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Based on the variational differential quadrature (VDQ) method, the bending and buckling characteristics of circular plates made of functionally graded graphene origami-enabled auxetic metamaterials (FG-GOEAMs) are numerically studied in this paper. It is considered that the plate is composed of multiple GOEAM layers with graphene origami (GOri) content that changes in layer-wise patterns. The results from genetic programming-assisted micromechanical models are also employed in order to estimate the material properties. The plate is modeled according to the first-order shear deformation plate theory whose governing equations are obtained using an energy approach in the context of VDQ technique. The governing equations are given in a new vector-matrix form which can be easily utilized in coding process of numerical methods. By means of VDQ matrix differential and integral operators, the governing equations are discretized and solved to calculate the lateral deflection and critical buckling load of plates under various boundary conditions. Selected numerical results are presented to investigate the influences of boundary conditions, GOri content, folding degree and distribution pattern on the buckling and bending behaviors of FG-GOEAM plates. [ABSTRACT FROM AUTHOR]

In this paper, the free vibration characteristics of stiffened sandwich plates with auxetic core and functionally graded piezoelectric face sheet are investigated. The sandwich plate configuration comprises three distinct layers: a top layer consisting of functionally graded piezoelectric material (FGPie), a core layer composed of auxetic material exhibiting a negative Poisson's ratio, and a bottom layer made of functionally graded material (FGM). The sandwich plate is reinforced by isotropic stiffeners along the x and y directions. A novel model is established based on the four-variable shear deformation refined plate theory and the pb2-Ritz method. This model offers the flexibility to analyze plates with diverse mechanical boundary conditions and supports two types of electrical boundary conditions: closed circuit and open circuit. The accuracy and convergence of the proposed model are validated through comparative analyses against published results, thereby confirming the reliability when analyzing the vibration characteristics of this complex sandwich structure. Furthermore, some new investigations are carried out to explore the influence of various parameters on the vibrational characteristics of the stiffened piezoelectric auxetic sandwich (SA-FGPie) plates. The results suggest that the properties of the reinforcing stiffeners, such as quantity or dimensions, alter the free vibration characteristics of the SA-FGPie plates significantly. In addition, parameters such as the volume fraction indexes of the FGPie and FGM layers, electrical boundary conditions or FGPie layer thickness, as well as geometric parameters of the auxetic unit cell also have a significant influence on the vibration response of SA-FGPie plates. However, the influence of these parameters depends on the specific boundary conditions. [ABSTRACT FROM AUTHOR]

This paper describes the nonlinear vibration of a novel smart plate with an auxetic metamaterial core and piezoelectrically actuated multiscale hybrid nanocomposite porous layers (GPL/CF/PVDF) using Reddy's higher-order shear deformation theory (HSDT). Using the rule of mixture (ROM) and Halpin–Tsai model (HT), the current properties of electroelastic layers were determined. Smart plate equations are detected using Hamilton's principle, Maxwell's law, and von Karman nonlinearity terms. The generalized differential quadrature method (GDQM) is then employed to discretize the governing equations of a sandwich plate for various boundary conditions. In addition, the smart plate's nonlinear frequency ratio and nonlinear natural frequency are detected using the angle of auxetic cell, the electric voltage, and the graphene nanoplatelet weight fraction. In addition, the influence of the porosity constant, the thickness of the auxetic core, and the thickness of the smart graphene-reinforced hybrid nanocomposite layer on (ω nl / ω l) and ω nl were computed and presented in each figure. [ABSTRACT FROM AUTHOR]

Bi-level tailoring of cellular metamaterials involving a dual design space of unit cell and elementary beam level architectures has recently gained traction for the ability to achieve extreme elastic constitutive properties along with modulating multi-functional mechanical behavior in an unprecedented way. This article proposes an efficient analytical approach for the accurate evaluation of all constitutive elastic constants of asymmetric multi-material variably-thickened hexagonal lattices by considering the combined effect of bending, stretching, and shearing deformations of cell walls along with their rigid rotation. A tri-member unit cell is conceptualized, wherein all nine constitutive constants are obtained through the mechanics under one cell wall direction and subsequent repetitive coordinate transformations. We enhance the design space of lattice metamaterials substantially here by introducing multiple exploitable dimensions such as asymmetric geometry, multi-material unit cells and variably-thickened cell walls, wherein the conventional monomaterial auxetic and non-auxetic hexagonal configurations can be analyzed as special cases along with other symmetric and asymmetric lattices such as a range of rectangular and rhombic geometries. The generic analytical approach along with extensive numerical results presented in this paper opens up new avenues for efficient optimized design of the next-generation multi-functional lattices and cellular metamaterials with highly tailored effective elastic properties. • Bi-level tailoring of cellular metamaterials involving a dual design space of unit cell and elementary beam-level architectures. • Accurate evaluation of all constitutive elastic constants of asymmetric multi-material variably-thickened hexagonal honeycomb lattices. • Expanded design space by introducing multiple exploitable dimensions such as: asymmetric geometry, composite multi-material unit cells, variably-thickened cell walls (derived through physics-based rationale) and their coupled effect. • New avenues for efficient optimized design of the next-generation multi-functional lattices and cellular metamaterials with highly tailored effective elastic properties. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to evaluate the dynamic behaviour of sandwich toroidal shells composed of a core with negative Poisson ratio (auxetic honeycomb material) and nanocomposite enriched coating layers under impulsive/periodic pressures considering the geometrical nonlinearity. The set of nonlinear equilibrium equations based on the first-order shear deformation theory are and the resultant nonlinear differential motion equations are approximately solved by the Galerkin method and 4th-order Runge–Kutta solution, respectively. The achieved responses show that the amplitude of outward deformations is intensively increased when the proposed sandwich shells are subjected to rectangular periodic and impulsive loadings which shows the destructive effects of this type dynamic loading. The performed parametric studies shows that these destructive effects can be controlled by changing the geometrical properties of the honeycomb cells and the volume fractions of the nanocomposites in the coating layers. It is notable that in the previous studies the nonlinear dynamic response of toroidal shells subjected to various periodic and impulsive pressures was not investigated. However, in the present work, the mentioned dynamic responses were achieved and investigated without spending time-consuming computational. In fact, the novelty of this work is to develop such a robust and efficient tool. [ABSTRACT FROM AUTHOR]

By using the first order shear deformation theory (FSTD), this paper presents the results of the nonlinear dynamic behavior and natural frequencies of sandwich plate supported by elastic foundations in thermal environment and subjected to mechanical load and blast loading. This work takes advantage of the sandwich plate configuration with three layers: graphene platelet –reinforced composite (GPL) layer – auxetic layer – FGM layer, to analyze the dynamic and vibration problem, in which the auxetic core layer has a negative Poisson's ratios and the FGM layer is reinforced by stiffeners made of full metal or full ceramic depending on a situation of stiffeners at the metal-rich or ceramic-rich side of the plate respectively. Corresponding to the combination of material layers, the mechanical quantities of the problem are processed and calculated to suit the structure and reinforcement conditions. Numerical results are provided to explore the influences of geometrical parameters, elastic foundation parameters, GPL volume fraction, blast and mechanical loads on the nonlinear dynamic behavior and vibration of sandwich plate resting on elastic foundation and in thermal environment. In addition, the study is not only assumed that the material properties depend on environment temperature variation, but also considered the thermal stresses in the stiffeners, as well as considered the effect of imperfections in the original shape of the structure. [ABSTRACT FROM AUTHOR]

In this paper, an analytical investigation is presented on the natural frequency analysis of sandwich plate resting on Winkler-Pasternak type elastic foundations in thermal environment. The sandwich plate consists of an auxetic honeycomb core with negative Poisson's ratio, which is assumed to perfectly bond to two carbon nanotube reinforced composite (CNTRC) face sheets to ignore potential interface effects or imperfections in bonding. The material properties of CNTRC are assumed to be temperature dependent. The volume fraction of carbon nanotube (CNT) varies through the thickness dimension according to linear functions with five different distribution patterns of CNT including UD, FG-O, FG-V, FG-Λ and FG-X. The governing equations of motion are derived based on the Reddy's first order shear deformation plate theory and Hamilton's principle, and the expression of the natural frequency is performed via Galerkin method. Artificial neural network (ANN) model is established to accurately predict the natural frequency of the sandwich plate on the basis of 1450 data points collected from analytical results. The effects of various material and geometrical parameters on the natural frequency of the sandwich plate are investigated in details. [ABSTRACT FROM AUTHOR]

[Display omitted] • Crumpled structures show auxetic behavior, with a shear to compression ratio > 1. • The ratio of shear to compression moduli decreases with increasing compaction. • The orientation of internal layers in crumpled structures affects their shear response. • Low friction allows for easier internal rearrangements of energy focusing regions. Crumpled systems (CSs) can be used as building blocks of mechanical metamaterials with low sensitivity to defects. But to exploit the potential of CSs for novel applications, extensive understanding of the physics of these systems is needed and, so far, the shear response of CSs has not been studied. Here we study the shear response of CSs via short/large amplitude oscillatory shear (SAOS/LAOS) while investigating the effect of several parameters. The training of crumpled paper reduced long-range correlations and resulted in an increase of the shear modulus with compaction, not observed for untrained paper. The presence of stacked layers parallel to the shear direction, in contrast to those positioned perpendicularly, resulted in lower shear storage modulus and increased energy dissipation through layers sliding. Reducing the surface friction allowed for easier internal rearrangements during shear deformations. In general, the shear resistance increases less with the increasing level of compaction than the compaction stiffness. However, it can be tuned by friction between the layers and their orientation. The estimated Poisson's ratio of CSs reveals their auxetic nature. Our results pave the way to better understand the full mechanical response of CSs and tune their desired properties for practical applications. [ABSTRACT FROM AUTHOR]

This work describes the identification of the shear modulus of open cell polyurethane thermoformed auxetic foams from 3- and 4-point bending tests. The foams are incorporated in sandwich beams with carbon fibre/epoxy face skins, and benchmarked against similar sandwich structures made with the conventional counterpart open cell foam. Three types of beams are tested: one with auxetic foams, another type related to a conventional foam core with the same thickness of the auxetic porous materials, and a third type of beam consisting in conventional foam with a thickness corresponding to an iso-weight configuration to the auxetic specimen. The auxetic foam has a shear modulus 7% lower than the one of the bulk conventional specimens, but higher shear stresses at large deformations and a smoother strain stiffening response compared to the beams with the conventional thinner core. The paper also highlights the low shear wave speed of these auxetic foams compared to other porous polymers used in helmet and head protection applications, as well as potential uses of the quasi-zero-stiffness behavior here observed for the auxetic foam sandwich beam. [ABSTRACT FROM AUTHOR]

Auxetic cellular solids in the forms of honeycombs under blast load have great potential in a diverse range of applications, including core material in sandwich plates composite components. Based on Reddy’s first-order shear deformation plate theory, this paper presents an analysis of the nonlinear dynamic response and vibration of sandwich plates with negative Poisson’s ratio in auxetic honeycombes on elastic foundations subjected to blast and mechanical loads. A three-layer sandwich plate is considered discretized in the thickness direction by using analytical methods (stress function method, approximate solution), Galerkin method, and fourth-order Runge-Kutta method. The results show the effects of geometrical parameters, material properties, mechanical and elastic foundations on the nonlinear dynamic response, and vibration of sandwich plates. [ABSTRACT FROM AUTHOR]

Functionally graded (FG) graphene origami (GOri)-enabled auxetic metamaterial (GOEAM) structures have shown great potential for various engineering applications due to their exceptional mechanical and physical properties such as high strength-to-weight ratio, tuneable stiffness and strength, and negative Poisson's ratio (NPR). This paper aims to investigate the buckling and dynamic instability behaviours of FG-GOEAM beams with variable thickness immersed in a fluid, with a particular focus on the influence of NPR. The material properties such as Young's modulus and Poisson's ratio of the GOEAM are determined by using a genetic programming (GP)-based micromechanics model. Within the framework of the first-order shear deformation theory and by employing Hamilton's principle and modelling the fluid effect as added mass, the governing equations of motion are established and are then discretised by means of differential quadrature (DQ) method to obtain a linear system of Mathieu-Hill equations from which the principal instability regions of the FG-GOEAM beam are determined by Bolotin's method. A comprehensive parametric study is conducted to reveal the effects of GOri's folding degree, distribution, weight fraction, as well as fluid density and beam dimensions on the static and dynamic instability behaviours of the FG-GOEAM beam immersed in fluid. Numerical results show that the FG-GOEAM beam with NPR considerably outperforms its pristine metallic counterpart in terms of resistance against static buckling and dynamic stability. • Metamaterial properties are determined by genetic programming-assisted micromechanics models. • Auxetic effect on buckling behaviour and principal instability region is comprehensively investigated. • Added mass model is used to include the fluid effect on the buckling and dynamic stability of the novel FG-GOEAM beam. • FG-GOEAM beam outperforms its pristine metallic counterpart in terms of buckling resistance and dynamic stability. [ABSTRACT FROM AUTHOR]

Auxetic metamaterials with negative Poisson's ratio (NPR) are attracting tremendous attention due to their unusual and intriguing mechanical properties. This paper proposes a novel functionally graded (FG) beam made of graphene origami (GOri)-enabled auxetic metamaterials (GOEAMs) and investigates its nonlinear free vibration characteristics tuned by GOri. The beam consists of multilayer GOEAMs with GOri content changed across the beam thickness in a layer-wise mode such that the auxetic property and other material properties are varied in a graded form and can be effectively estimated by genetic programming (GP)-assisted micromechanical models. The Timoshenko beam theory and von Kármán type nonlinearity are adopted herein to derive the nonlinear kinematic equations that are numerically solved by the differential quadrature (DQ) approach. Detailed parametric studies are performed to discuss the influences of GOri content, distribution pattern, GOri folding degree, and temperature on the nonlinear frequencies of FG-GOEAM beams. Numerical results indicate that the nonlinear free vibration behaviors of the beam can be effectively tuned via GOri parameter and distribution. • Nonlinear free vibration characteristics of shear deformation metamaterial beams are investigated. • Tunability of the nonlinear vibration performance is achieved via graphene origami material parameters. • Influences of functionally graded and homogeneous metamaterial distribution patterns are discussed. • Graded metamaterial distributions offer superior beam stiffness with higher nonlinear natural frequency. [ABSTRACT FROM AUTHOR]

This paper investigates tunable nonlinear bending behaviors of functionally graded composite beams made of graphene origami (GOri)-enabled auxetic metal metamaterials (GOEAMs) within the theoretical framework of the first-order shear deformation theory and von Kármán type nonlinearity. The beam is comprised of multiple GOEAM layers with GOri content and folding degree being variables to effectively control its auxetic property that is graded from layer to layer across its thickness direction. Our developed genetic programming (GP)-assisted micromechanical models are used to estimate the position- and temperature-dependent Poisson's ratio and other material properties of each GOEAM layer in the beam. The nonlinear governing equations of the FG-GOEAM beam are derived by the principle of virtual work and numerically solved by the differential quadrature (DQ) method. A detailed parametric investigation is conducted to examine the effects of GOri content, folding degree, and temperature on the tunability of the nonlinear bending deflection and normal stress of the FG metamaterial beam. Numerical results offer significant insights into the design of FG-GOEAM beam structures with enhanced bending performances. [ABSTRACT FROM AUTHOR]

This paper studies the free vibration behavior and dynamic responses of functionally graded (FG) beams made of novel graphene origami (GOri)-enabled auxetic metal metamaterials (GOEAMs) under an impulsive load within the framework of the first-order shear deformation beam theory. The auxetic property of the beam is effectively controlled by graphene content and GOri folding degree that are graded across the thickness direction of the beams in a layer-wise manner such that Poisson's ratio and other material properties are position-dependent and are estimated by the genetic programming (GP)-assisted micromechanical models. The governing equations are derived by using Lagrange equation approach together with Ritz method. Newmark- β method is employed to solve the governing equations for obtaining dynamic responses of the beams subjected to three different impulsive loads. A comprehensive parametric study is performed to examine the effects of graphene content, GOri folding degree and distribution patterns as well as temperature on the natural frequencies and dynamic responses of the beams. Numerical results show that high tunability in structural vibration characteristics can be achieved via GOri, which offers important insight into the application of FG-GOEAM beams in aerospace engineering structure for significantly improved dynamic structural performance. [ABSTRACT FROM AUTHOR]

• Buckling and postbuckling performances of shear deformation metamaterial beams are investigated. • Effects of graphene origami content, folding degree, and temperature are discussed in detail. • Symmetrical metamaterial distribution X offers significantly higher resistance against buckling and postbuckling. • Buckling and postbuckling responses FG-GOEAM beams are insensitive to temperature change. Auxetic metamaterials have emerged as novel advanced materials with unique physical and mechanical properties that conventional materials do not possess. This paper examines the buckling and postbuckling properties of functionally graded (FG) graphene origami (GOri)-enabled auxetic metallic metamaterial (GOEAM) beams. The beam is comprised of multiple GOEAM layers with GOri content varying in layer-wise patterns to realize gradient-changing Poisson's ratio and stiffness coefficient through the beam thickness. The material properties of each GOEAM layer are estimated by the genetic programming (GP)-assisted micromechanical models. The first-order shear deformation theory and von Kármán type nonlinearity are employed to derive the nonlinear governing equations that are numerically solved by the differential quadrature method (DQM). Numerical investigations are carried out with the main focus on the impacts of GOri content, distribution pattern, folding degree, and temperature on the buckling and postbuckling behaviors of FG metamaterial beams. The theoretical results show that GOri is capable of contributing to the formation of auxetic metal metamaterial, leading to the tunable bucking and postbuckling properties of FG beams, which sheds significant insights into the design of high-performance structures. [ABSTRACT FROM AUTHOR]

This paper presents a study on the auxetic behaviour of the materials composed of hollow spheres. Although, as a newly developed material, the hollow sphere structures have gained a great deal of scientific attention, few studies have acknowledged its auxetic performance. Auxetic materials or materials with a negative Poisson’s ratio have been a subject of intensive research due to their unusual and, in many extents, superior mechanical properties. A number of different auxetic systems that have been developed commonly based on designing special geometry of the material microstructure. However, in the hollow sphere structures, this mechanism is essentially different and the auxetic effect is attributed to the peculiarities of deformation of a thin-wall hollow sphere and to the interaction between the spheres in the assembly. In this study it is shown that the negative Poisson’s ratio in this material is due to the high ratio between tangential to normal stiffnesses of a thin-wall hollow sphere. To evaluate the mechanical properties of these materials a homogenisation procedure based on the Cosserat 3D continuum theory is adopted. In this procedure, an assembly of the flexible thin-wall spheres is modelled as a stack of rigid spheres connected by a set of linear springs. The developed continuum model is validated against the direct finite element analysis of a regular assembly of the hollow spheres. Influence of the various design parameters on the macroscopic mechanical behaviour of the hollow sphere materials is investigated. The numerical study is focused on the auxetic behaviour of various kinds of packing arrangements of the hollow spheres. [ABSTRACT FROM AUTHOR]

Solids that exhibit negative Poisson s ratio are called auxetic materials. This paper examines the extent of transverse shear deformation with reference to bending deformation in simply supported auxetic plates as a ratio of Mindlin-to-Kirchhoff plate deflection for polygonal plates in general, with special emphasis on rectangular plates. Results for square plates show that the Mindlin plate deflection approximates the Kirchhoff plate deflection not only when the plate thickness is negligible, as is obviously known, but also when (a) the Poisson's ratio of the plate is very negative under all load distributions, as well as (b) at the central portion of the plate when the load is uniformly distributed. Hence geometrically thick plates are mechanically equivalent to thin plates if the plate Poisson'si ratio is sufficiently negative. The high suppression of shear deformation in favor of bending deformation in auxetic plates suggests its usefulness for bending-based plate sensors that require larger difference in the in-plane strains between the opposing plate surfaces with minimal transverse deflection. [ABSTRACT FROM AUTHOR]

Modelling and analysis of compressive and thermal postbuckling of sandwich cylindrical panels supported by an elastic foundation are presented in this paper. The sandwich cylindrical panel is composed of auxetic graphene-reinforced metal matrix composite (GRMMC) core with negative Poisson's ratio (NPR) and two metal face sheets. Two cases of the compressive postbuckling of auxetic sandwich cylindrical panels under axial compression in thermal environments and the thermal postbuckling of auxetic sandwich cylindrical panels caused by uniform temperature rise are considered. In the GRMMC core, the volume fraction of graphene through the thickness domain is arranged as a piece-wise functionally graded (FG) pattern. The material properties of both metal face sheets and the GRMMC core are assumed to be temperature dependent. The governing equations of the auxetic sandwich cylindrical panels are formulated based on the framework of the Reddy's third order shear deformation theory. The von Kármán-type kinematic nonlinearity, the thermal effect, the panel-foundation interaction and the initial geometric imperfection of the panel are also taken into account. The postbuckling solutions are obtained by employing a singular perturbation technique along with a two-step perturbation approach. The effects of the FG pattern, the face sheet-to-core-to-face sheet thickness ratio, and foundation stiffness on the postbuckling behavior of sandwich cylindrical panels with FG auxetic GRMMC core are studied in detail. [ABSTRACT FROM AUTHOR]

In this paper, modeling and analysis of postbuckling of sandwich cylindrical shells surrounded by an elastic medium are presented. The sandwich cylindrical shells consist of two metal face sheets and auxetic graphene-reinforced metal matrix composite (GRMMC) core with in-plane negative Poisson's ratio (NPR). Two cases of the compressive postbuckling of sandwich cylindrical shells under axial compression in thermal environments and the thermal postbuckling of sandwich cylindrical shells caused by a uniform temperature rise are considered. Each ply of auxetic GRMMC core possesses in-plane NPR and can have different graphene volume fraction to achieve a piece-wise functionally graded (FG) distribution through the thickness domain of the core. The thermo-mechanical properties of both metal face sheets and the GRMMC core are temperature dependent. The governing equations are formulated based on the Reddy's third order shear deformation shell theory coupled with von Kármán kinematic nonlinearity. The shell-foundation interaction and the thermal effects are considered in the modeling. Applying a singular perturbation technique in conjunction with a two-step perturbation approach, we obtain the postbuckling solutions for perfect and imperfect sandwich cylindrical shells. The effects of the FG pattern, the face sheet-to-core-to-face sheet thickness ratio, and the foundation stiffness on the postbuckling behaviors of sandwich cylindrical shells with auxetic GRMMC core are studied in detail. • Postbuckling of sandwich cylindrical shells with auxetic GRMMC core is presented for the first time. • Both in-plane negative Poisson's ratios and functionally graded patterns are considered. • The material properties of GRMMC core and face sheets are temperature dependent. [ABSTRACT FROM AUTHOR]

The mechanics of beam vibration is of fundamental importance in understanding the shift of resonant frequency of microcantilever and nanocantilever sensors. Unlike the simpler Euler-Bernoulli beam theory, the Timoshenko beam theory takes into consideration rotational inertia and shear deformation. For the case of microcantilevers and nanocantilevers, the minute size, and hence low mass, means that the topmost deviation from the Euler-Bernoulli beam theory to be expected is shear deformation. This paper considers the extent of shear deformation for varying Poisson's ratio of the beam material, with special emphasis on solids with negative Poisson's ratio, which are also known as auxetic materials. Here, it is shown that the Timoshenko beam theory approaches the Euler-Bernoulli beam theory if the beams are of solid cross-sections and the beam material possess high auxeticity. However, the Timoshenko beam theory is significantly different from the Euler-Bernoulli beam theory for beams in the form of thin-walled tubes regardless of the beam material's Poisson's ratio. It is herein proposed that calculations on beam vibration can be greatly simplified for highly auxetic beams with solid cross-sections due to the small shear correction term in the Timoshenko beam deflection equation. [ABSTRACT FROM AUTHOR]

This paper investigates the thermo-mechanical postbuckling behaviors of sandwich plates with auxetic graphene-reinforced metal matrix composite (GRMMC) core resting on elastic foundations. Two cases of the compressive postbuckling of sandwich plates subjected to uni-axial compression in thermal environments and the thermal postbuckling of sandwich plates subjected to a uniform temperature rise are considered. The auxetic GRMMC core having negative Poisson's ratio (NPR) is assumed to be piece-wise functionally graded (FG) by changing the volume fraction of graphene through the thickness domain of the core. The material properties of both metal face sheets and the GRMMC core are assumed to be temperature dependent. The Reddy's third order shear deformation plate theory and the von Kármán-type kinematic nonlinearity are used to formulated the governing equations of the sandwich plate which account for the plate-foundation interaction and the thermal effects. The postbuckling solutions are obtained by employing a two-step perturbation approach. The results reveal that the compressive postbuckling and thermal postbuckling behaviors of sandwich plates with auxetic GRMMC core are significantly influenced by the FG pattern, the face sheet-to-core-to-face sheet thickness ratio, and foundation stiffness. [ABSTRACT FROM AUTHOR]

• Nonlinear thermo-buckling and postbuckling analysis. • The imperfect eccentrically stiffened FGM double curved shallow auxetic shells. • The shell subjected to uniform external pressure, axial compressive, thermal loads. • Using analytical method, the FSDT, the Galerkin and stress function methods. • Taking account the effect of pores and temperature-dependent material properties. It is the first time the nonlinear thermo-mechanical analysis (buckling and postbuckling) of imperfect eccentrically stiffened (ES) double curved shallow shells made of auxetic material under uniform external pressure, axial compressive and thermal loads has been studied by adopting analytical method. The double curved shallow sandwich shell is constructed by an auxetic honeycomb core layer with negative Poisson's ratio and two isotropic homogeneous skin layers. In the present study, the outer surface of the structure is reinforced by a system of FGM stiffeners and taking the influence of pores in the stiffeners into account to increase the load capacity of the structure. Besides, the material properties of the shells and stiffeners are both temperature-dependent. The first-order shear deformation theory is applied to derive equilibrium and compatibility equations of double curved shallow auxetic shell, considering both the geometrical nonlinearity in the Von Karman sense and initial geometrical imperfections and shells placed on the Winkler – Pasternak foundation. The Galerkin and stress function methods are proposed to determine the critical load value and the deflection– load curve by taking the root form of the two-term rotation angles to give the Galerkin integral an equilibrium equation. Several comparisons with results in other literature are made to examine the reliability and accuracy of the method used in the present study. Finally, the effects of thermal environment, reinforced stiffeners, elastic foundation, pores and parameters of auxetic core layer on the buckling and postbuckling loads are evaluated in this paper. The numerical and graphical results show that the reinforced stiffeners, auxetic core, temperature and porous distribution have significantly influenced on the buckling and postbuckling loads of ES double curved shallow auxetic honeycomb sandwich shells. [ABSTRACT FROM AUTHOR]

Recently, auxetic cellular solids in the forms of honeycombs and carbon nanotube reinforced composite (CNTRC) have great potential in a diverse range of applications. This paper studies the nonlinear free and forced vibration of sandwich cylindrical panel on visco-Pasternak foundations in thermal environment subjected to blast load The sandwich cylindrical panel consists of auxetic honeycombs core layer and two CNTRC face sheets. The Poisson' ratio of the auxetic core is negative and the material properties of CNTRC face sheets are assumed to continuously vary in the thickness direction according to four different types of linear functions. The blast load is determined from the distance of the center of blast to center of the structure and the mass of explosive materials. The fundamental equations are established based on Reddy's higher order shear deformation shell theory taking into account the effect of initial imperfection and visco-Pasternak foundations. The Galerkin and Runge–Kutta methods are used to obtain the nonlinear dynamic response and the natural frequency of the sandwich cylindrical panel. The numerical results show the effect of geometrical parameters, visco foundations, initial imperfection, temperature increment, nanotube volume fraction and blast load on the nonlinear vibration characteristics of the sandwich cylindrical panel. The accuracy of present approach and theoretical results is verified by some comparisons with the known data in the literature. • Nonlinear forced vibration. • Sandwich cylindrical panel with negative Poisson's ratio auxetic honeycombs core and CNTRC face sheets. • Using Redyy's higher-order shear deformation shell theory. • Galerkin's method and Runge–Kutta method are applied. • Taking into account the effect of initial imperfection and visco-Pasternak foundations. [ABSTRACT FROM AUTHOR]

Auxetic materials have recently emerged as new types of advanced materials with unique material properties that conventional materials do not possess. In this paper, we examine the effect of in-plane negative Poisson's ratio (NPR) on the thermal postbuckling behavior of graphene-reinforced metal matrix composite (GRMMC) laminated cylindrical shells. The shell consists of GRMMC layers arranged in a piece-wise functionally graded (FG) pattern and is subjected to a uniform thermal load surrounded by an elastic medium. Based on the molecular dynamics simulation results, it is noted that the temperature-dependent material properties of GRMMCs can be expressed as a nonlinear function of temperature. The thermal postbuckling problem of shells is modeled under the framework of the Reddy's third order shear deformation theory and solved by using a singular perturbation technique in conjunction with a two-step perturbation approach. Numerical investigations are carried out for the postbuckling of (10/-10/10/-10/10) S and (10/-10/10) S shells with in-plane NPR. It is found that the FG-X pattern can enhance the buckling temperature and the thermal postbuckling strength of the shells. The anomaly is that the thermal buckling load and postbuckling strength of UD (10/-10/10) S shell are slightly higher than those of UD (10/-10/10/-10/10) S GRMMC laminated cylindrical shell. • Both piece-wise FG configurations and in-plane NPRs are considered. • Temperature dependent material properties for both graphene reinforcements and metal matrix are considered. • Buckling temperatures of UD (10/-10/10) S shell are slightly higher than those of UD (10/-10/10/-10/10) S shell. • Thermal postbuckling load–deflection curves of UD (10/-10/10) S shell are higher than those of UD (10/-10/10/-10/10) S shell. [ABSTRACT FROM AUTHOR]

Auxetic materials are one of the metamaterials that have potential applications in many scientific and engineering fields. In this paper, an investigation is presented on the postbuckling responses of axially loaded graphenereinforced metal matrix composite (GRMMC) laminated cylindrical panels with in-plane negative Poisson's ratio (NPR). The panels are made of GRMMC laminates and rest on an elastic foundation in thermal environments. The graphene volume fraction in GRMMC layer may vary across the panel thickness in order to achieve a piece-wise functionally graded (FG) pattern. The GRMMC layers have in-plane NPR and temperature dependent material properties. The governing differential equations for the GRMMC laminated cylindrical panels are formulated based on the Reddy's third order shear deformation shell theory and are solved by using a singular perturbation technique along with a two-step perturbation approach. Numerical investigation is carried out to study the influence of the in-plane NPR, the FG patterns, the thermal environmental conditions and the foundation stiffness on the postbuckling responses of the GRMMC laminated cylindrical panels under axial compressive load. The results reveal that the in-plane NPR can lead to a substantial change of the postbuckling behaviors of the GRMMC laminated cylindrical panels. • A novel auxetic material structure is modeled. • Both in-plane negative Poisson's ratios and functionally graded patterns are considered. • The material properties of GRMMC layer are anisotropic and temperature dependent. • The new findings for the postbuckling behaviors of GRMMC laminated panels are presented. [ABSTRACT FROM AUTHOR]