Sandwich Shells Research Articles

Thermo-Electro-Mechanical Analysis of Micropolar FGP Cylindrical Shell Covered with Piezoelectric Actuator Layers

An investigation is performed in this paper to analyze the nonlinear thermo-electro-mechanical response of long sandwich cylindrical shells with functionally graded porous (FGP) core and thin piezoelectric actuator layers. The FGP core of the sandwich shell is assumed to be temperature- and microstructure-dependent. It is assumed that the sandwich shell is subjected to uniform lateral pressure loading in a thermo-electrical environment. The equilibrium equations of the shell with infinite length are established with the aid of the virtual displacement principle and von Kármán kinematic assumptions. The governing equations are obtained in terms of displacement components based on the first-order shear deformation model of shallow cylindrical shells and the modified couple stress theory. These nonlinear differential equations are analytically solved for a sandwich shell having both the simply-supported and clamped–clamped edge conditions by employing a two-step perturbation technique. Analytical closed-form solutions are determined as a relationship including the load parameter and the mid-span deflection. The comparison examples are made with the existing results in the literature for a simple functionally graded shell, where good agreement is obtained. It is shown that the nonlinear response of the sandwich shell is highly dependent upon the temperature variation, power law index, porosity coefficient, couple stress parameter, piezoelectric layers, and geometrical parameters of the shell.

Meta-honeycomb sandwich tubes: Designing, manufacturing, and crashworthiness performance

Sandwich tubes with meta-honeycomb core of zero Poisson's ratio were designed and fabricated. The meta-honeycomb can realize free curl deformation of cylindrical surface, which is beneficial to manufacture cylindrical sandwich shells with large curvature. For the hexagonal honeycomb structure, forcing the honeycomb panel to roll can lead to localized fragmentation of the honeycomb. However, if the Poisson's ratio is negative by changing the cell shape, then it can allow the structure to achieve greater centripetal curvature. Lateral and axial compression tests were carried out to investigate the crushing behaviors of these composite honeycomb sandwich tubes (CHSTs). The CHST has stable crushing curve and crushing pattern, just like thin-walled aluminum tubes. With higher peak force, plateau force, and specific energy absorption, the CHST is more stable and efficient in energy absorption than thin-walled composite tubes.

Vibrations of Cylindrical Sandwich Shell with Fused Deposition Processed Honeycomb Core and Carbon Nanotubes Reinforced Composite Faces Sheets

Vibrations of Cylindrical Sandwich Shell with Fused Deposition Processed Honeycomb Core and Carbon Nanotubes Reinforced Composite Faces Sheets

Deflection of FGM sandwich conoidal shell with porous core

The maximum deflection of functionally graded sandwich conoidal (FGSC) shell with porous core is studied in this paper. Even and uneven porosity distribution is considered to investigate the effect of porosity in the core of the FGSC shell. The inclusion of porosity (even or uneven) in the core makes the sandwich shell lighter. The modified power law is used to account the porosity distribution. The governing equations are developed based on improved mathematical model. An isoparametric finite element (FE) having 9 nodes and 63 degrees of freedom have been used. The improved mathematical model is executed in the present FE code. The numerical results in terms of maximum deflections are compared with available results in the literature. A broad parametric study is carried out to check the effect of porosity, volume fraction index and material properties on the maximum deflection of FGSC shell with porous core.

Hygro-thermo-mechanical analysis of sandwich shallow shells considering the effects of transverse normal strain

The static response of softcore doubly-curved sandwich shallow shells under hygro-thermo-mechanical loading is presented herein using a fifth-order shell theory which considers the effects of transverse normal strains and stresses at the same time. The present theory accounts for non-linear variations of displacements. The strain-displacement relations take into account only small curvatures following a shallow shell description. The present theory ensured the traction-free boundary conditions at the top and the bottom faces of the shell. The governing equations along with the natural and essential boundary conditions are derived using the principle of virtual work. The governing equations are solved by using Navier’s method. Three layered sandwich shallow shells of double curvature subjected to hygro-thermo-mechanical loading are analyzed. The accuracy and efficacy of the present theory are proved by applying it to the benchmark solutions available in the literature and then the present theory is extended for the analysis of softcore sandwich shells of double curvature. Since an exact 3D elasticity solution is not available for many such problems; this paper can be serving as a benchmark reference solution for future researchers working in this area.

Higher-order static and free vibration analysis of doubly-curved FGM sandwich shallow shells

Plenty of research papers are available on the static and free vibration analysis of single-layer FG shells, however, literature on the analysis of FGM sandwich shells of double curvature is limited. Especially, the authors have not found any paper on the analysis of hyperbolic and elliptical paraboloid FGM sandwich shells. Therefore, FGM sandwich shallow shells with double curvature are analyzed in this study for the static and free vibration conditions. Face sheets of sandwich shells are made up of functionally graded material whereas the core is made up of isotropic material. A functionally graded material considered herein is a combination of alumina and aluminum. Sandwich shallow shells on rectangular planform are modeled using various equivalent single-layer shell theories via unified formulation considering the effects of shear deformation and rotary inertia. Different shell theories recovered from the present unified formulation satisfy the transverse shear stress-free conditions on the lower and upper surfaces of the shell. Hamilton's principle is applied to the present unified formulation for establishing equations of motion. Solutions to free vibration and static problems of simply-supported sandwich shells are obtained using Navier's technique. The numerical results of frequencies, displacements, and stresses are obtained for various types of shells, different sandwich schemes, different values of the power-law factor, and radii of curvature. The results available in the literature are used for the comparison of the present results and found in good agreement with those. However, many new and useful results are also reported in this paper for the reference of readers.

The effect of auxeticity on the vibration of conical sandwich shells with ring support under various boundary conditions

Auxetic materials, materials demonstrating negative Poisson's ratio, have revolutionized the use of materials in industries, as they demonstrate superb acoustic response, fracture resistance, and energy absorption. For the first time, this study embraces the free vibration of conical shells consisting of an auxetic core with and without ring support under various boundary conditions. First, the material characteristics of the auxetic core are calculated by means of a micromechanical approach. Afterwards, the kinematic motion equations of the conical shell are derived utilizing the first-order shear deformation theory. Finally, the governing equations are solved using the powerful generalized differential quadrature element method (GDQEM). The primary goal of this paper is to study the role of implementing an auxetic core as well as ring support in determining the vibrational behavior of the structure. The results of the study showed that the honeycomb interior angle and the presence of ring support can significantly affect the natural frequency of the structure. Lower frequencies can be reached as the interior angle increases. The importance of ring position is found to be highly dependent on the longitudinal mode shapes of vibration. The impact of ring position on natural frequencies is affected by the semi-vertex angle of the cone, and a shift in frequency peaks can be observed by increasing the semi-vertex angle.

On the response of the sandwich shell subjected to thermo-mechanical shock loading

This research proposes an innovative way to analyze thermoelastic reaction of the sandwich cylindrical shells with axially graded graphene-plates reinforced composite (AG-GPLRC) face-sheets and polymer-made core exposed to the coupled thermomechanical shock load. Governing equations are established on the platform of general representation of the elasticity theory. Besides, energy balance equation is considered on the bases of Lord–Shulman theorem to declare the dependency of the system’s response to time. Analytical Navier’s approach is employed through the axial direction and numerical differential quadrature method (DQM) is employed across the radial direction to provide a semi-analytical solver for spatial response of the system. In order to solve the temporal behavior of the structure, Laplace transform utilized in conjunction of the modified Dubner and Abate’s method. A comparative analysis is performed to validate the results obtained in this research with those reported by published articles. Results of this study can be directly involved in the future studies on the thermoelastic behavior of the advanced materials in exposure of the thermomechanical shocks.

Ballistic response of sandwich shell panels: A comparative study

The present work was carried out to explore the impact response of hemispherical (HSS), cylindrical (CSS) and flat sandwich structures (FSS) subjected to high-velocity impact through experimental and numerical simulations. All three-sandwich structures comprised of Al 1100-H12 face skins and Al -3003 H12 honeycomb core. For the direct comparison, the radius and thickness of all three-sandwich structures were kept identical. The high velocity impact tests were performed by using a pneumatic air gun. The hemispherical and conical shape projectiles were impacted typically at the centre (axis) of the sandwich structures with varying impact velocity. The finite element simulations were carried out through commercially available software Abaqus/explicit. The numerically obtained test results were validated through the experimental results to check the accuracy of the modelling. The response of all three structures was examined by comparing their ballistic resistance, failure mechanics and energy absorption characteristics. In addition, the parametric study was conducted numerically by changing the face skin thickness, cell length and cell wall thickness to find out their influence on the impact response of all three structures. The results revealed that the hemispherical structures showed higher impact resistance in terms of higher ballistic limit velocity and energy absorption. The ballistic limit of the HSS structure was 14.6% and 36.5% higher than the CSS and FSS structure respectively against hemispherical nosed projectile whereas the corresponding value against conical projectile was 9.9% and 20.6% respectively.

Vibration of hybrid eccentrically stiffened sandwich auxetic double curved shallow shells in thermal environment

Adding stiffeners or forming a sandwich structure are two ways to reduce unnecessary risks or costs for structures made of advanced materials. Through the proposal of a hybrid sandwich shell model consisting of three layers: Functionally graded graphene platelets reinforced composite layer (FG-GPL), Auxetic core layer, and Functionally graded material layer (FGM) with reinforcement stiffeners, this study presents an analytical solution to illustrate the significant effects of geometrical and material parameters as well as stiffeners on the vibration of sandwich double-curved shallow shells (SDCS shells) subjected to blast loading in a temperature environment and visco-Pasternak medium. The results demonstrate that the shell with stiffener has a higher load-carrying capacity compared to a non-stiffener case and the combination of material layers in a hybrid shell has significant advantages over a homogeneous shell, even under blast load. These findings have practical implications for expanding the application fields of sandwich structures by synthesizing the benefits of each material layer.

Failure mechanisms and acoustic emission pattern recognition of all-CFRP cylindrical honeycomb sandwich shell under three-point bending

The winding-based method is used for fabricating all carbon fiber reinforced plastic (CFRP) cylindrical honeycomb sandwich shell. The theoretical model of multi-failure modes of the cylindrical honeycomb sandwich shell is established under three-point bending. The multiple failure mechanisms of the honeycomb sandwich shell under three-point bending are revealed by the established three-dimensional failure mechanism map. The theoretical prediction of multi-failure modes is verified by experiments and finite element method. The acoustic emission (AE) technology is implemented to detect the evolution rule of internal damage of honeycomb sandwich shell. The damage patterns of the acoustic emission signals with different failure modes are identified by the unsupervised k-means clustering algorithm. The meso-damage mechanisms are also disclosed by the digital microscope. It was found that high peak frequency of the AE signals represents the face-core debonding failure. Finally, the optimal geometric design of the honeycomb sandwich shell under the bending load was carried out. The damage characteristics from mesoscale damage to macroscale failure provide a crucial foundation for discriminating multiple damage failure modes of structures.

Vibration analysis of sandwich cylindrical shells made of graphene platelet polymer–viscoelastic–ceramic/metal FG layers

In this paper, natural frequencies and loss factors of cylindrical sandwich shells composed of the viscoelastic core layer, surrounded by functionally graded graphene-platelet reinforced polymer composite (FG-GPLRPC) and ceramic/metal (FG-ceramic/metal) are investigated. The viscoelastic layer is modeled via the fourth parameter fractional viscoelastic pattern, and the functionally graded ceramic/metal layer is theoretically modeled using a power-law function. The uniform, symmetric and un-symmetric patterns are considered for simulating the graphene platelet (GPL) nanofillers distributions along with the thickness direction. The classical shell theory is used for functionally graded layers and properties of the effective materials of GPLRPC multilayers are determined by using a modified Halpin–Tsai micromechanics model and the rule of mixture. The governing equations of motion are extracted by applying the Lagrange equation and the Rayleigh-Ritz method. The determinant of the coefficient matrix of the characteristic equation is calculated, and the natural frequencies and loss factors of the system are extracted. A study of the interactions of materials and geometrical factors such as the ratio of radius to length, the properties of functionally graded materials, and GPL weight fractions for patterns of proposed distributions are presented and some conclusions have been formed.

Analytical study on sandwich shells considering partial degree of composite action

This paper is focused on a new structural type - sandwich shell, which includes inner and outer shells connected by hoop connectors to achieve composite action; and a functional layer in the middle. Considering that the hoop connectors are not completely rigid, there will be limited slip between the inner and outer shells, which will lead to partial Degree of Composite Action (DCA). Due to the existence of the hoop connectors and shear lag effect, the stress distribution along the width direction of the shell is uneven, which can be described by effective width. Considering all these factors, this paper first develops an analytical model for sandwich shells with different configurations of connectors; and uses finite element analysis results to verify the analytical model. Next, a parametric study is conducted using the analytical model to study the effects of material strength, the ratio of the thickness of the functional layer to the thickness of the single layer shell, and the ratio of the arc length to the width of the sandwich shell on the effective width. It is found that DCA can significantly affect the stress and strain distributions of the sandwich shell. The effective width for 100% DCA can be used as a conservative value to represent those of other DCAs. Finally, a simplified calculation formula, which can be used in practical design, is derived based on the effective width for 100% DCA.

Mechanical property of cylindrical sandwich shell with gradient core of entangled wire mesh

To explore the wide-frequency damping and vibration-attenuation performances in the application of aerospace components, the cylindrical sandwich shell structure with a gradient core of entangled wire mesh was proposed in this paper. Firstly, the gradient cores of entangled wire mesh in the axial and radial directions were prepared by using an in-house Numerical Control weaving machine, and the metallurgical connection between skin sheets and the gradient core was performed using vacuum brazing. Secondly, to investigate the mechanical properties of cylindrical sandwich shells with axial or radial gradient cores, quasi-static and dynamic mechanical experiments were carried out. The primary evaluations of mechanical properties include secant stiffness, natural frequency, Specific Energy Absorption (SEA), vibration acceleration level, and so on. The results suggest that the vibration-attenuation performance of the sandwich shell is remarkable when the high-density core layer is at the end of the shell or abuts the inner skin. The axial gradient material has almost no influence on the vibration frequencies of the shell, whereas the vibration frequencies increase dramatically when the high-density core layer approaches the skin. Moreover, compared to the conventional sandwich shells, the proposed functional grading cylindrical sandwich shell exhibits more potential in mass reduction, stiffness designing, and energy dissipation.

On the large amplitude vibration of shallow sandwich shells with FG-GNPRP core considering initial geometric imperfections

The present study investigates the influence of initial geometric imperfections on large amplitude vibration of shallow sandwich shells with functionally graded graphene nanoplatelets reinforced porous (FG-GNPRP) core embedded between two aluminium facets. The aluminium core is reinforced with graphene nano-platelets (GNP) and the effective properties such as elastic modulus, and mass density, etc. are estimated using Halpin-Tsai and Voigt models, respectively. The continuous functions are adopted to accomplish micro-structural gradation while creating pores which imparts the variation in material properties along thickness direction. The nonlinear governing equations based on higher order shear deformation theory and Sander’s approximation are derived using variational approach. The nonlinearity is introduced in von-Kármán sense and various imperfection modes such as sine, global and local types are considered in transverse direction. The nonlinear results are accessed using finite element method in conjunction with direct iterative technique. The influence of porosity, GNP weight fraction, imperfection amplitude, thickness, side, and radius ratios on the vibration response of the sandwich shells is explored in detail.

Design of double-layered framed plate with equivalent impedance

To get clear the vibration mechanism of sandwith shell using the experiment method, a double-layered plate is designed for the sandwich shell by matching the equivalent impedance. Numerical analysis is conducted, and In 10Hz-4000Hz, the differenceof impedance from double-layered plate and sandwich shell should be less than 10%. A new design is given for the double-layered plate, and which is quite simple for construction. Then, the double-layered plate could be applied to conduct series vibration tests to get clear the influence of sandwich core material on structural vibration, while it could also reduce the costs of money and construction time.

Finite element analysis of thermoelastic free vibration behaviour of hardcore higher-order doubly curved sandwich shell panel

Free vibration analysis is carried through for functionally graded material (FGM) sandwich structure under uniform thermal loading and the material property variation according to the power-law distribution. A self-prepared computer code in MATLAB numeric computing environment based on finite element scheme using higher-order kinematics and replicating quadratic function is equipped for the computation of responses for symmetric as well as unsymmetric doubly curved sandwich structure under diverse support conditions. For numerical approximation while deriving the system of equations, Hamilton's principle is utilised to evaluate the thermo-elastic natural frequencies and the critical buckling temperature. An isoparametric Lagrangian element with zero order Hermitian interpolation function is utilised for model discretisation. After establishing the convergence and validity, the present higher-order model is further hold out for solving diverse numerical illustrations and functional inferences those will assist in designing the imminent graded structures serving under intense thermal loading in high-performance engineering applications.

Wave propagation analysis of cylindrical sandwich shell with auxetic core utilizing first-order shear deformable theory (FSDT)

The high mechanical properties of auxetic materials with negative Poisson’s ratio make them suitable for a variety of applications. This article investigated how the auxetic layer affects wave propagation and its effective characteristics in cylindrical sandwich shells. An analytical solution is established to describe wave propagation through wave frequency and wave velocity according to first-order shear deformable shell theory. Moreover, the Hamilton principle was applied. Then, the governing equation was solved by utilizing an analytical method. Different parameters such as auxetic cell angle inclined and dimensions on wave behavior were investigated. The final step is to conduct a numerical investigation. The results are reported in the form of several figures and analyze how each parameter influences wave propagation.

Dynamic and electrical damping of deep spherical sandwich shells with electrorheological fluid core and FG-GPLRC skins

This paper focuses on the vibration and damping of a deep spherical sandwich shell with a new composition. The shell is made with a core of electrorheological (ER) fluid and skins made of a nanocomposite material with graphene platelets (GPL) to make them stronger. The displacement field is governed by first-order sandwich theory. The properties of the skins, ER fluid, and sealants are dependent on the position, applied electric field, and frequency, respectively. Combining the strain-displacement relation based on the deep shells and linear constitutive laws based on the Hooke and Kelvin-Voigt theories provides the governing motion equations of this structure. The highly coupled differential equations are solved by a semi-analytical solution. The analytical portion is a trigonometric expansion (TE) technique that solves the equations along the circumferential direction. The generalized differential quadrature (GDQ) method is employed as the numerical part to solve the remaining equations along the meridional path. After performing the convergence and verification studies, the frequencies and loss factors correlated to the first ten vibrational angular modes under the effect of various parameters are analyzed.

Investigation on nonlinear bending behavior of sandwich shell panel with cutout using HSDT and FE approach

The nonlinear deflection response of the sandwich shell panel with cutout is analyzed, numerically in the present article. The numerical model of the said curved panel is derived using higher-order shear deformation theory and finite element approximations. The geometrical nonlinearity is being considered via Green-Lagrange’s strain-displacement relation. The governing equation of the nonlinear bending analysis is derived using the energy approach and variational principle. Model accuracy is analyzed as a first step by matching current model responses with previously available data. Further, the model’s capability is explored by solving various new numerical examples and discussed in detail.