Sandwich Shells Research Articles

Static and Transient Response Analysis of Arbitrary Laminated Composite and Sandwich Shells by the FSDT Meshless Method

This paper, for the first time, presents a novel meshless method based on the first-order shear deformation theory (FSDT) and moving-least squares (MLS) approximation to carry out static and transient response analysis on arbitrary laminated and sandwich shell structures. The novelty of the method lies in the implementation of MLS in the curvilinear shell formulation, and the derivation of meshless governing equations on the static and transient response of arbitrary laminated and sandwich shells according to the principle of minimum potential energy and Hamilton’s principle, respectively. The concept of a Convected coordinate system is adopted to deal with arbitrary curvilinear surfaces. Both the position and displacement vectors of shells are approximated by MLS, which is conceptually the same procedure as that in the isoparametric finite element method (FEM). The numerical integration of the stiffness matrices is conducted by the simple Gaussian integral in the Convected coordinate system. Because the moving-least squares (MLS) approximation does not satisfy the Kronecker delta condition, the full transformation method is used to modify the meshless governing equations. Numerical examples are calculated to investigate the static and transient response analysis of laminated and sandwich structures with different geometrical shell shapes, including square plates, spherical shells, doubly-curved shells, and cylindrical shells. The numerical tests show that the proposed method is reliable, and robust and produces accurate results compared to the analytical and numerical solutions taken from the previous literature.

Free vibration and supersonic flutter analyses of a sandwich cylindrical shell with CNT-reinforced honeycomb core integrated with piezoelectric layers

In this research, the free vibration and supersonic flutter analyses of a cylindrical sandwich shell with a reinforced honeycomb core (RHC) integrated with piezoelectric face sheets are investigated. The core is a honeycomb structure enriched with fibers and carbon nanotubes (CNTs). The layers of the shell are modeled based on the Cooper-Naghdi shell theory and the continuity conditions between the layers are considered. The aerodynamic pressure of the supersonic flow is modeled using the linear piston theory. Hamilton’s principle is used to derive the governing equations. A semi-analytical solution is presented including an exact solution in the circumferential direction followed by a numerical solution in the longitudinal direction via the differential quadrature method (DQM). The effects of several parameters on the frequencies, the corresponding damping coefficients, and the critical aerodynamic pressure are investigated. It is concluded that improving the stiffness of the honeycomb core with the CNTs does not necessarily improve the aeroelastic stability of the shell. The presented results can be used in the design and analysis of aerospace structures.

Free vibration analysis of sandwich shells with cutouts: An experimental and numerical study with artificial neural network modelling

This article investigates the free vibration and damping characteristics of cylindrical sandwich shells with cutouts using both experimental and numerical approaches. The effects of cutout shape, size, and position on the dynamic response of cylindrical sandwich shells are explored. Moreover, Artificial Neural Network (ANN) models are constructed to predict the dynamic behavior of the sandwich shell with a cutout. A user-friendly application, Sandwich Shell Vibration Analysis (SSVibA), is developed, incorporating the ANN models to predict the non-dimensionalized natural frequencies and modal loss factors of the sandwich shell under different shell geometries, boundary conditions and cutout configurations. The objective of the present research is to advance the understanding of the dynamic behavior of sandwich structures by integrating experimental investigations, numerical analyses, and ANN modeling.

Investigation of the nonlinear dynamics of thin sandwich shells composed of functionally graded materials with double curvature in thermal environments

Double curvature structures play a crucial role as load-bearing components across various engineering fields. Functionally graded materials, blending metals and ceramics, boast superior material characteristics, fueling their expanding applications. This study pioneers the non-linear dynamic analysis of sandwich shells that feature functional gradient compositions in thermal settings. We assume that both the upper and lower shells of these double curvature structures are crafted from functionally graded materials, with a ceramic core. This variation in material exhibits a ceramic layer on the inner surface and a metallic layer on the outer surface, showing properties that vary along the shell thickness in a power-law gradient. Non-linear dynamic equations are derived using third-order shear theory, encompassing geometric non-linearity and shear deformation. Employing the Galerkin method, we discretize the equations of motion into a non-linear dynamic system with five degrees of freedom, and subsequently give an analytical expression for the nonlinear naturalfrequency by means of multiscale analysis. Our discussion examines the impacts of structural parameters, porosity volume fraction, volume fraction index, and temperature differences on the non-linear/linear frequency ratio of doubly curved sandwich shells. Calculations reveal a sharp rise followed by a rapid decline in the non-linear/linear frequency ratio with increasing structural aspect ratio b/a. Conversely, it decreases with increasing thickness-to-length and radius-to-length ratios, with temperature differences initially reducing and later increasing it. These findings offer practical insights for designing functional gradient double curvature sandwich shells.

Surface matching design of carbon fiber composite honeycomb

Applying carbon fiber composite honeycomb in curved sandwich shells faces challenges due to the saddle-shaped bending surface in hexagon configurations and potential damage during the shape-forming process. This study analyzes the bending deformation of honeycombs by developing large deformation theoretical model for their bending surfaces. The study introduces two novel honeycomb configurations—Boomerang-shaped with a positive Poisson's ratio and Jellyfish-shaped with a negative Poisson's ratio—achieved through curved-wall design and fabrication using a modified carbon fiber composite tape winding molding process. Experimental tests, including bending deformation and shape-forming tests, measure the three-dimensional bending surfaces and mechanical responses of carbon fiber composite honeycombs. Additionally, a developed finite element model analyzes the damage states of various carbon fiber composite honeycombs during shape-forming processes. The results reveal the bending deformation of carbon fiber composite honeycombs and present damage state cloud maps to facilitate the optimal matching of objective sandwich shells with minimal scathe.

Enhanced meshfree method with nodal integration for analysis of functionally graded material sandwich curved shells

This paper presents a nodal integration technique, the sub-domain stabilized conforming integration (SSCI), for the meshfree radial point interpolation method (RPIM) applied to the static and modal analysis of functionally graded material (FGM) sandwich curved shells. FGM sandwich shells with different kinds of core and face sheets are considered in this work while the interested curved shell is formulated by the first-order shear deformation theory. The numerical integration technique to compute the stiffness and mass matrices in the equilibrium equation is the SSCI, which is a stabilized nodal integration with strain smoothing to preserve the accuracy and stability of the numerical results. The RPIM shape functions are utilized in this study for interpolating both the field variables and the geometry of the curved shell due to their ability to satisfy the Kronecker delta property, a rare advantage among meshfree methods. The static and modal analysis of different geometry curved shells with various sandwich FGMs are conducted. Through several numerical examples, the accuracy and efficiency of the SSCI technique in the meshfree RPIM are demonstrated and discussed.

Flexural behavior of innovative multifunctional concrete sandwich shells with different types of connectors

AbstractThis study develops an innovative multifunctional concrete sandwich shell based on a combined experimental and finite element (FE) study on its flexural behavior. The sandwich shell is made up of inner and outer concrete layers connected by connectors, with a middle functional layer that provides various functions such as insulation, acoustic, and vibration control. Bending tests were conducted on four groups of specimens, including three groups of sandwich shells with different types of connectors, that is, truss, grid, and plate connectors, and one reference group of solid shells. Loads, displacements, and strains were recorded during the tests. The FE analysis showed good correlation with the experimental results. Furthermore, a parametric study was conducted using the FE model to evaluate the influence of different parameters, such as middle layer thickness and number of connectors. The results show that the performance of the sandwich shell is comparable to, and in some cases better than, that of the solid shell, depending on the type of connectors used. This study provides a proof of concept for the sandwich shell and establishes a prototype structure for future research.

Smart analysis of sandwich foldable cylinders as gymnastic accessories

A novel smart analysis of sandwich composite cylindrical shell is presented in this article. It is assumed that the sandwich shell is manufactured from the graphene origami reinforced copper core between two intelligent layers. The proposed structure in this article can be used as an idealized model for cylinder shapes in gymnastic sport and physical therapy units. The virtual work principle in the piezo elasticity framework and the cylindrical coordinate system is extended to derive governing equations. To arrive at more accurate results, a third order shear deformable model is extended for kinematic relations. The electro elastic responses are explored using the analytical method to seek impact of main parameters of the composite structure such as foldability parameter, graphene content percent, and applied electric potential on the electro elastic strain, deformation and stress results.

The aeroelastic stability characteristics of a ring-stiffened conical three-layered sandwich shell with an FG auxetic honeycomb core utilizing zig-zag shell theory

This paper is devoted to the supersonic flutter analysis of a ring-stiffened conical three-layered sandwich shell consisting of an auxetic honeycomb (AH) core fabricated from functionally graded material (FGM). The face sheets are manufactured of FGM as well in which the volume fraction of the ceramic increases from zero at the inner surface to one at the outer surface based on a power-law function. The sandwich shell is mathematically modeled based on the Murakami's zig-zag shell theory and the aerodynamic pressure is modeled utilizing piston theory. The derivation of governing equations along with compatibility and boundary conditions are performed using Hamilton's principle and are solved through a semi-analytical solution consisting of an exact solution in the circumferential direction followed by an approximate solution in the meridional direction. The flutter boundaries are attained to investigate the variations of the natural frequencies and damping ratios to find the critical aerodynamic pressure (CAP). The impacts of several factors on the CAP are examined such as the power-law index, geometric characteristics of the cells in the FGAH, thickness of the honeycomb core, location of the ring, and boundary conditions. It is observed that an optimal location can be found for the ring support somewhere between the middle length and large radius of a conical shell that provides the best aeroelastic stability.

Vibration analysis of functionally graded carbon nanotube‐reinforced composite open cylindrical shells with damping film embedded

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

Traveling wave vibration characteristic analysis of FRC sandwich cylindrical shells with FGP-GPLRC core under discontinuous elastic boundary conditions

In this study, a fiber-reinforced composite (FRC) sandwich cylindrical shell with a functionally graded porous graphene platelet reinforced composite (FGP-GPLRC) core is investigated, and the traveling wave vibration characteristics of this new sandwich cylindrical shell under discontinuous elastic boundary conditions are analyzed for the first time. The influences of centrifugal and Coriolis forces are introduced into the model. By employing the first-order shear deformation theory (FSDT) and the continuity assumption of the layerwise theory, the governing equations of the rotating sandwich shell are obtained. The artificial springs are implemented at the ends of the sandwich shell to represent the discontinuous elastic boundary conditions. The natural frequency of the shell is solved via the Rayleigh-Ritz method and the state space method. Then, the approach proposed is validated by comparing the present results with those reported in the literature and the finite element method. Finally, the effects of various parameters on the traveling wave frequency of the shell are evaluated. It was found that in practical engineering, the appropriate thickness of the FGP-GPLRC core should be selected according to the boundary conditions and other factors, and the ply angle should be adjusted to obtain more stability of vibration.

Free vibration analysis of laminated composite and sandwich shells using wavelet finite element method

The present work carries out free vibration analysis of laminated composite shells and panels using wavelet finite element method (WFEM). Two different wavelets, namely, Haar and B-spline wavelet on the interval (BSWI) are employed. The analysis is carried out using higher-order zigzag theory (HOZT), and the WFEM is set up according to Hamilton’s principle. The two-dimensional scaling functions are employed to substitute the interpolation functions as used in the FEM. Owing to the capability of the WFEM to work efficiently with lesser degrees of freedom compared to the traditional FEM, the proposed methodology is validated with the results available.

On the nonlinear buckling and postbuckling responses of sandwich FG‐GRC toroidal shell segments with corrugated core under axial tension and compression in the thermal environment

AbstractThis paper presents an analytical approach for buckling and postbuckling analysis for functionally graded graphene‐reinforced composite (FG‐GRC) toroidal shell segments with the trapezoidal or round corrugated core under the axial tension and compression. The considered shells are placed in a thermal environment and surrounded by an elastic foundation. Based on the von Kármán‐Donnell shell theory with geometrical nonlinearities, Stein and McElman approximation, and a homogenization technique for corrugated shells, the basic equations of shells are established. The previous homogenization technique is improved by adding the thermal forces in the internal force expressions. The shell‐foundation interaction is expressed using the model of the Pasternak assumption. The Ritz energy method is used to obtain the pre‐buckling and postbuckling behaviors of the shells, from which the critical buckling tensions and compressions can be investigated. The influences of FG‐GRC face sheets, corrugated core, and foundation on the buckling behavior of sandwich shells can be shown in the numerical analysis.Highlights Postbuckling of toroidal shell segments with the corrugated core is analyzed. A homogenization technique is improved for the thermal forces in the core. The shells are made of functionally graded graphene‐reinforced composite. The nonlinear Kármán‐Donnell shell theory and Ritz energy method are applied. Special effects of input parameters on the buckling behavior are investigated.

Exact solutions for clamped spherical and cylindrical panels via a unified formulation and boundary discontinuous method

Numerous works in both recent and historical literature have concentrated on formulating theories to perform static analysis on simply-supported shell structures. However, it is worth noting that obtaining analytical solutions for clamped boundary conditions presents a strong challenge. In this paper, closed-form solutions for clamped cross-ply laminated and sandwich shells are achieved by employing a robust and hybrid methodology not previously reported in the literature. The high versatility of the Carrera Unified Formulation (CUF), based on the Equivalent-Single-Layer (ESL) description, is utilized to implement several refined shell theories. The Principle of Virtual Displacements (PVD) is utilized to derive the strong form of the governing equations in terms of displacement variables. As the main novelty, these equations are solved by the Boundary Discontinuous Fourier-based method (BDM) which provides highly accurate analytical solutions. The validity and robustness of the proposed methodology are assessed through a detailed comparison with references available in the open literature, as well as with FEM 3D results obtained with commercial software. Furthermore, the stress recovery technique is exploited to fulfill zero-stress and interlaminar continuity (IC) conditions. The findings might be useful in training artificial intelligence (AI) models, which, for instance, could facilitate the development of digital twin structures.

Flutter of a Sandwich Shell with Inner Cylinder and Annular Ribs

Flutter of a Sandwich Shell with Inner Cylinder and Annular Ribs

Vibration Correlation Technique: Methodology Applied to Buckling of Large-Scale Sandwich Cylindrical Shell

This paper assesses the Vibration Correlation Technique's (VCT) applicability within the context of sandwich cylindrical shells through detailed numerical investigation. The study utilizes a sandwich shell from NASA's Shell Buckling Knockdown Factor project. Finite element models are implemented, incorporating initial mid-surface and thickness imperfections to replicate NASA's buckling test campaign. The numerical results are compared to the experimental data, validating the nonlinear solution with an approximate deviation of 1%. Subsequently, the VCT experimental campaign is numerically conducted through free vibration analyses at different load levels, enabling a comprehensive evaluation of VCT's applicability. The results verified the effectiveness of the VCT, demonstrating a deviation of less than 10% when estimating the buckling load for load levels below 65% of the nonlinear buckling load. Overall, the findings confirm the non-destructive nature of the VCT when employed on such structures, supporting future practical applications.

Vibration analysis of anisogrid composite lattice sandwich truncated conical shells: Theoretical and experimental approaches

Drawing upon both theoretical and experimental methodologies, this study investigates the vibrational characteristics of lattice sandwich truncated conical shells featuring composite ribs made of carbon and E-glass fibers. Toward this aim, the equations of motion along with the corresponding boundary conditions of such sandwich shells are derived using classical Donnell’s shell theory and the smeared stiffness technique. Subsequently, the governing equations are solved to obtain a closed-form expression for natural frequencies employing the Galerkin method. In addition, ABAQUS simulations are presented to study the vibration behavior of single-skin and three-skin conical shells. To validate the theoretical methods, the specimens of three-layer sandwich conical shells were fabricated from two Kevlar fabric laminates and a composite lattice core with hexagonal cells using a manual filament winding process. The composite ribs consist of carbon and E-glass fibers with a ratio of 3:1. Finally, experimental modal tests were conducted to extract natural frequencies and mode shapes by measuring frequency responses at 40 points over a duration of 60 s using a laser vibrometer. A strong correspondence is observed between the theoretical outcomes (utilizing the Galerkin and FE methods) and the experimental findings (with a maximum discrepancy of approximately 16% for the initial four mode shapes). Findings indicate that the excellent performance of the composite lattice core in vibration behavior, which can increase approximately 19% and 16% the natural frequencies corresponding to the first and second mode shapes, respectively.

An emerging shellwich lattice material: Unlocking design freedom and enhancing mechanical properties

This study proposes a novel sandwich shell lattice material called “shellwich”, which offsets the shell lattice to both sides to form panels and achieves the matching of porous material core layer with shell lattice panels. The shellwich lattices (P-BCC) with Schwarz Primitive (P) shell lattice panels and a body-centered cubic (BCC) truss lattice core layer are designed and fabricated. Compression experiments are carried out to explore the mechanical responses of the P-BCC experimentally and numerically. Compared with the P shell and BCC truss lattices, the P-BCC shellwich lattice demonstrates excellent mechanical properties, including widely tailorable elasticity and enhanced energy absorption. Furthermore, the effects of structural parameters on the elastic responses and energy absorption of the P-BCC are discussed. This study provides insights into the design of sandwich structures and lattice materials with high-performance and multifunctional properties, opening up new possibilities for lightweight structures, energy-absorbing systems and other engineering applications.

Analytical Study of Geometric Effects on Functionally Graded Carbon Nanotube Sandwich Shells

Analytical Study of Geometric Effects on Functionally Graded Carbon Nanotube Sandwich Shells

Thermal buckling analysis of composite doubly‐curved shells with viscoelastic core

AbstractComposite sandwich double‐curved shells (CSDCS) have been extensively employed in the engineering domain of variable temperature environments; consequently, it becomes very significant and essential to present the thermal buckling characteristics of CSDCS to supply some valuable numerical results. The no‐linear strain–displacement relationship due to temperature variation has been taken into consideration based on the Von‐Karman non‐linear strain theory, and Hamilton's principle is adapted to derive the buckling differential equations of the CSDCS. The Navier method is employed to solve the eigenvalue problem for obtaining the critical buckling temperature. Finally, through studying the variation rule of thermal buckling temperature (CBT), several interesting findings on thermal buckling of the CSDCS are shown, as follows: As the h3/h1 rises, the CBTs of CSDCS first decrease then increase. With the increase of radius value, the CBTs of spherical shells decline, the CBTs of models (1,1) and (2,2) of hyperbolic paraboloidal shells are essentially unchanged, but the ones of models (1,2) and (2,1) decrease. As the h2 increases, the CBT progressively grows after the initial reduction. With the increase in aspect ratio, the CBTs for modes (1,1) and (2,1) of CSDCS gradually increase, and the ones of modes (1,2) and (2,2) shows an increase after an initial decrease. The CBTs of CSDCS gradually increase as the shear module of damping layer increases.Highlights Thermal buckling of composite doubly‐curved sandwich shells was studied. A solution was proposed to derive the buckling differential equations. The change rules of critical buckling temperature were obtained.