adapt the PBF-EB process for the production of functionally graded materials (FGMs). In this way, two pre-alloyed powders—a stainless steel (SS) powder and a highly alloyed cold work tool steel (TS) powder—were combined during processing in an S20 Arcam machine. Feasibility experiments were first carried out in a downscaled build setup, in which a single powder container was installed on top of the rake system. In the container, one powder was placed on top of the other (SS/TS) so that the gradient materials were produced as the powders were spread and intermixed during the build. The process was later scaled up to an industrial machine setup, where a similar approach was implemented using two configurations of powder disposal: SS/SS + TS/TS and TS/TS + SS/SS. Each configuration had an intermediate layer of powder blend. The FGMs obtained were characterized in terms of their microstructure and local and macromechanical properties. For the microstructural analysis, optical microscopy, scanning electron microscopy (SEM), and energy-dispersive X-ray spectroscopy (EDX) were performed on the polished cross-sections. This provided evidence of gradual microstructural and compositional transitions in the samples, with a shift from SS to TS and vice versa. Nanoindentation experiments confirmed that there was a consequent gradient in the hardness, stiffness, and wear ratio from the softer and ductile SS to the harder and stiff TS. Scratch experiments revealed gradual evolution in the sliding wear behavior of the printed materials. A "progressive spring" and a "hardness-tailored punching tool" were fabricated as demonstrators. The results obtained demonstrate the great potential to gradually tailor the composition, microstructure, mechanical properties, and wear resistance by combining different powders, and they suggest that any PBF-EB system can be repurposed to build gradient materials without hardware modification. Potential applications include the tooling industry, where hard and wear-resistant materials are needed for the surfaces of tools, with tougher and more ductile materials used in the cores of tools. [ABSTRACT FROM AUTHOR]

A novel two-dimensional elasticity solution is presented in this paper, specifically designed for studying the vibration of functionally graded porous (FGP) beams. The kinetics of the beam are defined by two-dimensional elasticity theory, and Lagrange's equations are used to derive the governing equations of motion. The Ritz method devises the expansion of displacement variables in polynomial and trigonometric series in the thickness and axial directions. Furthermore, microvoids can emerge as a result of technical issues during the manufacture of functionally graded materials (FGMs), leading to the development of porosities. The porosity distribution functions, one for three porosity distributions: uniform porosity (UP), non-uniform porosity-I (NUP-I), and non-uniform porosity-II (NUP-II), are considered in the problem. This study investigates the impact of the gradation exponents (p) in the z-direction, the slenderness ratio (L/h), the distribution of porosity, the porosity coefficient (e), and various boundary conditions on the natural frequencies. A comparison with the findings from higher-order shear deformation theory (HSDT) validated the accuracy and effectiveness of the proposed methodology. [ABSTRACT FROM AUTHOR]

In the present study, the governing equation of pressurized axisymmetric thick cylinders made of Functionally Graded materials (FGMs) with large deformations is derived using the Nonlinear Plane Elasticity Theory (NPET). Because of large deformations along the radial direction and hence the existence of nonlinear terms in kinematic equations, the governing equation is a nonlinear second-order equation with variable coefficients, which is solved in plane stress and plane strain states using the perturbation technique. According to the equilibrium equation, boundary conditions and different end conditions of the cylinder: open ends and closed ends; radial, axial, and circumferential stresses and radial displacement in cylindrical shells are analytically calculated. To investigate the accuracy of the results obtained from the analytical solution, the numerical finite element modeling of the mentioned cylinder with ABAQUS software based on the nonlinear elasticity theory is done and the results of the two methods are compared. This research reveals that the obtained results by the mentioned analytical solution procedure have good accuracy for cylindrical shells under pressure load. The aim of this study is to provide a mathematical solution for the nonlinear analysis of large deformations of FGM cylinders. [ABSTRACT FROM AUTHOR]

This study delves into the investigation of shear horizontal transverse waves within a structure composed of a layer and a semi-infinite medium. The layer considered in this work is made of functionally graded magneto-electro-elastic material, and the semi-infinite medium is comprised of functionally graded piezoelectric material with a linear gradedness parameter. Additionally, the layer and semi-infinite medium has a mechanical imperfect interface. Furthermore, the solutions for the layer and semi-infinite medium are derived utilizing the WKB approximation technique. This involves initially transforming the partial differential equation into an ordinary differential equation through basic variable separation and the ordinary differential equation is solved by WKB approximation technique. The obtained results lead to dispersion relations presented in determinant form for two cases: electrically open and short. To explore the influences of various parameters on shear horizontal transverse waves, a specific model is considered. This model is composed of a layer made of magneto-electro-elastic material (BaTiO3-CoFe2O4) and a semi-infinite medium consisting of piezoelectric material (BaTiO3). Also, the graphs are plotted to visualize the variation in shear horizontal transverse waves in relation to both phase velocity and wave number. [ABSTRACT FROM AUTHOR]

In this paper, a coupled displacement field (CDF) method was proposed to examine the free vibration behavior of a functionally graded (FG) rectangular plate with simply supported (SSSS) and clamped (CCCC) boundary conditions. The composition of the functionally graded rectangular plate is ceramic on the top and metal on the bottom. According to the power-law exponent form, the rectangular plate material properties vary continuously in the thickness direction. The trial functions signifying the displacement constituents of the cross-sections of the plate are stated in simple algebraic polynomial forms. The lateral displacement field is derived in terms of the total rotations with the help of coupling equations. By utilizing the energy formulation, the undetermined coefficients are obtained. The frequency parameters with various aspect ratios, thickness ratios, and power-law for all edges are simply supported and clamped boundary conditions are derived. To validate the numerical results, a comparison of frequency parameters is done with other literature. [ABSTRACT FROM AUTHOR]

This paper presents the free vibration and buckling analyses of multi-directional functionally graded porous doubly curved shallow shells resting on Pasternak elastic foundations in a thermal environment. For the first time, a linear finite element formulation using the refined high-order shear deformation theory, combined with the Hermitian function, is developed to compute the vibration and buckling behaviour of doubly curved shallow shells. Mechanical properties of MFGP material change according to the length, width and thickness directions and the porosity distribution including even and uneven. The doubly curved shallow shell is operated in uniform, linear and non-linear temperature environments. The convergence and accuracy of the proposed method are verified by comparing numerical results with published works. In addition, a comprehensive numerical investigation was carried out to evaluate the influence of parameters on the natural frequency and critical buckling behaviour of MFGP doubly curved shallow shells. [ABSTRACT FROM AUTHOR]

AbstractThis paper presents an innovative computational approach for modeling continuous material gradation in functionally graded sandwich beams (FGSBs) with porous cores, utilizing Ansys Mechanical APDL (Ansys Parametric Design Language). The material properties of the FGSBs are modeled to vary progressively in the thickness direction based on a power-law distribution. The uniform, symmetric, and asymmetric porosity patterns were examined to assess the impact of different core configurations. The beams are meticulously modeled using the SOLID186 element, with material gradation and porosity distribution rules explicitly coded in Ansys via its APDL tool. Two boundary conditions were explored, namely clamped-clamped and clamped-free, considering a comprehensive three-dimensional representation of the beams. The accuracy of the proposed approach was validated by comparing the results of free vibration, buckling, and static bending analyses with those from a quasi-3D deformation theory-based finite element model, as well as with findings from existing literature. An extensive parametric study delves into the effects of the porosity coefficient, core porosity distribution, skin-to-core thickness ratio, power-law index, slenderness, and boundary conditions on the mechanical behavior of FGSBs. The study’s findings demonstrate strong concordance with the literature, confirming the precision and reliability of the proposed technique. This validation paves the way for its application in various research areas involving FG sandwich structures across different engineering disciplines. [ABSTRACT FROM AUTHOR]

This article presents a new method called the artificial neural networks-genetic programming (ANNs-GP) algorithm, which effectively predicts the bending behavior of functionally graded graphene origami-enabled auxetic metamaterial (FG-GORAM) structures under transient conditions. Functionally graded materials (FGMs) display spatial heterogeneity in their composition and microstructure, resulting in distinctive mechanical characteristics that make them well-suited for a wide range of engineering applications. The objective of this study is to create a prediction model that can accurately capture the intricate transient bending behavior of FGM structures. To do this, the researchers have used the ANN-GP technique, which combines ANNs with GP. The ANN component acquires knowledge from a dataset including actual or simulated bending data, while the GP component fine-tunes the structure and parameters of the neural network to improve its ability to make accurate predictions. The proposed algorithm combines the strengths of ANNs and GP to accurately predict the bending behavior of FG-GORAM structures. This algorithm is robust and efficient, allowing designers and engineers to optimize the performance and reliability of these structures in various applications. The effectiveness of the ANN-GP method is proved by comparing it to experimental or simulated data. This shows that the algorithm has the potential to be a useful tool for designing and analyzing sophisticated materials and structures. [ABSTRACT FROM AUTHOR]

The present study is focused on the development of an analytical solution for the buckling analysis of carbon nanotube reinforced functionally graded (FG-CNTRC) laminated plates resting on Pasternak elastic foundation and subjected to different nonuniform edge loads. The analytical solution is formulated using a two-step procedure: First, an accurate in-plane stress solution is developed by superimposing three suitable Airy's stress functions; second, the stress solution is utilized to compute the critical buckling loads using the Galerkin's procedure. Results from parametric studies show that the buckling behavior of FG-CNTRC plates greatly depends on the type of nonuniform loads, plate configurations, and support parameters. [ABSTRACT FROM AUTHOR]

Monotonic or cyclic uni-axial loading tests on specimens with or without notch are designed to characterize the materials, and to develop in their results a formulation of the material either analytically or by prediction using a numerical technique, by the finite element method and using the ABAQUS calculation code, The novelty in this work lies in the way the notch itself is subjected to stress. Many studies have focused solely on damage to structures caused by the presence of notches, whereas in reality it's the notches themselves that are subjected to sometimes severe and complex loading, The latter rapidly undermines the service life of these structures, strongly destabilizing the notch to the point of damage by a cyclic and uni-axial loading mode is the embodiment by a numerical prediction of this new idea in this work, which is based beforehand under simple condition on a validation of the numerical model to that of the experimental results, The fatigue behavior of the structure under the equivalent Von Mises flow stress is given by the combined hardening law, and the damage to the structure by crack initiation and propagation is also given by the XFEM (Extend Finite Element Method) technique, in the second part of this work, a reinforcement of the notch in the structure by a locally graded concept with another material surrounding the notch is proposed in order to delay damage under these loading conditions, the results of damage under the effect of the proposed parameters (grading concept and volume fraction index) have been highlighted in this work. [ABSTRACT FROM AUTHOR]

Based on the theory of nonlocal elasticity and nonlocal heat conduction, a new dual-phase-lag heat conduction model with memory dependent effect is proposed in this article to explore the thermodynamic behavior of functionally graded rotating piezoelectric rods under the action of moving heat sources. Assuming that the material properties of functionally graded piezoelectric rods vary exponentially along the length direction, the end of the rod is rigid and fixed without voltage. Use Laplace transform to transform the problem into the spatial domain and perform analytical solutions, then use inverse Laplace transform to obtain the time-domain solution. Numerical solutions were performed for dimensionless displacement, temperature, electric potential, and stress, and the variation patterns of the physical quantities involved were described in graphical form. The calculation provides the effects of functional gradient non-uniformity index, thermal nonlocal parameters, kernel function, and viscoelastic parameters on the physical quantities involved. [ABSTRACT FROM AUTHOR]

Reinforcement in composite and notched structures has long been the objective of many researchers. One of the commonly used solutions is hybrid composite. Other recently reemerged solutions are graded materials. These respond, according to their modes of solicitation, to the targeted resistance objectives. However, composites with UD (unidirectional) fiber quality limit the choice of structural grading solely based on their thickness. Using the finite element method and the ABAQUS calculation code, this work presents the embodiment through numerical prediction of an idea based on the concept of material grading by FGM function. The objective of this approach is to introduce the volumetric fraction of the FGM concept into the Fiber-Matrix mixing laws in UD composite. Thickness-graded composites are subjected to a volumetric fraction function raised to the power of a parameter called volumetric fraction index (n). These structures, according to the proposed concepts, are analyzed under thermomechanical loading. The proposed grading of these composites is based on the presence of fibers in the matrix, where the fiber is denser on one side, called the simple concept C-S. The other two symmetrical concepts, named C-2 and C-3, present denser fibers in the middle and on both sides of the plate, respectively. These proposed concepts aim to observe how damage is caused by different responses and levels. The results under the different analyzed parameters are evaluated and compared to the results of the two other non-graded composites, thus showing the limits of those that are graded in terms of properties. According to the thermomechanical loading, the proposed graded composite has demonstrated a resistance overcapacity by the grading index (n) or their locations by concept C1- and C-2 of fibers have played a role in optimizing this capacity. The results also show that damage is caused by deformation overcapacity. [ABSTRACT FROM AUTHOR]

In this study, molecular dynamics simulation is carried out to investigate the mechanical properties and failure behavior of a novel carbon nanotube-reinforced aluminum-copper alloy nanocomposite (Al–Cu/CNT). The study explores the influence of several key parameters, including the volume fraction of the carbon nanotubes (CNT), the diameter of CNT, the structure (zigzag, armchair, and chiral) of CNT, and the applied strain rate on the mechanical behavior of Al–Cu /CNT nanocomposite structure. The MD simulation results reveal that increasing the volume fraction of the CNT evidently increases the modulus of elasticity whereas it has no detrimental effect on the failure strain levels of the nanocomposites. The size of the CNT exhibits an inverse relationship with the elastic modulus. It is noted that increasing the size of the armchair CNTs results in lower elastic modulus levels and higher failure strain levels. The failure behavior of the Al–Cu /CNT nanocomposite is observed to vary according to the structure of the CNT. The nanostructure with zigzag CNTs experiences a gradual failure mode whilst armchair CNTs lead to a sudden failure in the nanostructures. The applied strain rate plays a minor role on the elastic modulus, but a slight increase in failure strain levels is observed at higher strain rates. The mechanical behavior of functionally graded Al–Cu alloy reinforced with CNT is also investigated (Al–Cu FGM/CNT). Minor changes are noticed in the elastic modulus and the failure strain levels of Al–Cu FGM/CNT with different material variations. [ABSTRACT FROM AUTHOR]

Functionally graded materials (FGMs) using the finite element method (FEM) with C0 elements, focusing on the examination of material variable parameters. The research advances the understanding of FGMs through a thermo-structural analysis of an FGM disk, assessing its response under thermal and mechanical loads. Thermal and thermo-mechanica analysis demonstrates the precision of the proposed approach in delineating the complex behavior of FGMs under diverse conditions. The research contributes to enrich the comprehension of FGM behavior using simple FEM models. [ABSTRACT FROM AUTHOR]

This investigation focuses on the nonlinear behavior of porosity-dependent functionally graded (FG) truncated conical small-scale structures. The modified coupled stress theory, as well as the energy method, are applied to generate the nonlinear partial differential equations (PDEs) related to buckling analysis of simply supported nonuniform micro-cylindrical structures. The material dispersion is gradually changed along the length of the structures between the Nickel and concrete, while the porosity voids are scattered in the radial direction, and the external radius of the structure decreases along the length direction via nonlinear mathematic equations applicable in sports structures. The PDEs are numerically solved via the generalized differential quadrature method (GDQM) coupled with the numerical iterative technique. In this particular context, the aim is to predict nonlinear results using a newly developed methodology that employs artificial neural networks (ANNs). The predictions generated by this approach will be compared against previously obtained data and validated to ensure their accuracy and reliability. The ANN methodology is expected to provide a more robust and comprehensive framework for predicting nonlinear results, which would be helpful in a variety of settings, from scientific research to engineering applications. [ABSTRACT FROM AUTHOR]