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The buckling and free vibration of initially stressed functionally graded cylindrical shell reinforced with non-uniformly distributed graphene platelets (GPLs) are investigated using the state-space formulation based on three-dimensional elasticity theory. The shell is under an axial initial stress and composed of multilayers with GPLs uniformly dispersed in each individual layer but its weight fraction changing layer-by-layer along the thickness direction. The modified Halpin-Tsai model and rule of mixtures are employed to evaluate the effective elastic properties of the GPL-reinforced shell. Analytical buckling and frequency solutions are obtained for simply supported shells. Numerical results are presented for functionally graded GPL-reinforced cylindrical shells with five GPL dispersion patterns (GPL-UD, GPL-V, GPL-A, GPL-X, and GPL-O). The effects of GPL weight fraction, dispersion pattern, geometry, and size as well as the influence of initial stress on the buckling and free vibration characteristics of the shell are discussed in detail. It is found that the addition of a small amount of GPLs significantly increases the critical buckling stress and natural frequencies. The GPL-X pattern outperforms other patterns for thin composite shells while the uniform pattern GPL-UD works better for thick composite shells. [ABSTRACT FROM AUTHOR]

This paper is focused on the in-plane crushing of two-dimensional (2D) porous structures with a special attention on the effect of functionally graded (FG) porosities. The dynamic response and energy absorption of closed-cell metal foams with different porosity distributions are investigated by using finite element (FE) analysis. Two symmetric, two asymmetric and one uniform distributions of internal pores along the impact direction are constructed with Voronoi tessellation. The proposed porous structure is crushed under the impact of a rigid panel with a constant velocity. The deformation of cell walls is simulated using a plastic kinematic material model. The erosion criteria and hourglass control are applied to ensure the accuracy of numerical results, which are validated against the experimental data from open literature. The effects of varying parameters on the energy absorption, deformation pattern, and stress-strain curve of the FG porous structure are discussed. The dynamic response is found to be influenced by different random cell geometries, porosity gradients, cell wall thicknesses, internal pore numbers, and impact velocities. The effective way to improve the energy absorption capability of the porous structure under a constant-velocity impact is proposed, shedding new insights into the deformation mechanism of the FG porous structure for engineering design. [ABSTRACT FROM AUTHOR]

This paper presents static bending and compressive buckling analyses of functionally graded multilayer graphene nanoplatelet (GPL)/polymer composite plates within the framework of the first-order shear deformation theory. The GPL weight fraction shows a layer-wise change along the thickness direction with GPLs uniformly dispersed in the polymer matrix in each individual layer. The effective Young's modulus of the nanocomposites is estimated through the Halpin-Tsai micromechanics model while the effective Poisson's ratio is determined by the rule of mixture. Analytical solutions are obtained for the static deflection and critical buckling load of the simply supported functionally graded GPL/polymer plates by using the Navier solution technique. Numerical results show that GPL distribution pattern, weight fraction, and geometry and size have significant influences on the bending and buckling behaviors of the functionally graded GPL reinforced nanocomposite plate. [ABSTRACT FROM AUTHOR]

This paper deals with the thermal buckling and postbuckling of functionally graded multilayer nanocomposite plates reinforced with a low content of graphene platelets (GPLs). It is assumed that GPL reinforcements are randomly oriented and uniformly dispersed in each individual GPL-reinforced composite (GPLRC) layer but the concentration follows a layer-wise variation across the plate thickness. The modified Halpin-Tsai micromechanics model that takes into account the GPL geometry effect is adopted to estimate the effective Young's modulus of GPLRC layers. Within the framework of the first-order shear deformation theory, the nonlinear governing equations are derived by applying the principle of virtual displacements and then solved by using a differential quadrature-based iteration technique. Parametric studies are conducted to examine the influences of GPL distribution pattern, concentration and geometry, as well as in-plane force on the thermal buckling and postbuckling behaviours. Our results show that distributing more GPLs near the surface layers is capable of reinforcing the thermal buckling and postbuckling performances of GPLRC plates. Whether the thermal buckling and postbuckling resistance increases or decreases with the increases in GPL weight fraction, aspect ratio and width-to-thickness ratio is highly dependent on the GPL distribution pattern. [ABSTRACT FROM AUTHOR]

Within the framework of three-dimensional elasticity theory, this paper investigates the axisymmetric bending of novel functionally graded polymer nanocomposite circular and annular plates reinforced with graphene nanoplatelets (GPLs) whose weight fraction varies continuously and smoothly along the thickness direction. The generalized Mian and Spencer method is utilized to obtain the analytical solutions of nanocomposite circular and annular plates under a combined action of a uniformly distributed transverse load and a through-thickness steady temperature field. Three different distribution patterns of GPLs within the polymer matrix are considered. The present analytical solutions are validated through comparisons against those available in open literature for the reduced cases. A parametric study is conducted to examine the effects of GPL weight fraction, distribution pattern, plate thickness to radius ratio, and boundary conditions on the stress and deformation fields of the plate. The results show that GPL nanofillers with a low content can have a significant reinforcing effect on the bending behavior of the thermo-mechanically loaded plate. [ABSTRACT FROM AUTHOR]

This paper studies the nonlinear free vibration of a multi-layer polymer nanocomposite beam reinforced by graphene platelets (GPLs) non-uniformly distributed along the thickness direction. Theoretical formulations are based on Hamilton’s principle, Timoshenko beam theory, and von Kármán nonlinear strain-displacement relationship. The effective Young’s modulus of the GPL/polymer composites is estimated by Halpin-Tsai micromechanics model to account for the effects of GPL geometry and dimensions. The vibration frequencies and amplitude of the beam are obtained numerically by employing Ritz method. The influences of the distribution pattern, weight fraction, geometry and size of GPL nanofillers, the total number of layers together with the vibration amplitude and boundary conditions on the nonlinear free vibration behavior are investigated. The results show that adding a very small amount of GPLs into polymer matrix as reinforcements significantly increases the natural frequencies of the beam. Using larger sized GPLs with fewer single graphene layers and placing more GPLs near the top and bottom surfaces of the beam are the most effective ways to strengthen the beam stiffness and increase the linear and nonlinear natural frequencies. [ABSTRACT FROM AUTHOR]

This paper studies free vibration and elastic buckling of functionally graded porous nanocomposite beams where the internal pores and graphene platelets (GPLs) are layer-wise distributed in the matrix either uniformly or non-uniformly according to three different patterns. A multilayer beam model is proposed with material parameters varying across layers to achieve graded distributions in both porosity and nanofillers. Mechanical properties of closed-cell cellular solids under Gaussian Random Field scheme are used to determine the variation of Poisson's ratio and the relationship between porosity coefficients and mass density. The elastic modulus of the nanocomposite is obtained by using Halpin-Tsai micromechanics model. Theoretical formulations are based on Timoshenko beam theory and Ritz method is employed to obtain the dimensionless fundamental natural frequency and critical buckling load of porous nanocomposite beams. A comprehensive parametric study is carried out, with a particular focus on the effects of weight fraction, distribution pattern, geometry and size of GPL reinforcements on the free vibration and buckling behaviors of the nanocomposite beam with different metal matrixes and porosity coefficients. The results indicate that the effective stiffness of the porous nanocomposite beam can be best improved when both porosity distribution and GPL dispersion pattern are non-uniform but symmetric. [ABSTRACT FROM AUTHOR]

This paper studies the nonlinear bending behavior of a novel class of multi-layer polymer nanocomposite beams reinforced with graphene platelets (GPLs) that are non-uniformly distributed along the thickness direction. Nonlinear governing equation is established based on Timoshenko beam theory and von Kármán nonlinear strain-displacement relationship. The effective Young's modulus of the nanocomposites is determined by modified Halpin-Tsai micromechanics model. Ritz method is employed to reduce the governing differential equation into an algebraic system from which the static bending solutions can be obtained. A comprehensive parametric study is then conducted, with a particular focus on the influences of distribution pattern, weight fraction, geometry and size of GPLs together with the total number of layers on the linear and nonlinear bending performances of the beams. Numerical results demonstrate the significantly improved bending performance through the addition of a very small amount of GPLs into polymer matrix as reinforcements. It is found that dispersing more GPLs that are in square shape with fewer single graphene layers near the top and bottom surfaces of the beam is the most effective way to reduce bending deflections. Beams with a higher weight fraction of GPLs that are symmetrically distributed in such a way are also less sensitive to the nonlinear deformation. [ABSTRACT FROM AUTHOR]

This paper investigates the imperfection sensitivity of thermal post-buckling behaviour of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) beams subjected to in-plane temperature variation. The material properties of FG-CNTRCs are assumed to be graded in the thickness direction and temperature-dependent. A generic imperfection function is used to model various possible imperfections, including sine type, global and localized imperfections. The governing equations are derived based on the first-order shear deformation beam theory and von-Kármán geometric nonlinearity. The differential quadrature method in conjunction with modified Newton–Raphson technique is employed to determine the thermal post-buckling equilibrium path of imperfect FG-CNTRC beams. Thermal buckling is treated as a subset problem. A parametric study is conducted to examine the effects of imperfection mode, half-wave number, location and amplitude on their thermal post-buckling performance. The influences of distribution pattern and volume fraction of carbon nanotubes, boundary conditions and slenderness ratio are discussed as well. The results indicate that the thermal post-buckling is highly sensitive to the imperfection mode, half-wave number, location as well as its amplitude. It is also shown that the clamped-clamped FG-CNTRC beam is more sensitive to imperfections than those with other boundary conditions whereas other parameters do not substantially affect the imperfection sensitivity of thermal post-buckling behaviour. [ABSTRACT FROM AUTHOR]

This paper investigates the free and forced vibration characteristics of functionally graded multilayer graphene nanoplatelet (GPL)/polymer composite plates within the framework of the first-order shear deformation plate theory. The weight fraction of GPL nanofillers shows a layer-wise variation along the thickness direction with GPLs uniformly dispersed in the polymer matrix in each individual layer. The effective Young’s modulus is predicted by the modified Halpin-Tsai model while the effective Poisson’s ratio and mass density are determined by the rule of mixture. Governing differential equations of motion are derived and Navier solution based technique is employed to obtain the natural frequencies and dynamic response of simply supported functionally graded GPL/polymer plates under a dynamic loading. A parametric study is conducted, with a particular focus on the effects of GPL distribution pattern, weight fraction, geometry and size as well as the total number of layers on the dynamic characteristics of the plates. [ABSTRACT FROM AUTHOR]

The nonlinear free vibration behavior of shear deformable sandwich porous beam is investigated in this paper within the context of Timoshenko beam theory. The proposed beam is composed of two face layers and a functionally graded porous core which contains internal pores following different porosity distributions. Two non-uniform functionally graded distributions are considered in this paper based on the equivalent beam mass, associated with a uniform distribution for purpose of comparison. The elastic moduli and mass density are assumed to vary along the thickness direction in terms of the coefficients of porosity and mass density, whose relationship is determined by employing the typical mechanical characteristic of an open-cell metal foam. The Ritz method and von Kármán type nonlinear strain-displacement relationships are applied to derive the equation system, which governs the nonlinear vibration behavior of sandwich porous beams under hinged or clamped end supports. A direct iterative algorithm is then used to solve the governing equation system to predict the linear and nonlinear frequencies which are presented by a detailed numerical study to discuss the effects of porosity coefficient, slenderness ratio, thickness ratio and to compare the varying porosity distributions and boundary conditions, providing a feasible way to improve the vibration behavior of sandwich porous beams. [ABSTRACT FROM AUTHOR]

This paper investigates the free vibration and elastic buckling of sandwich beams with a stiff core and functionally graded carbon nanotube reinforced composite (FG-CNTRC) face sheets within the framework of Timoshenko beam theory. The material properties of FG-CNTRCs are assumed to vary in the thickness direction, and are estimated through a micromechanical model. The governing equations and boundary conditions are derived by using Hamilton's principle and discretized by employing the differential quadrature (DQ) method to obtain the natural frequency and critical buckling load of the sandwich beam. A detailed parametric study is conducted to study the effects of carbon nanotube volume fraction, core-to-face sheet thickness ratio, slenderness ratio, and end supports on the free vibration characteristics and buckling behavior of sandwich beams with FG-CNTRC face sheets. The vibration behavior of the sandwich beam under an initial axial force is also discussed. Numerical results for sandwich beams with uniformly distributed carbon nanotube-reinforced composite (UD-CNTRC) face sheets are also provided for comparison. [ABSTRACT FROM AUTHOR]

Monomorph and bimorph actuators made of piezoelectric materials are widely used in smart materials and structural control. Recent studies show that their performances can be remarkably improved by the use of functionally graded piezoelectric materials (FGPMs) whose compositional profile and effective material properties are graded along the thickness direction. This paper investigates the linear and nonlinear vibration behaviors of monomorph and bimorph made from a mixture of PZT4 and PZT-5H with material composition following a power law distribution. Theoretical formulations are based on von Kármán kinematic relationships and Timoshenko beam theory to account for the effect of transverse shear deformation. The differential quadrature method (DQM) and the second-order backward difference scheme are employed to obtain the linear and nonlinear vibration frequencies. A parametric study is conducted to investigate the influences of volume fraction index, slenderness ratio, nonlinear deformation and different loading conditions. [ABSTRACT FROM AUTHOR]

Abstract: This paper studies the dynamic response of functionally graded beams with an open edge crack resting on an elastic foundation subjected to a transverse load moving at a constant speed. It is assumed that the material properties follow an exponential variation through the thickness direction. Theoretical formulations are based on Timoshenko beam theory to account for the transverse shear deformation. The cracked beam is modeled as an assembly of two sub-beams connected through a linear rotational spring. The governing equations of motion are derived by using Hamilton’s principle and transformed into a set of dynamic equations through Galerkin’s procedure. The natural frequencies and dynamic response with different end supports are obtained. Numerical results are presented to investigate the influences of crack location, crack depth, material property gradient, slenderness ratio, foundation stiffness parameters, velocity of the moving load and boundary conditions on both free vibration and dynamic response of cracked functionally graded beams. [Copyright &y& Elsevier]

Abstract: This paper studies the parametric instability of functionally graded beams with an open edge crack subjected to an axial pulsating excitation which is a combination of a static compressive force and a harmonic excitation force. It is assumed that the materials properties follow an exponential variation through the thickness direction. Theoretical formulations are based on Timoshenko beam theory and linear rotational spring model. The governing equations of motion are derived by using Hamilton’s principle and transformed into a set of Mathieu equations through Galerkin’s procedure. The natural frequencies with different end supports are obtained. The boundary points on the unstable regions are determined by using Bolotin’s method. Numerical results are presented to highlight the influences of crack location, crack depth, material property gradient, beam slenderness ratio, compressive load, and boundary conditions on both the free vibration and parametric instability behaviors of the cracked functionally graded beams. [Copyright &y& Elsevier]

With the recent developments in structural analysis and material technologies, engineers can now use framing systems and construction materials in a more efficient manner. This results in a reduction in safety margins and the reserve capacity of structures to accommodate abnormal or accidental loading conditions. The consideration of progressive failure or collapse in the design process has also become increasingly important. In view of this, there is a need to modify traditional teaching methods in the education of the new generation of structural engineers with the view to build up their conceptualisation of local and global structural behaviour to gain a clear understanding of the progressive failure or collapse of structural systems. In achieving this goal, we propose to educate structural engineering students using 'virtual' experiments in a self-learning environment that allows them to observe changes in structural behaviour instantly as one changes to structural geometry, support conditions, member properties and loading conditions. A user-friendly 2D structural analysis software application called iSA (Instant Structural Analysis) has been developed as a prototype self-learning environment for this purpose. This article presents some of the essential requirements of the prototype to render it a suitable tool for the teaching and learning of structural analysis and design. [ABSTRACT FROM AUTHOR]

Abstract: This paper models van der Waals (vdW) force for axially compressed multi-walled carbon nanotubes (CNTs), whereby each tube is treated as a cylindrical shell continuum. Explicit formulas are derived for predicting the critical axial strain of a triple-walled CNT using a more refined vdW model. The analysis of a cylindrical shell continuum model of multi-walled CNTs using this refined vdW force model is carried out to study the influence of the effect of vdW interaction between different layers of a CNT and the size effect of a CNT on the vdW interaction. It is shown herein that the greatest contribution to the vdW interaction comes from the adjacent layers and the contribution from a remote layer may be neglected. The vdW interaction is found to be strongly dependent on the radius of the tube, especially when the radius is small enough (<7nm). When the radius is large enough (>40nm), the vdW interaction coefficient c ij can be taken as a constant value (i.e. independent of radius). However, these constant values are different for the vdW interaction between two different layers of a multi-walled CNT. The effect of the vdW interaction on the critical axial strain of a triple-walled CNT for the cases of before and after buckling is also examined for various innermost radii. [Copyright &y& Elsevier]

• A new opto-electro-thermo-elastic model is established for lead halide perovskites. • Light illumination has an important effect on the static and dynamic performance. • Electric field also greatly affects the mechanical behaviours of perovskite plates. • Photostriction and electrostriction must be considered in perovskite device design. Metal-halide perovskites are rapidly emerging as promising candidates for next-generation solar cells and photoelectric technologies. However, their structural behaviours considering opto-electro-thermo-mechanical properties in multi-physics fields have not yet been fully understood, thus limiting their engineering applications. This paper proposes a new opto-electro-thermo-elastic model taking into account photostriction, photothermal effect, electrostriction, and piezoelectricity for lead halide perovskites and investigates their static and dynamic opto-electro-thermo-mechanical behaviours. The governing equations of perovskite plates are derived within the theoretical framework of first-order shear deformation theory and are numerically solved using the Chebyshev-Ritz method. Comprehensive parametric studies are carried out to examine the influences of multi-physics fields on the critical light intensity, critical electric field, static bending, elastic buckling, free vibration, as well as dynamic responses of perovskite plates. Numerical results show that light illumination, photoinduced temperature rise, and applied electric field play an important role in bending deformation, dynamic deflection, critical buckling load, and free vibration frequency hence need to be taken into consideration for the design of perovskite-based photoelectric devices. [Display omitted] [ABSTRACT FROM AUTHOR]

This article studies nonlinear dynamic buckling of imperfect beams made of functionally graded (FG) metal foams subjected to a constant velocity with various boundary conditions. Four types of FG porosity patterns, including two symmetric porosity distributions, non-symmetric porosity distribution, and uniform porosity distribution, are considered. By introducing the first mode function as a trial function, the Galerkin method is utilized to transform the governing equations into ordinary differential equations, which were then solved by the fourth-order Runge–Kutta method. The proposed methods are validated by using finite element method (FEM) and finally a detailed parametric study is conducted. [ABSTRACT FROM AUTHOR]

The surging interest in porous lightweight structures has been witnessed in recent years to pursue material innovations in broad engineering disciplines for sustainable developments and multifunctional proposes. Functionally graded (FG) porous composites represent a novel way to adjust mechanical characteristics by controlling the porosity distributions. However, the further advance in this field is challenged by the scale gap between mesoscopic and macroscopic aspects of porous structural analysis, i.e. how the local cellular morphologies impact the overall behaviors. The purpose of this paper is to bridge this gap by conducting a theoretical investigation on the performance of inclined self-weight sandwich beams with FG porous cores, where Young's modulus is obtained with representative volume elements (RVEs) in a multiscale modeling study and depends on the cellular morphologies: average cell size and cell wall thickness. The material properties of closed-cell steel foams are adopted in a two-step assessment on target beams, including a static calculation to examine their bending deformations under gravitational loading which are then imported into a forced vibration analysis considering constant and harmonic moving forces. Timoshenko beam theory is used to establish the displacement field, while Ritz and Newmark methods are employed to solve the governing equations in terms of bending, free vibration, and forced vibration. The inclined beams are assumed to rest on a Pasternak foundation, and the corresponding structural responses can be determined based on the specific cell size and cell wall thickness, of which the effects are quantitatively revealed: the stiffness degradation induced from cellular morphologies increases the dynamic deflections, while the corresponding self-weight static deformations are reduced and the fundamental natural frequencies are raised. The influence from geometrical, boundary, and foundation conditions is also discussed to provide a comprehensive overview. This will be valuable for engineers to develop devisable foam-based load-carrying components with enhanced properties. [ABSTRACT FROM AUTHOR]

Functionally graded porous structures (FGPSs), characterized by a continuous spatial gradient in both porosity and material properties, have been considered as the new generation lightweight structures. Research activities on FGPSs have grown rapidly in recent years. This paper is devoted to review the existing research works on FGPSs and to highlight the important advances in this emerging area. It consists of: (i) a brief introduction of porous materials and Functionally graded porous materials (FGPMs); (ii) an elaboration of the key factor and micromechanical models related to material properties of FGPMs; (iii) a comprehensive review of mechanical analysis of FGPSs; (iv) a detailed discussion of the main challenges and future research directions; (v) a conclusion. [ABSTRACT FROM AUTHOR]

In this work, a new adhesion model is proposed to analyze the peeling behavior of hyperelastic beams from a rigid flat substrate by utilizing a recently developed finite strain Euler beam model and the concept of adhesion energy. Both the large strain effect and bending effect are taken into account in the model. Hence, the model can be seen as a generalization of the extensible elastica-type adhesion model to the finite strain case, and it can also be taken as a generalization of the hyperelastic membrane-type adhesion model to the hyperelastic beam case. In the modeling process, the variational method is used to derive the equilibrium equation and associated boundary conditions, including one that physically means the local peeling (fracture) criterion. A first integral is found for hyperelastic beams and it is used to derive an equivalent global peeling criterion. Moreover, an analytical formula for the peeling force during steady peeling is also obtained. Furthermore, numerical solution procedures and results are presented to discuss the effects of large strain and bending deformation on the peeling behavior of the hyperelastic beam. The developed model will contribute to the modeling and understanding of the adhesion and fracture behaviors of soft structures and biomimetic adhesives. [ABSTRACT FROM AUTHOR]

Based on the Euler–Bernoulli beam element theory, a nonlinear finite element method is proposed to solve the mechanical response of functionally graded shape memory alloys (FG-SMAs) three-point bending beam considering the tension–compression asymmetry under the loading process. The Auricchio's shape memory alloy (SMA) constitutive model was used to describe the phase transformation relationship of SMA. The constitutive model of the power exponent distribution law of FG-SMA was developed by using the theory of composite mechanics. Using the virtual work principle, the bending beam equilibrium equation of FG-SMA was developed. The finite element method and Newton–Raphson method were used to solve the equilibrium equation of the three-point bending beam of FG-SMA. The accuracy of the proposed method was verified by comparing the present results obtained by the nonlinear finite element method with the existing literature. Then three-point bending beam analysis of FG-SMA was carried out. The results show that the increase in the graded index and tensile asymmetry coefficient increases the stiffness of the beam. When the SMA enters phase transformation, the increase in temperature will reduce the deflection of the beam. In addition, the strain variation in the mid-span section near pure shape memory alloy layer is more obvious than that near pure ceramic layer due to temperature. The compressive axial load is more likely to cause beam bending than tensile axial load. [ABSTRACT FROM AUTHOR]

Abstract This paper deals with the buckling behavior of corrugated thin plates made of multilayer functionally graded (FG) graphene nanoplatelets (GPLs) reinforced nanocomposites (FG-GPLRC) within the framework of classical plate theory. The GPLs are uniformly dispersed in each individual layer with its weight fraction following a layer-wise variation along the thickness direction. The effective Young modulus of each layer is determined by the modified Halpin-Tsai model while the Poisson's ratio is predicted based on the rule of mixture. It is assumed that the plate is subjected to either compression or shear or both on the edge. Analytical critical buckling solutions are obtained for both unilateral buckling when the plate is resting on a rigid foundation and bilateral buckling without the constraint of the foundation. A parametric study is conducted to investigate the influences of distribution pattern, geometry, size, and weight fraction of GPL nanofillers as well as the corrugated profile and rigid foundation on the buckling performance of the plate. It is found that the buckling resistance of the corrugated plate can be effectively enhanced by adding a small amount of GPLs into the matrix according to FGX distribution pattern and when the inclination angle is 45 degrees. [ABSTRACT FROM AUTHOR]

Highlights • A dynamic homogenization model is developed for corrugated sandwich plates. • Analytical solutions are derived for low-frequency dispersion relations. • The spectral element method is used to validate the homogenization model. Abstract In the present work, a new dynamic homogenization model is developed to investigate the long-wavelength wave propagation in a corrugated sandwich plate. With the harmonic motion assumption and using a shifting operator, the governing equations of the plate are firstly represented in a state-space form. Then, a dynamic homogenization model is developed via the two-scale homogenization method. Based on this model and considering the propagation of sinusoidal waves, the dispersion relations and corresponding wave modes can be easily obtained. In order to validate the developed homogenization model, the obtained dispersion relations are compared with those predicted by the spectral element method. It is found that the present method gives accurate results in low frequency range. Furthermore, the effects of some geometric and material parameters on the dispersion relations for the corrugated sandwich plate are also discussed. The developed homogenization model is expected to be helpful in the prediction and control of dynamic responses of corrugated or even lattice sandwich structures. Graphical abstract Image, graphical abstract [ABSTRACT FROM AUTHOR]

This paper is concerned with the buckling and free vibration behaviors of functionally graded (FG) porous nanocomposite plates reinforced with graphene platelets (GPLs). The porous plates are constructed based on a multiplayer model with GPLs uniformly or non-uniformly distributed in the metal matrix containing open-cell internal pores. The modified Halpin-Tsai micromechanics model, the extended rule of mixture, and the typical mechanical properties of open-cell metal foams are used to determine the effective properties of the porous nanocomposite. By using the first-order shear deformation plate theory (FSDT) to account for the transverse shear strain and Chebyshev-Ritz method to discretize the displacement fields, the governing equations are derived and then solved to calculate the critical uniaxial, biaxial and shear buckling loads and natural frequencies of the plates with different porosity distributions and GPL dispersion patterns. After a convergence and validation study to verify the present analysis, a comprehensive parametric investigation on the influences of the weight fraction and geometric parameters of GPL nanofiller and the porosity coefficient is conducted to identify the most effective way to achieve improved buckling and vibration resistances of the porous nanocomposite plate. [ABSTRACT FROM AUTHOR]

This paper investigates the parametric instability of functionally graded graphene reinforced nanocomposite plates that undergo a periodic uniaxial in-plane force and a uniform temperature rise. The plate is composed of multiple graphene platelet reinforced composite (GPLRC) layers in which graphene platelets (GPLs) are uniformly distributed in each individual layer with GPL concentration varying layer-wise across the plate thickness. The modified Halpin–Tsai model that takes into account the GPL geometry effect is employed to calculate the Young's modulus of the GPLRC. Based on the first-order shear deformation theory, the governing equations are deduced and then are solved by using the differential quadrature approach integrated with the Bolotin's method. A parametric study is undertaken to show the influences of GPL distribution pattern, concentration and geometry, temperature change, static in-plane force, plate geometry and boundary condition on the parametric instability of functionally graded multilayer GPLRC plates. It is found that the addition of a small amount of GPL reinforcements considerably increases the critical buckling load and natural frequencies but reduces the size of unstable region. The reinforcing effect is the best when the surface layers of the plate are GPL-rich. [ABSTRACT FROM AUTHOR]

The present paper investigates the biaxially compressed buckling and postbuckling behaviors of functionally graded multilayer composite plates reinforced with a low content of graphene nanoplatelets (GPLs) that are randomly oriented and uniformly dispersed in the polymer matrix within each individual layer. The material properties of the GPL-reinforced composite (GPLRC), which are graded along the thickness direction due to a layer-wise change in GPL weight fraction, are evaluated through a micromechanics model. Theoretical formulations are based on the first-order shear deformation plate theory and von Kármán-type nonlinear kinematics and include the effect of an initial geometric imperfection. A two step perturbation technique is employed to determine the asymptotic postbuckling solutions and the biaxial compressive postbuckling equilibrium paths of both perfect and imperfect plates simply supported on all edges. The effects of GPL weight fraction, distribution pattern, geometry and size as well as total number of layers on the buckling and postbuckling behaviors of functionally graded GPLRC plates are examined in detail. [ABSTRACT FROM AUTHOR]

This paper presents size-dependent continuum mechanics models for the nonlinear band gap (BG) characteristics of a piezo-electro-magnetic phononic crystal (PC) micro and nanobeam under voltage-based control (VBC) and negative capacitance-based control (CBC) methods. Taking various size-dependent effects into account, the BG properties of a piezo-electro-magnetic PC micro/nanobeam are analyzed based on Rayleigh beam theory (RBT), plane wave expansion (PWE), Bloch theorem, and nonlinear von-Kármán method. The effects of electro-magneto-mechanical coupling fields, geometric parameters, and micro/nanobeam dimensions on BG properties are discussed. It is found that all BGs frequencies can be controlled by the applied physical fields and elastic medium. [ABSTRACT FROM AUTHOR]

The nonlinear free vibration and postbuckling behaviors of multilayer functionally graded (FG) porous nanocomposite beams that are made of metal foams reinforced by graphene platelets (GPLs) are investigated in this paper. The internal pores and GPL nanofillers are uniformly dispersed within each layer but both porosity coefficient and GPL weight fraction change from layer to layer, resulting in position-dependent elastic moduli, mass density and Poisson's ratio along the beam thickness. The mechanical property of closed-cell cellular solids is employed to obtain the relationship between coefficients of porosity and mass density. The effective material properties of the nanocomposite are determined based on the Halpin-Tsai micromechanics model for Young's modulus and the rule of mixture for mass density and Poisson's ratio. Timoshenko beam theory and von Kármán type nonlinearity are used to establish the differential governing equations that are solved by Ritz method and a direct iterative algorithm to obtain the nonlinear vibration frequencies and postbuckling equilibrium paths of the beams with different end supports. Special attention is given to the effects of varying porosity coefficients and GPL's weight fraction, dispersion pattern, geometry and size on the nonlinear behavior of the porous nanocomposite beam. It is found that the addition of a small amount of GPLs can remarkably reinforce the stiffness of the beam, and its nonlinear vibration and postbuckling performance is significantly influenced by the distribution patterns of both internal pores and GPL nanofillers. [ABSTRACT FROM AUTHOR]

This paper studies the dynamic instability of functionally graded multilayer nanocomposite beams reinforced with a low content of graphene nanoplatelets (GPLs) and subjected to a combined action of a periodic axial force and a temperature change. The weight fraction of GPL nanofillers is assumed to be constant in each individual GPL-reinforced composite (GPLRC) layer but follows a layerwise variation across the beam thickness. The Halpin-Tsai micromechanics model is used to estimate the effective Young’s modulus of GPLRC layers. The differential quadrature method is employed to convert the partial differential governing equations into a linear system of Mathieu-Hill equations, from which the principle unstable region of functionally graded multilayer GPLRC beams is determined by Bolotin’s method. Special attention is given to the effects of GPL distribution pattern, weight fraction, geometry and dimension on the dynamic instability behaviour. The thermal buckling and free vibration are also discussed as subset problems. Numerical results show that distributing more GPLs near the top and bottom surfaces can effectively increase the natural frequency and reduce the size of the unstable region. The influences of GPL geometry and dimension tend to be insignificant when the GPL width-to-thickness ratio is larger than 10 3 . [ABSTRACT FROM AUTHOR]

This paper investigates the buckling and postbuckling behaviours of functionally graded multilayer nanocomposite beams reinforced with a low content of graphene platelets (GPLs) resting on an elastic foundation. It is assumed that GPLs are randomly oriented and uniformly dispersed in each individual GPL-reinforced composite (GPLRC) layer with its weight fraction varying layerwise along the thickness direction. The effective material properties of each layer are estimated by the Halpin-Tsai micromechanics model. The nonlinear governing equations of the beam on an elastic foundation are derived within the framework of the first-order shear deformation beam theory then are converted into a nonlinear algebraic system by using the differential quadrature method. A detailed parametric study is carried out to examine the effects of the distribution pattern, weight fraction, geometry and size of GPL nanofillers, foundation stiffness parameters, slenderness ratio and boundary conditions on the buckling and postbuckling behaviours. The results show that GPLs have a remarkable reinforcing effect on the buckling and postbuckling of nanocomposite beams. [ABSTRACT FROM AUTHOR]

Various bifurcation behaviors, including asymmetric axial buckling induced by end thrust, bifurcation under external pressure, and eversion without any loading, of a soft circular hollow cylinder (or cylindrical shell) composed of functionally graded incompressible elastomeric material are considered in a unified way. Based on the nonlinear elasticity theory of a deformable continuous body undergoing large deformation and the linearized incremental theory for a superimposed infinitesimal deformation, an efficient approach for buckling analysis is developed and applied to the cylinder subjected to a combination of axial end thrust and internal/external pressure. It is based on the state-space formalism, which naturally avoids the derivatives of instantaneous material constants, enabling a convenient and accurate numerical implementation. Along with the layerwise method, an analytical characteristic equation (i.e. the bifurcation criterion) governing the general asymmetric buckling of the cylinder is derived. Detailed parametric studies are then carried out for a pressurized soft functionally graded hollow cylinder using an incompressible Mooney-Rivlin material model. The effects of material gradient on bifurcation induced either by end thrust or external pressure are discussed through numerical examples. Not only does this study provide an efficient tool for buckling analysis of soft cylinders, some findings that are unique to a functionally graded material are also highlighted. All in all, it is found highly possible to tune the bifurcation behavior of soft elastomeric cylindrical shells by tailoring material composition and/or adjusting the pressures acting on the surfaces of the cylinder. [ABSTRACT FROM AUTHOR]

This paper investigates the free and forced vibration characteristics of functionally graded (FG) porous beams with non-uniform porosity distribution whose elastic moduli and mass density are nonlinearly graded along the thickness direction. Both symmetric and asymmetric porosity distributions are considered. The relationship between coefficients of porosity and mass density is determined based on the typical mechanical property of an open-cell metal foam. Within the framework of Timoshenko beam theory to include the effect of transverse shear strain and by employing Lagrange equation method together with Ritz trial functions, the equation of motion is derived then solved by using Newmark- β method in the time domain. Natural frequencies and transient dynamic deflections are obtained for porous beams under different loading conditions, including a harmonic point load, an impulsive point load and a moving load with constant velocity. A detailed numerical study is conducted to examine the effects of varying porosity distribution, porosity coefficient, slenderness ratio and boundary condition, shedding important insights into the design of functionally graded porous beams to achieve improved dynamic behavior. [ABSTRACT FROM AUTHOR]

Highly tunable bandgaps of phononic crystals are of great significance in practical engineering applications. Solid-liquid transitions and graphene reinforcement are two efficient strategies to manipulate material properties, but their potential to enable bandgap tunability remains rarely explored. This study introduces phase-change materials with solid–liquid transition into phononic crystals containing graphene-reinforced composites to investigate their variation of dispersion features at different temperatures. Theoretical models of the present phononic crystals are formulated and solved by the state space approach and the transfer matrix method. Using published experimental data, the prediction models for the mechanical properties of the phase-change materials under continuous variation of temperature are established, based on which dispersion curves of graphene-reinforced phononic crystals featuring either single or double phase-change materials are depicted and discussed. A comprehensive study is conducted to analyze the effects of the filling fraction of phase-change materials and the volume fraction of graphene fillers in the composites on the thermal control of bandgaps in the structures. The results indicate that the solidification/liquidation of phase-change materials, related to temperature control, can greatly broaden/narrow the bandwidth of the bandgaps in the present structures. A switch-like behavior for the first bandgap, characterized by an open-close-open process as the temperature increases from −25 °C to 15 °C and then to 75 °C, can be achieved by introducing double phase-change materials into the structures. The results of this study explore the potential of graphene-reinforced composites and solid–liquid phase transitions in the design of high-performance tunable phononic crystals. [ABSTRACT FROM AUTHOR]

• Internal contact types and electron propagation paths in multidimensional nanocomposites for flexible sensors are presented for the first time. • The effects of contact types and electron propagation paths on sensor sensitivity and linearity are analysed, offering the possibility of regulating sensor performance. • Multi-dimensional nanocomposite flexible pressure sensors with good performance are designed and characterised. • A force platform for sensing the magnitude and trajectory of external forces is proposed for the first time and demonstrates good measurement capabilities. Flexible, wearable pressure sensors provide a convenient, timely, and portable solution for human motion detection. However, there is still a lack of reports on the synergistic effect of multidimensional hybrid polymer nanocomposites for modulating the sensor's key performance indexes. Herein, we present a cost-effective and scalable approach to preparing multidimensional hybrid polymer composites for piezoresistive pressure sensors. Composite charge-transfer paths and contact types are presented for the first time and analyzed in relation to the sensor sensitivity and linearity. The sensor has good characteristics, such as 0 ∼ 70 kPa range, 369.39 kPa−1 sensitivity, a minimum resolving power of 18 Pa and 68 ms, and 76 ms response and recovery times, owing to the interconnecting porous structure of MS and the synergistic effect of the composites. The sensor exhibited a stable piezoresistive response and good reproducibility over 9000 + cycles. The sensor was then attached to different parts of the human body and evaluated for its ability to detect various human movements, including speech and elbow flexion. Finally, a prototype haptic sensing array and a prototype force measurement platform based on these pressure sensors were demonstrated. [ABSTRACT FROM AUTHOR]

Abstract: This paper describes an investigation into a metallic energy dissipater designed for earthquake risk mitigation of civil structures. It is called the Perforated Yielding Shear Panel Device (PYSPD). It comprises of a thin perforated diaphragm plate welded inside a short length square hollow section. The device is to be connected in the lateral load resisting system of a structure with the diaphragm plate being in the plane of the building frame. It is a displacement-based device in which energy is dissipated through plastic shear deformation of its perforated diaphragm plate. The PYSPD is a modified version of the previously tested Yielding Shear Panel Device (YSPD). Perforations on the diaphragm plate alleviate demand on supporting elements which reduces undesirable local deformations near the connections. As a result more stable force-displacement hysteresis is obtained. Three patterns of perforations are studied. Finite element models confirm that diagonal tension field develops under shearing action but stress patterns are affected by perforations. Two plate slenderness and three perforation patterns combinations were tested experimentally. Under quasi-static condition, devices with certain plate slenderness produced stable and repeatable force-displacement hysteresis, and achieved large energy dissipation capability. Compared to un-perforated specimens, perforations reduce elastic stiffness and yield strength. Under design displacement it produced a stable hysteretic behavior and endured code requirements against low-cycle fatigue. [Copyright &y& Elsevier]

• Programmable acoustic lens is achieved by graphene-based phononic crystals. • A highly efficient and accurate acoustic lens on-demand design method is proposed. • Explicit expressions of refractive index are generated by genetic programming. • The ML models are trained based on theoretical formulations of phononic crystals. The advance of artificial intelligence and graphene-based composites brings new vitality into the conventional design of acoustic lenses which suffers from high computation cost and difficulties in achieving precise desired refractive indices. This paper presents an efficient and accurate design methodology for graphene-based gradient-index phononic crystal (GGPC) lenses by combing theoretical formulations and machine learning methods. The GGPC lenses consist of two-dimensional phononic crystals possessing square unit cells with graphene-based composite inclusions. The plane wave expansion method is exploited to obtain the dispersion relations of elastic waves in the structures and then establish the data sets of the effective refractive indices in structures with different volume fractions of graphene fillers in composite materials and filling fractions of inclusions. Based on the database established by the theoretical formulation, genetic programming, a superior machine learning algorithm, is introduced to generate explicit mathematical expressions to predict the effective refractive indices under different structural information. The design of GGPC lenses is conducted with the assistance of the machine learning prediction model, and it will be illustrated by several typical design examples. The proposed design method offers high efficiency, accuracy as well as the ability to achieve inverse design of GGPC lenses, thus significantly facilitating the development of novel phononic crystal lenses and acoustic energy focusing. [ABSTRACT FROM AUTHOR]

Abstract: Large amplitude free vibration of functionally graded carbon nanotube reinforced composite (CNTRC) beams with surface-bonded piezoelectric layers subjected to a temperature change and an applied voltage is studied in this paper. The governing equations of the piezoelectric CNTRC beam are derived based on Euler–Bernoulli beam theory, von Kármán geometric nonlinearity and the physical neutral surface concept. Both uniformly distribution (UD) and functionally graded (FG) distribution patterns of the single-walled carbon nanotube (SWCNT) reinforcements are considered. It is assumed that the material properties of the FG-CNTRC beam vary in the thickness direction, and that the SWCNTs are aligned and straight. Galerkin procedure is used to obtain the second order nonlinear ordinary equation in time with cubic nonlinear term. Multiple times scales method is then employed to determine the nonlinear free vibration characteristics of the beam clamped at both ends. The effects of the applied voltage, temperature change, beam geometry, the volume fraction and distribution pattern of the SWCNTs on the linear and nonlinear frequencies of the piezoelectric CNTRC beams are investigated through a comprehensive parametric study. [Copyright &y& Elsevier]

This article presents a dynamic stability analysis of functionally graded nanocomposite beams reinforced by single-walled carbon nanotubes (SWCNTs) based on Timoshenko beam theory. The material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTRCs) are assumed to vary in the thickness direction and are estimated through the rule of mixture. The differential quadrature method is employed to convert the governing differential equations into a linear system of Mathieu-Hill equations from which the boundary points on the unstable regions are determined by Bolotin's method. Free vibration and elastic buckling are also discussed as subset problems. A parametric study is conducted to investigate the influences of nanotube volume fraction, slenderness ratio, and end supports on the dynamic stability characteristics of FG-CNTRC beams. Numerical results for composite beams reinforced by uniformly distributed carbon nanotube are also provided for comparison. [ABSTRACT FROM AUTHOR]

Abstract: The bending, buckling and free vibration of annular microplates made of functionally graded materials (FGMs) are investigated in this paper based on the modified couple stress theory and Mindlin plate theory. This microplate model incorporates the material length scale parameter that can capture the size effect in FGMs. The material properties of the FGM microplates are assumed to vary in the thickness direction and are estimated through the Mori–Tanaka homogenization technique. The higher-order governing equations and boundary conditions are derived by using Hamilton’s principle. The differential quadrature (DQ) method is employed to discretize the governing equations and to determine the deflection, critical buckling load and natural frequencies of FGM microplates. A parametric study is then conducted to investigate the influences of the length scale parameter, gradient index and inner-to-outer radius ratio on the bending, buckling and vibration characteristics of FGM microplates with hinged–hinged and clamped–clamped supports. The results show that the size effect on the bending, buckling and vibration characteristics is significant when the ratio of the microplate thickness to the material length scale parameter is smaller than 10. [Copyright &y& Elsevier]

Abstract: This paper presents a study on the postbuckling response of a functionally graded cylindrical shell of finite length embedded in a large outer elastic medium and subjected to internal pressure in thermal environments. The surrounding elastic medium is modeled as a tensionless Pasternak foundation that reacts in compression only. The postbuckling analysis is based on a higher order shear deformation shell theory with von Kármán–Donnell-type of kinematic nonlinearity. The thermal effects due to heat conduction are also included and the material properties of functionally graded materials (FGMs) are assumed to be temperature-dependent. The nonlinear prebuckling deformations and the initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine the postbuckling response of the shells and an iterative scheme is developed to obtain numerical results without using any assumption on the shape of the contact region between the shell and the elastic medium. Numerical solutions are presented in tabular and graphical forms to study the postbuckling behavior of FGM shells surrounded by an elastic medium of tensionless elastic foundation of the Pasternak-type, from which results for conventional elastic foundations are obtained as comparators. The results reveal that the unilateral constraint has a significant effect on the postbuckling response of shells subjected to internal pressure in thermal environments when the foundation stiffness is sufficiently large. [Copyright &y& Elsevier]

Abstract: This paper investigates the nonlinear free vibration of functionally graded nanocomposite beams reinforced by single-walled carbon nanotubes (SWCNTs) based on Timoshenko beam theory and von Kármán geometric nonlinearity. The material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTRCs) are assumed to be graded in the thickness direction and estimated though the rule of mixture. The Ritz method is employed to derive the governing eigenvalue equation which is then solved by a direct iterative method to obtain the nonlinear vibration frequencies of FG-CNTRC beams with different end supports. A detailed parametric study is conducted to study the influences of nanotube volume fraction, vibration amplitude, slenderness ratio and end supports on the nonlinear free vibration characteristics of FG-CNTRC beams. The results for uniformly distributed carbon nanotube-reinforced composite (UD-CNTRC) beams are also provided for comparison. Numerical results are presented in both tabular and graphical forms to investigate the effects of nanotube volume fraction, vibration amplitude, slenderness ratio, end supports and CNT distribution on the nonlinear free vibration characteristics of FG-CNTRC beams. [Copyright &y& Elsevier]

Abstract: In this paper, the postbuckling response of beams made of functionally graded materials (FGMs) containing an open edge crack is studied based on Timoshenko beam theory and von Kármán nonlinear kinematics. The cracked section is modeled by a massless elastic rotational spring. It is assumed that material properties follow exponential distributions through thickness direction. Ritz method is employed to derive the nonlinear governing equations, which are then solved by using Newton–Raphson method to obtain the postbuckling load-end shortening curves and postbuckling deflection-end shortening curves. A detailed parametric study is conducted to study the influences of crack depth, crack location, material property gradient, and slenderness ratio on the postbuckling behavior of cracked FGM beams. It is found that both intact and cracked FGM beams exhibit similar postbuckling behavior under end shortening. Unlike isotropic homogeneous beams, bifurcation buckling does not occur for both intact and cracked FGM beams due to the presence of bending–extension coupling effect. [Copyright &y& Elsevier]

Free vibration and elastic buckling of beams made of functionally graded materials (FGMs) containing open edge cracks are studied in this paper based on Timoshenko beam theory. The crack is modeled by a massless elastic rotational spring. It is assumed that the material properties follow exponential distributions along beam thickness direction. Analytical solutions of natural frequencies and critical buckling load are obtained for cracked FGM beams with clamped-free, hinged-hinged, and clamped-clamped end supports. A detailed parametric study is conducted to study the influences of crack depth, crack location, total number of cracks, material properties, beam slenderness ratio, and end supports on the free vibration and buckling characteristics of cracked FGM beams. [ABSTRACT FROM AUTHOR]

The surface temperature distribution and thermo-elastic stress fields of an inhomogeneous coating system subjected to mixed Hertz pressure, tangential traction, and frictional heating are studied in this paper. The coating system consists of a surface coating and an intermediate functionally graded layer perfectly bonded to a substrate. The surface coating and the substrate are homogeneous materials with distinct physical properties while the intermediate layer is inhomogeneous with material properties changing exponentially along the thickness direction. It is assumed that the friction is of Coulomb type. Solutions for the temperature field and interfacial stresses are obtained using Fourier transform technique. The effects of total thickness, the graded layer thickness, Peclet number, and friction coefficient on the surface temperature field and interfacial stresses are investigated in detail. Direct comparisons with the results of a homogeneous single-layer coating system show that the use of the double-layer coating system can significantly reduce the surface temperature and interfacial normal stress. [ABSTRACT FROM AUTHOR]

Abstract: The frictionless contact problem of a functionally graded piezoelectric layered half-plane in-plane strain state under the action of a rigid flat or cylindrical punch is investigated in this paper. It is assumed that the punch is a perfect electrical conductor with a constant potential. The electro-elastic properties of the functionally graded piezoelectric materials (FGPMs) vary exponentially along the thickness direction. The problem is reduced to a pair of coupled Cauchy singular integral equations by using the Fourier integral transform technique and then is numerically solved to determine the contact pressure, surface electric charge distribution, normal stress and electric displacement fields. For a flat punch, the normal stress intensity factor and electric displacement intensity factor are also given to quantitatively characterize the singularity behavior at the punch ends. Numerical results show that both material property gradient of the FGPM layer and punch geometry have a significant influence on the contact performance of the FGPM layered half-plane. [Copyright &y& Elsevier]