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Nonlocal formulations are currently adopted to assess size effects in nanostructures. The Eringen differential constitutive model, due to its simplicity, is widely used to investigate the size-dependent behavior of beams at nanoscale. Nevertheless this theory provides vanishing size effects in nanobeams under point loads and exhibits stiffening phenomena in nanocantilevers for increasing values of the nonlocal factor. Accordingly, the analysis of structures like nanoactuators is commonly carried out by using more complex constitutive approaches, such as gradient or integral models. A new strategy is outlined in the present paper as a possibly convenient alternative, by equipping the Eringen differential law with an additional term involving the derivative of the axial stress. Effectiveness of the new methodology is tested with reference to simple case studies. [ABSTRACT FROM AUTHOR]

A new hyperbolic shear and normal deformation plate theory, presented in this paper, is used to study the static, free vibration and buckling analysis of the simply supported functionally graded sandwich plates on elastic foundation. This theory accounts for the realistic variations of the displacements through the thickness. In the analysis, two common types of FGM sandwich plates, namely, homogeneous face sheets with FGM core and FGM face sheets with homogeneous core are considered. The elastic foundation is described by the Pasternak model. The equations of motion are derived from Hamilton's principle. The closed form solutions are obtained by using Navier technique. Numerical results of present theory are compared with three-dimensional elasticity solutions and other higher-order theories reported in the literature. It can be concluded that the proposed theory is simple and efficient in predicting the mechanical behavior of functionally graded sandwich plates. [ABSTRACT FROM AUTHOR]

Thermoelastic analysis of composite cylindrical panel reinforced by single walled carbon nanotube (SWCNT) with simply supported edges by using three-dimensional theory of elasticity. Thermoelastic constant of carbon nanotube (CNT) as well as polymer matrix are assumed to be temperature independent. The volume fractions of oriented, straight SWCNTs are assumed to be uniformly distributed (UD) and or graded in the thickness direction according to four kinds of CNT distributions. The effective material properties of the nanocomposite cylindrical panel are based on rule of mixture. At first temperature distribution in three dimensions is obtained by solving heat conduction differential equation with variable coefficient. By applying Fourier series expansion to the stress and displacement fields along the axial and circumferential direction and state space technique along the radial direction thermoelastic analysis is carried out. Moreover, effects of volume fraction of carbon nanotube, uniform distribution and functionally graded distribution of CNT, mid radius to thickness ratio, length to mid radius ratio, thermal and mechanical surface boundary conditions on bending behavior of FG-CNTRC cylindrical panel are also examined. [ABSTRACT FROM AUTHOR]

The analytical approach is presented to investigate non-linear buckling analysis and post-buckling behavior of FGM toroidal shell segments filled inside by an elastic medium under external pressure loads including temperature effects. The governing equations of non-linear buckling of FGM toroidal shell segments are derived based on the classical thin shell theory with the geometrical nonlinearity in von Karman–Donnell sense, Stein and McElman assumption and elastic medium modeled by Pasternak's two-parameter elastic foundation. The static critical buckling loads and the post-buckling pressure–deflection curves in two cases: movable and immovable boundary conditions including temperature effects are obtained by using the Galerkin's method. In the paper, the results are also compared with the solutions published in the literature for the specific cases. Effects of geometrical and material parameters, elastic foundation and temperature on the nonlinear buckling behavior of shells are shown in obtained results. [ABSTRACT FROM AUTHOR]

This paper deals with the investigation of the effect of hygrothermal conditions on the bending of nanoplates using Levy type solution model employing the state-space concept. The nanoplates are assumed to be subjected to a hygrothermal environment. The two-unknown function plate theory is used to derive the governing differential equations on the basis of Eringen's nonlocal elasticity theory. The governing equations contain the small scale effect as well as hygrothermal and mechanical effects. These equations are converted into a set of first-order linear ordinary differential equations with constant coefficients. Analytical solution of bending response for nanoplates under combinations of simply supported, clamped and free boundary conditions is obtained. Comparison of the results with those being in the open literature is made. The influences played by small scale parameter, temperature rise, the degree of moisture concentration, boundary conditions, plate aspect ratio and side-to-thickness ratio are studied. [ABSTRACT FROM AUTHOR]

A method of solution that extends to the case of curved laminated structures the traditional approach developed by Newmark et al. for straight beams is presented. The method is specialized to curved laminated glass, a composite formed by two external glass layers that sandwich a very thin polymeric interlayer. The effect of curvature on the shear coupling of glass plies through the interlayer is examined in the paradigmatic example of a laminated beam with constant moderate curvature under radial loading with different boundary conditions, varying the initial camber, the end constraints and the elastic properties of the polymer. Comparisons with numerical experiments confirm the accuracy of the proposed modeling. In general the response of a curved structure is greatly influenced by the axial force it undergoes, and such internal action is mainly governed, for fixed applied loads, by the boundary conditions at the extremities. The axial force produces the arch-response of the structure, which is not substantially affected by the shear coupling of glass through the interlayer. On the other hand, such coupling has major effects on the bending properties. [ABSTRACT FROM AUTHOR]

In this paper, the predictions of elastic constants of 2.5D (three-dimension angle-interlock woven) continue carbon fiber reinforced silicon carbide (C/SiC) composites are studied by means of theoretical model and numerical simulation. A semi-analytical method expressing elastic constants in terms of microstructure geometrical parameters and constitute properties has been proposed. First, both the geometrical model of the 2.5D composite and the representative volume element (RVE) in both micro- and meso-scale are proposed. Second, the effective elastic properties of the RVE in 2.5D C/SiC composites are obtained using finite element method (FEM) simulation based on energy equivalent principle. Finally, the remedied spatial stiffness average ( RSSA ) method is proposed to obtain more accurate elastic constants using nine correction factor functions determined by FEM simulations, also the effects of geometrical variables on mechanical properties in 2.5D C/SiC composites are analyzed. These results will play an important role in designing advanced C/SiC composites. [ABSTRACT FROM AUTHOR]

The elastostatic problem of functionally graded circular nanobeams under torsion, with nonlocal elastic behavior proposed by E ringen , is preliminarily formulated. Exact solutions are detected for nanobeams with arbitrary axial gradations of elastic properties and radially quadratic distributions of shear moduli. Extension of the treatment to nonlocal viscoelastic composite circular nanobeams is then performed. An effective solution procedure based on L aplace transform is developed, providing a new correspondence principle in nonlocal viscoelasticity for functionally graded materials. Displacements, shear strains and stresses are established for nonlocal viscoelastic nanobeams made of periodic fiber-reinforced materials, with polymeric matrix described by a M axwell model connected in series with a V oigt model. [ABSTRACT FROM AUTHOR]

This paper presents an exact elasticity model for a fluid-loaded periodically rib-stiffened plate covered by a decoupling acoustic coating layer, which is built upon the plain strain elasticity theory. The acoustical coating layer is assumed to be perfectly bonded to the parallelly rib-stiffened plate, which is impinged by a time-harmonic plane sound wave. The theoretical model begins with Navier–Cauchy equations of motion to describe the vibration behavior of the rib-stiffened plate and the acoustic coating layer, and utilizes the acoustic equation to model the fluid motion. Applying the continuities of displacements and stresses at the interfaces of the plate, the coating layer and the fluid mediums, the vibroacoustic governing equation can be solved to obtain the sound transmission loss (STL) of the structure. The plane strain model is verified by comparing with the thin-plate model, and good agreements have been achieved between the two predictions. Based upon the theoretical model, the influences of the geometrical parameters of the structure, sound incidence angle, the dilatation and shear wave speeds in the acoustic coating layer on the STL of the structure are numerically explored. Results reveal the significant effect of the decoupling acoustic coating layer on the noise reduction of the periodically rib-stiffened structures. [ABSTRACT FROM AUTHOR]

The elastostatic problem of a functionally graded K irchhoff plate, with no kinematic constraints on the boundary, under constant distributions of transverse loads per unit area and of boundary bending couples is investigated. Closed-form expressions are provided for displacements, bending–twisting curvatures and moments of an isotropic plate with elastic stiffness and boundary distributed shear forces, assigned respectively in terms of the stress function and of its normal derivative of a corresponding S aint -V enant beam under torsion. The methodology is adopted to solve circular plates with local and E ringen -type elastic constitutive behaviors, providing thus new benchmarks for computational mechanics. The proposed approach can be used to obtain other exact solutions for plates whose planform coincides with the cross-section of beams for which the P randtl stress function is known in an analytical form. [ABSTRACT FROM AUTHOR]

In the paper the behavior of composite-reinforced masonry structures is discussed. One focuses on the problem of the reinforced structure under different modeling of the basic material keeping into account possible strength in tension of the masonry material. Actually the presence of the reinforcement requires the development of a specialized treatment, that is presented in the paper, with the purpose of exploring the dependence of the solution on more or less refined hypotheses about the masonry material in the presence of reinforcement. The original set up leads to the formulation of new bounding theorems for masonry structures reinforced by composites, with the masonry possibly modeled by an elastic brittle assumption. [ABSTRACT FROM AUTHOR]

Improvement of the interfacial toughness of composite sandwich by stitching process is studied in this paper. Double cantilever beam tests are performed to quantify the influence of the presence of the through-the-thickness reinforcement on the skin–core interfacial toughness. The compliance method is used to determine the energy release rate but with a specific formula where an exponential fitting is preferred instead of the power classical fitting. The failure mechanisms for energy absorption are observed and experimental crack travel through the stitches gives an explanation of the particular evolution of the loading curve. An analytical approach is also proposed to predict the overall behavior of the interface. The classical theory of crack propagation is adapted in order to consider the lack of symmetry of the test as the crack does not propagate in the middle of the specimen and to consider additional plate device strengthen the brittle skin of the sandwich. The result of the model is satisfying for the unstitched structure and the range of the predicted critical energy release rate is in accordance with the experimental result. Regarding stitched sandwich, the limits of the model is highlight due to the theory that does not take into account the transverse reinforcement. [ABSTRACT FROM AUTHOR]

In recent years, nonlocal elasticity theory is widely used for the analytical and computational modeling of nanostructures. This theory, developed by Eringen, has shown to be practical for the vibration and buckling analysis of nanoscale structures and reliable for predesign procedures of nano-devices. This paper considers buckling and dynamic analysis of multi-nanoplate systems. This type of system can be relevant to composite structures embedded with graphene sheets. Exact solutions for the natural frequencies and buckling loads of multi-nanoplate systems have been proposed by considering that the multi-nanoplate system is embedded within an elastic medium. Nonlocal elasticity theory is utilized for the mathematical establishment of the system. The solutions of the homogenous system of differential equations are obtained using the Navier's method and trigonometric method. An asymptotic analysis is proposed to show the influence of increasing number of nanoplates in the system. Analytical expressions are validated with existing results in the literature for some special cases. Numerical results based on the analytical expressions is shown to quantify the effects of the change in nonlocal parameter, stiffness coefficients of the elastic mediums and the number of layers on the natural frequencies and buckling load. [ABSTRACT FROM AUTHOR]

Abstract: Presented in this paper is analysis of buckling of double-orthotropic nanoplates based on nonlocal elasticity theory. It is assumed that two nanoplates are bonded by an internal elastic medium and surrounded by external elastic foundation. Three characteristic types of buckling are considered. Governing equations are derived based on nonlocal theory, while the expressions for the buckling load are given in explicit form for a nanoplate with all edges simply supported. Explained in detail is the influence of small scale coefficient, aspect ratio, and stiffness of internal elastic media and external elastic foundation, on the nondimensional buckling load. [Copyright &y& Elsevier]

Abstract: The subject of this paper is the plate composed of two identical isotropic outer layers and a more compliant inner interlayer, perfectly connected to one another at the interface (three-layered plate). This paper presents a model that describes the behavior of this plate by a system of exact analytical (explicit) equations. An analytical model is preferred over finite element models and simplified formulas if it is fast and easy-to-use. Thus, modeling has been developed within the framework of two-dimensional elasticity, instead of three. In so doing, the model also represents a means for attaining full comprehension of the involved phenomena, something that neither three-dimensional elasticity nor finite element models and simplified formulas can attain. The two-dimensional behavior is governed here by using assumptions that do not impose constraints on the behavior. Starting from these assumptions, the paper illustrates the relationships between displacements and interface stresses. The subsequent sections of the paper describe the model and present some real case applications. The contribution of this paper is to consider both the shear modulus and the elastic modulus of the interlayer. Thus, this model applies to three-layered plates with any interlayer, whether utterly compliant or relatively stiff. Conversely, the previous exact analytical models assumed zero elastic modulus, and hence they applied to utterly compliant interlayers only. Hence, not only does the new model predict the exact behavior of plates that the former analytical models described only approximately, but this model may also be used as a benchmark for finite element models, which cannot assign zero value to the elasticity modulus of the interlayer together with the actual shear modulus. [Copyright &y& Elsevier]

Abstract: Based on a modified couple stress theory, a model for sigmoid functionally graded material (S-FGM) nanoplates on elastic medium is developed. The two main advantages of the modified couple stress theory over the classical couple stress theory are the inclusion of asymmetric couple stress tensor and the involvement of only one material length scale parameter. Analytical solution for buckling analysis of S-FGM nanoplates on elastic medium is presented. The present models contain one material length scale parameter and can capture the size effect, and two-constituent material variation through the plate thickness. The governing equations are derived from minimum total potential energy principle based on a modified couple stress theory, and the power law variation of the material through the thickness of the plate. Material properties of functionally graded plate are assumed to vary according to two power law distribution of the volume fraction of the constituents. It is assumed that the elastic medium is modeled as Pasternak elastic medium. Buckling response of rectangular S-FGM nanoplates is derived, and the obtained results are compared well with reference solutions. The effects of power law index, small scale coefficient, aspect ratio, side-to-thickness ratio, loading types, and elastic medium parameter on the buckling load of S-FGM nanoplates have been discussed. [Copyright &y& Elsevier]

Abstract: This paper investigates the large amplitude vibration behavior of a shear deformable FGM cylindrical panel resting on elastic foundations in thermal environments. Two kinds of micromechanics models, namely, Voigt model and Mori–Tanaka model, are considered. The motion equations are based on a higher order shear deformation shell theory that includes shell panel-foundation interaction. The thermal effects are also included and the material properties of FGMs are assumed to be temperature-dependent. The equations of motion are solved by a two step perturbation technique to determine the nonlinear frequencies of the FGM cylindrical panel. Detailed parametric studies are carried out to investigate effects of volume fraction index, temperature variation, panel curvature ratio, foundation stiffness and in-plane boundary conditions on nonlinear vibration behaviors of FGM cylindrical panels. The results confirm that in most cases Voigt model and Mori–Tanaka model have the same accuracy for predicting the vibration characteristics of FGM cylindrical panels. [Copyright &y& Elsevier]

Young’s modulus of unidirectional glass fiber reinforced polymer (GFRP) composites for wind energy applications were studied using analytical, numerical and experimental methods. In order to explore the effect of fiber orientation angle on the Young’s modulus of composites, from the basic theory of elastic mechanics, a procedure which can be applied to evaluate the elastic stiffness matrix of GFRP composite as an analytical function of fiber orientation angle (from 0° to 90°), was developed. At the same time, different finite element models with inclined glass fiber were developed via the ABAQUS Scripting Interface. Results indicate that Young’s modulus of the composites strongly depends on the fiber orientation angles. A U-shaped dependency of the Young’s modulus of composites on the inclined angle of fiber is found, which agree well with the experimental results. The shear modulus is found to have significant effect on the composites’ Young’s modulus, too. The effect of volume content of glass fiber on the Young’s modulus of composites was investigated. Results indicate the relation between them is nearly linear. The results of the investigation are expected to provide some design guideline for the microstructural optimization of the glass fiber reinforced composites. [ABSTRACT FROM AUTHOR]

In this paper, a non-classical beam model based on the Eringen’s nonlocal elasticity theory is proposed for nonlinear vibration of nanobeams with axially immovable ends. This non-classical (nonlocal) beam model incorporates the length scale parameter (nonlocal parameter) which can capture the small scale effect. The Hamilton’s principal is employed to derive the governing equations and the related boundary conditions together with Euler–Bernoulli beam theory and the von-Kármán’s nonlinear strain–displacement relationships. An approximate analytical solution is obtained for the nonlinear frequency of the nanobeam by utilizing the Galerkin method and He’s variational method. In the numerical results, the ratio of nonlinear frequency to linear frequency is presented for three different boundary conditions. The effect of nonlocal parameter on the nonlinear frequency ratio is examined. Also, some illustrative examples are also presented to verify the present formulation and solutions. Good agreement is observed. These results can be used as benchmark for future studies. [ABSTRACT FROM AUTHOR]

Abstract: Defects created during the manufacture of an oxide/oxide and two non-oxide (SiC/SiNC and MI SiC/SiC) ceramic matrix composites (CMCs) were categorized as follows: (1) Intra-yarn defects such as dry fibers, (2) Inter-yarn defects such as those at crossover points, matrix voids, shrinkage cracks and interlaminar separation, and (3) Architectural defects such as layer misalignment. Their impact on elastic properties was analytically investigated using a stiffness averaging approach considering the defects to have volumetric and directional influences. In-plane tensile and shear moduli as well as the through-thickness compressive modulus were experimentally evaluated. Results of analytical model were around 7% on average from the mean value of the experimental data. It was observed that interlaminar separation drastically reduced the through-thickness modulus by about 63% for the SiC/SiNC, 40% for the MI SiC/SiC and around 32% for the oxide/oxide composites. Shrinkage cracks in oxide/oxide composite reduced the in-plane tensile and shear moduli by 14% and 8.8%, respectively. [Copyright &y& Elsevier]

Abstract: In this study, the free vibration behavior of circular graphene sheet under in-plane pre-load is studied. By using the nonlocal elasticity theory and Kirchhoff plate theory, the governing equation is derived for single-layered graphene sheets (SLGSs). The closed-form solution for frequency vibration of circular graphene sheets under in-plane pre-load has been obtained and nonlocal parameter appears into arguments of Bessel functions. The results are subsequently compared with valid result reported in the literature. The effects of the small scale, pre-load, mode number and boundary conditions on natural frequencies are investigated. The results are shown that at smaller radius of circular nanoplate, the effect of in-plane pre-loads is more importance. [Copyright &y& Elsevier]

Abstract: In this study, a review of the progress made in analytical modeling of 2D and 3D textile composites is presented. The review covers the most known analytical models developed in the last 30years to evaluate the elastic properties of textile composites. A discussion of these models is presented, where the corresponding advantages and disadvantages are revealed. In addition, a comparative study of some selected analytical models is presented. Results obtained from previous analytical, numerical and experimental studies are presented in order to show the potential of investigated analytical models. It is shown that recently developed analytical models, applied on different kinds of textile composites, could yield good results, while maintaining more flexibility, easy to apply and the less time consuming in comparing with numerical FE (Finite Element) models. [Copyright &y& Elsevier]

Abstract: In the present paper, a consistent power series solution is proposed for dynamic behaviors analysis of circular sandwich plates with functionally graded face sheets/cores, for the first time. The proposed solution is a combination of the finite Taylor’s transform and the fourth-order Runge–Kutta procedure. The extension-bending coupling and the higher-order inertias are considered in the present research. The formulation guarantees continuity of the transverse stress components at the interfaces between layers. Another novelty is proposing a zigzag formulation whose results are corrected on the basis of the dynamic three-dimensional theory of elasticity. An interesting discussion for defining explicit/implicit layerwise shear correction factors is also presented. Furthermore, results reveal that using functionally graded face sheets or cores with transition variations of the material properties may lead to very smooth through-the-thickness stress distributions. Consequently, some of the failure modes may be prevented at the interfaces between the layers. [Copyright &y& Elsevier]

Abstract: Vibration of nanotubes embedded in an elastic matrix is investigated by using the nonlocal Timoshenko beam model. Both a stress gradient and a strain gradient approach are considered. The Hamilton’s principle is adopted to obtain the frequencies of the nanotubes. The dependencies of frequency on the stiffness and mass density of the surrounding elastic matrix, the nonlocal parameter, the transverse shear stiffness and the rotary inertia of the nanotubes are obtained. The results show a significant dependence of frequencies on the surrounding medium and the nonlocal parameter. The frequencies are over-predicted by using the Euler beam model that neglects the shear stiffness and rotary inertia of the nanotubes. It is also found that the lower bound and the upper bound for the frequencies of nanotubes are, respectively, provided by the strain gradient model provides and the stress gradient theory. Explicit formulas for the frequency are obtained and therefore are easy to use by material scientists and engineers for the design of nanotubes and nanotubes based composites. [Copyright &y& Elsevier]

Abstract: In this paper exact closed-form solutions of 3-D elasticity theory are presented to study both in-plane and out-of-plane free vibrations for thick functionally graded simply supported rectangular plates. The solution procedure of the transverse vibration utilizes Levinson’s representation form to describe the displacement; in this way, the 3-D elasto-dynamic equations are written in terms of some suitable independent functions satisfying ordinary differential equations. A similar procedure is presented for in-plane vibration by introducing an appropriate displacement field. In each case, the obtained ordinary differential equations are analytically solved and boundary conditions are satisfied. The proposed solutions are validated by comparing some of the present results with corresponding results known in the literature as well as with 3-D Finite Element Method. Finally, the influence of inhomogeneity on the natural frequencies for a thick functionally graded rectangular plate is discussed. [Copyright &y& Elsevier]

Abstract: The comprehensive free vibration analysis of doubly-curved shallow shells which are made of an orthotropic material is presented. The size effect is taken into consideration using the gradient elasticity theory. Novozhilov’s linear shallow shell theory is used and it is assumed that the shell is simply supported. The governing equations of the doubly-curved shallow shells with consideration of the length scales are developed. Analytical solutions to the equations are proposed to obtain the frequencies of the shells. Numerical results are presented for various shell curvatures including spherical, cylindrical and hyperbolic paraboloidal shells and compared with those available in the literature. [Copyright &y& Elsevier]

Abstract: Over the years new coating design and technology for structures have received much attention mainly due to the demand for longer life span and durability. Conventional coating general consists of few homogeneous layers being deposited on the parent material or substrate. These layers are very vulnerable to cracking followed by de-bonding due to mismatch thermo-mechanical property. To avoid such coating failures, functionally graded material (FGM) is proposed in the coating design. Hence, this study analyzes FGM plates subjected to transverse load with clamped edges. Three configurations were considered. The first involves a two-layer plate in which a homogeneous coating layer was coated on a homogeneous substrate. The second involves a two layer system with the first layer as a FGM coating followed by the homogeneous substrate and the final configuration was a three layer system. The top and bottom layers are homogenous coating and substrates respectively, and the interlayer is composed of FGM. The Young’s modulus of FGM plates is assumed to vary in the thickness direction based on the sigmoid functions and the Poisson’s ratio remain constant throughout the FGM plate. The analysis was carried out in the context of two-dimensional elasticity theory and the method of superposition was used to find a series solution. The deflections, strains, and stresses were evaluated and the differences between the elastic behaviors of all three design configurations were investigated. [Copyright &y& Elsevier]

Abstract: In this paper, using the first-order shear deformation theory (FSDT) and matched asymptotic method (MAM) of the perturbation theory, an analytical solution for deformations and stresses of axisymmetric clamped–clamped thick cylindrical shells with variable thickness made of functionally graded materials (FGMs) subjected to internal pressure are presented. The governing equations are a system of ordinary differential equations with variable coefficients. Using the MAM of the perturbation theory, these equations could be converted into a system of algebraic equations and two systems of differential equations with constant coefficients. The displacements and stresses along the radius and length have been plotted and distribution of these is compared with the solution using finite element method (FEM). [Copyright &y& Elsevier]

Abstract: An analytical approach for free vibration analysis of all edges simply-supported double-orthotropic nanoplates is presented. The two nanoplates are assumed to be bonded by an internal elastic medium and surrounded by external elastic foundation. The governing equations are derived based on the nonlocal theory and the expressions of the natural frequencies are proposed in an explicit form. The suggested model is justified by a good agreement between the results given by present model and available data in literature. The model is used to study the vibration of double-orthotropic nanoplates for three typical deformation modes. The influences of small scale coefficient, stiffness of the external and internal mediums and aspect ratio on the frequencies of the double-orthotropic nanoplates are also elucidated. [Copyright &y& Elsevier]

Abstract: Interaction of Carbon Nanotubes (CNTs) and nanovoids embedded in a metal matrix is studied comparatively. For this purpose, two nearby CNTs/nanovoids are modeled as two similar cylindrical inclusions/holes in an infinite matrix. The nonlocal stresses around the CNTs/nanovoids are obtained by applying the integral constitutive equation of the nonlocal elasticity to the stresses from the complex stress potential method. Also, in order to bring different nonlocality effects of dissimilar media into account, the influence function of the nonlocal elasticity is modified. Effects of the CNTs/nanovoids size and distance as well as far-field loading ratio on the stress state in the matrix are investigated. The CNTs strengthening effect on the matrix is shown through lower stresses at the CNTs and matrix interface in comparison to the applied stress. Furthermore, it is indicated that the modified nonlocal analysis brings out the interaction of CNTs/nanovoids at smaller distances in comparison with those the classical analysis used to predict. In other words, higher volume fraction of the CNTs/nanovoids can be incorporated in the metal matrices without devastating effects of their interactions. [Copyright &y& Elsevier]

Abstract: This article provides an improvement of the technology of through-the-thickness reinforcement of thermosetting composite sandwiches by the insertion of stitching yarns. The aim of this work is to propose a model that would lead to the representation of the tri-dimensional elastic and ultimate performances of these 3D structures under out-of-plane shearing and compressive stress. To reach that goal, an analytical approach is proposed without the contribution of the numerical finite element technique. From experimental observations, this complex structure can be considered as a simple lattice made up of the stitches treated as bars composed of the UD impregnated yarns. The transverse compression and the out-of-plane shear module can be determined from the geometrical parameters of the structure. Moreover, the ultimate stress can be approximated once the cinematic of the failure of the structure has been experimentally identified for each stress case. Finally, the buckling of stitches ends up in the ruin of the material in each case. Thus, a classical theory of buckling can be used and a particular work has been done on the representation of the anchorage point of the stitches on the skin. The final model which is endowed with a good sensitivity enables us to predict the ultimate values in both loading cases. Finally, the variation of stitching angle allows to virtually optimize the material used according to the external loading. [Copyright &y& Elsevier]

Abstract: The nonlinear free vibration of nanobeams with considering surface effects (surface elasticity, tension and density) is studied using Euler–Bernoulli beam theory including the von kármán geometric nonlinearity. The component of plane stress, , is assumed to vary linearly through the beam thickness and satisfy the balance conditions between nanobeam bulk and its surfaces. Accordingly, surface density is introduced into the governing equation of the nonlinear free vibration of nanobeams. It is seen that the effect of surface density is independent of amplitude ratio. In addition, it is observed that in lower modes, surface density has insignificant effects on the variation of the natural frequency versus mode number, whereas this is not the case in higher modes where the surface density causes the normalized natural frequencies of the nanobeams to increase drastically. Moreover, it is shown that the effect of the surface density on the variation of the natural frequency of the nanobeam versus the thickness ratio decreases consistently with the increase of the mode number. [Copyright &y& Elsevier]

Abstract: The present work describes the development of a complete theoretical framework of wave propagation in cylindrical waveguides possessing microstructure. In parallel, a thorough investigation of the full 3-D model of wave propagation in cylinders is presented. The first step is the spectral decomposition of the boundary value problem emerging via wave propagation analysis. The spectral representation of the specific gradient elasticity problem reflects the ability to construct all the possible propagating modes in cylindrical geometry. Several byproducts arise along the present work, which constitute generalizations of well known important features of classical elasticity and are indispensable for modeling the gradient elasticity problem. We note the construction of the set of dyadic Navier eigenfunctions which constitute the generalization of the Navier eigenvectors. The restriction of the Navier eigendyadics on cylindrical surfaces gives birth to the dyadic cylindrical harmonics, which constitute the generalization of the well known vector harmonics. This set is also a basis in the sense that the trace of every dyadic field on a cylindrical surface can be represented as a countable superposition of dyadic cylindrical harmonics. The method aims at providing the necessary theoretical establishment for the determination of the dispersion curves emerging in cortical bones. [Copyright &y& Elsevier]

Abstract: In the current paper, we have investigated the dependence of the effective elastic properties of a composite material on the fiber/matrix interface elastic property. The model composite consists of a single cylindrical fiber embedded in a concentric cylindrical matrix material. A three dimensional mathematical method has been developed connecting the interface properties with the effective axial Young’s modulus of the composite structure. Special effort has been devoted to decode information about the quality of the interface by exploiting the information provided by the elastic effective parameters. In particular, the effective modulus vs. stiffness coefficient curves have been generated for Ti/SiC composites. The aforementioned curves reveal the characteristics of the transition from the regime of perfect interface to the realm of complete debonding. [Copyright &y& Elsevier]

Abstract: A refined shear deformation theory for free vibration of functionally graded plates on elastic foundation is developed. The displacement field is chosen based on assumptions that the in-plane and transverse displacements consist of bending and shear components, and the shear components of in-plane displacements give rise to the parabolic variation of shear strain through the thickness in such a way that shear stresses vanish on the plate surfaces. Therefore, there is no need to use shear correction factor. Material properties of functionally graded plate are assumed to vary according to power law distribution of the volume fraction of the constituents. The elastic foundation is modeled as Pasternak foundation. Equations of motion are derived using Hamilton’s principle. Closed-form solution of rectangular plates is derived, and the obtained results are compared well with three-dimensional elasticity solutions and third-order shear deformation theory solutions. Finally, the influences of power law index, thickness ratio, foundation parameter, and boundary condition on the natural frequency of plates have been investigated. [Copyright &y& Elsevier]

Abstract: A rigorous first order shear deformation theory is employed along with modified ABD parameters to analyze static and free vibration behavior of generally laminated deep curved beams. The deepness term (1+ z/R) is exactly integrated into ABD parameters formulation and equivalent modulus of elasticity is used instead of traditional stiffness terms to account for deepness and material coupling of the beam structures, respectively. Static as well as free vibration analyses were performed and the results for deflection, moment resultants, and natural frequencies were obtained. The exact solution for simply supported boundary condition as well as numerical solutions using GDQ for other boundary conditions are presented. Results are compared with those obtained using accurate three dimensional finite element simulations using commercial software. It has been shown that when considering more accurate stiffness parameter, FSDT can accurately predict static and free vibration behaviors of composite deep beams of any lamination and boundary condition. [Copyright &y& Elsevier]

Abstract: An expression of Young’s modulus of short inorganic fiber reinforced polymer composites was derived based on the tensile strength equation proposed in the previous paper, and the factor affecting the Young’s modulus was analyzed. This equation was applied to estimate the Young’s modulus of short inorganic fiber reinforced polymer composites. The results showed that the relative Young’s modulus increased nonlinearly with increasing fiber volume fraction, while increased linearly with an increase of fiber length-diameter ratio. Finally, the equation was verified preliminarily by using the measured Young’s modulus of the short glass fiber (SGF) reinforced polycarbonate/acrylnitrile–butadiene–styrene copolymer composites and the polypropylene reinforced respectively with SGF and short carbon fiber reported from literature, good agreement was found between the predictions and the experimental data. [Copyright &y& Elsevier]

Abstract: This paper is intended to examine the effect of inclusion shapes, inclusion contents, inclusion elastic constants, and plate thickness on the dispersion relations and modes of wave propagation in inclusion-reinforced composite plates. The shape of inclusion is modeled as spheroid that enables the composite reinforcement geometrical configurations ranging from sphere to short and continuous fiber. Mori–Tanaka mean-field theory is used to predict the effective elastic moduli of the composite plate explicitly. The effective elastic moduli are able to elucidate the effect of inclusion’s shape, stiffness, and volume fraction on the composite’s anisotropic elastic behavior. The resulting moduli are then used to determine the dispersion relations and the modal patterns of Lamb waves using the dynamic stiffness matrix method. The types (symmetric or antisymmetric) of Lamb waves in an isotropic plate can be classified according to the wave motions are symmetrical or antisymmetric about the midplane of the plate. Classifying the wave type in an anisotropic plate is not as simple as that in an isotropic plate, and has not received proper attention in the literature. The wave types and orders are identified by analyzing the dispersion curves and inspecting the calculated modal patterns, and the results indicate that the Lamb waves in an orthotropic composite plate can also be classified as either symmetric or antisymmetric waves. It is also found that the inclusion contents, aspect ratios and plate thickness affect propagation velocities, higher-order mode cutoff frequencies, and modal patterns. Propagation speed is generally increased with the aspect ratio, e.g., using longer fibers generally results in a higher propagation speed. [Copyright &y& Elsevier]

Abstract: A new shear deformation theory for sandwich and composite plates is developed. The proposed displacement field, which is “m” parameter dependent, is assessed by performing several computations of the plate governing equations. Therefore, the present theory, which gives accurate results, is relatively close to 3D elasticity bending solutions. The theory accounts for adequate distribution of the transverse shear strains through the plate thickness and tangential stress-free boundary conditions on the plate boundary surface, thus a shear correction factor is not required. Plate governing equations and boundary conditions are derived by employing the principle of virtual work. The Navier-type exact solutions for static bending analysis are presented for sinusoidally and uniformly distributed loads. The accuracy of the present theory is ascertained by comparing it with various available results in the literature. [Copyright &y& Elsevier]

Abstract: The structural performance of multi-cell composite tapered beams when subjected to constrained torsional loading is examined in this paper. A simplified analytical procedure for determining the constrained torsional response of a specific class of multi-cell composite tapered beams is outlined in some detail. The constrained condition analyzed is that of the cantilevered multi-cell beam with torque applied at the free end of the beam. In order to avoid the elastic couplings in the beams between bending, torsion and axial effects, laminates are symmetrically layed-up about their own mid-planes in such a manner that they possess in-plane orthotropy. The analysis approach essentially makes use of the existing theories of torsion appropriate to isotropic constructions, which are suitably modified to account for the non-isotropic nature of compositematerial. The details of the finite element analysis are also included in the paper. The comparisons between the theory and finite element results are shown to give close agreement. [Copyright &y& Elsevier]

Abstract: A closed-form solution is obtained to determine the buckling and post-buckling behavior of elastically restrained composite panels under compressive loading. The approach allows to study the response of stiffened panels undergoing local buckling modes, taking into account the restraints provided by the stiffeners to the rotation of the skin edges. The panels are modeled as thin plates referring to Marguerre type equations together with classical lamination theory. The equations are written in non-dimensional form, allowing for the study of a wide class of orthotropic laminates. The problem is formulated in terms of out of plane displacement, represented with a single-mode approximation, and Airy stress function. The compatibility equation is solved exactly, while the method of Galerkin is applied to impose the equilibrium. The buckling load, the out of plane displacement at different load levels, and the post-buckling stiffness are derived and compared with finite element analyses, revealing good accuracy. Sensitivity analyses are also performed obtaining design charts. [Copyright &y& Elsevier]

Abstract: In this paper we employ the direct approach to the theory of rods and beams, which is based on the deformable curve model with a triad of rotating directors attached to each point. We show that this model (also called directed curve) is an efficient approach for analyzing the deformation of elastic beams with a complex material structure. Thus, we consider non-homogeneous, composite and functionally graded beams made of isotropic or orthotropic materials and we determine the effective stiffness properties in terms of the three-dimensional elasticity constants. We present general analytical expressions of the effective stiffness coefficients, valid for beams of arbitrary cross-section shape. Finally, we apply this method for FGM beams made of metal foams and compare our analytical results with the numerical results obtained by a finite element analysis. [Copyright &y& Elsevier]

Abstract: The previous experimental evidence revealed that tensile fracture of a carbon nanotube (CNT) is triggered from the outermost layer of the graphene sheets, and then the crack grows toward the inner sheets. This work studies load transfer among the graphene sheets when a crack grows into the inner sheets. Both shear-lag modeling and finite element analysis (FEA) have been employed for analyzing the stress distribution in the graphene sheets. Numerical computations are given to the cases in which the wall numbers are two, five, and ten, respectively. The effects of the number of layers and the aspect ratio on the load transfer efficiency have been examined. The energy release and the effective Young’s modulus of a fractured CNT with respect to the number of broken layers are computed. The stress concentration at the crack tip grows with the radial crack propagation. The increase in the interlayer shear stress leads to crack deflection that forms the sword-and-sheath type of tensile fracture. [Copyright &y& Elsevier]

Abstract: Axial buckling analysis of double-walled Boron Nitride nanotubes (DWBNNTs) embedded in an elastic medium under combined electro-thermo-mechanical loadings is presented in this article. Virtual displacement method based on nonlocal cylindrical piezoelasticity continuum shell theory is employed to derive the equilibrium equations. Boron Nitride nanotube (BNNT) is assumed to be surrounded by a bundle of carbon nanotubes (CNTs) as elastic medium for reinforcement. The elastic medium is simulated as Winkler–Pasternak foundation, and adjacent layers interactions are assumed to have been coupled by van der Walls (vdW) force evaluated based on the Lennard–Jones model. The effects of parameters such as electric and thermal loads, elastic medium and small scale are investigated on the buckling behavior of the DWBNNTs. The electric field and its direction are found to have affected the magnitude of the critical buckling load. Moreover, an analysis is carried out to estimate the nonlocal critical electro-thermo-mechanical load for the axial buckling of embedded DWBNNTs. [Copyright &y& Elsevier]

Abstract: First gradient elasticity theory considering surface energy is employed to investigate the axisymmetric deformation of circular nanotubes, in which the microstructural and surface effects are taken into account. The governing equilibrium equation is derived and the corresponding analytical solutions are obtained. It is demonstrated that the total stress decreases with the increase of the intrinsic bulk size, while it increases with the increase of the directional surface energy length parameter. These parameters have strong influences on the mechanical behavior of the embedded nanotubes and thus should be considered in the practical analysis of nanostructures. [Copyright &y& Elsevier]

Abstract: Predicting the elastic constants of braided composites has gained increasing importance over the years. This is mostly due to the broad use of the braided composites and the need to accurately predict their response during stiffness critical applications. This paper outlines an analytical study to predict longitudinal elastic modulus of two-dimensionally braided composites. The developed model analyzes a small repeating representative block, a unit cell, of the braided structure. Unlike most of the previous studies in the field, the model recognizes the effects of curvature of the unit cell on tubular braided composites as a function of braided tube diameter. This paper outlines the development of the proposed analytical model, as well as validation of the model for stiffness critical applications by comparison of the results with available literature data and experimental findings. [Copyright &y& Elsevier]