Spherical Sandwich Shells Research Articles

Prediction the Radial Natural Characteristic of Sandwich Spherical Shell Based on Wave Propagation

Prediction the Radial Natural Characteristic of Sandwich Spherical Shell Based on Wave Propagation

Free vibration analysis of functionally graded sandwich spherical shells with honeycomb core resting on Kerr foundation using the MITC4 element

ABSTRACT The main object of this paper is to further extend the MITC4 element to analyse the free vibration of FG sandwich spherical shells with a honeycomb core (so-called h-FGSS shells) resting on Kerr foundation (KF). The MITC4 originates from a three-dimensional continuum description degenerated to shell behaviour which can be applied to both thick and thin shells. The h-FGSS shell consists of an inner honeycomb core and two different FG skin layers. FSDT is used due to its simplicity and efficiency. The KF includes three parameters as upper springer stiffness ( k U ), upper springer stiffness ( k L ), and the shear layer stiffness ( k S ). The performance and accuracy of the present formulation are verified through comparative examples. Furthermore, the numerical and graphical results show a general picture of the influence of the input parameters on the free vibration of h-FGSS shells, especially the geometrical parameters of the honeycomb core.

Nonlinear transient analysis of functionally graded sandwich spherical shells subjected to blast loading in the thermal environment

The main goal of this paper is to analyze the nonlinear transient of FGSS shells subjected to blast loading in a thermal environment using the MITC4 based on FSDT. The MITC4 originates from a three-dimensional continuum description degenerated to shell behaviour which can be applied to both thick and thin shells. The FGSS shell is composed of a metal core sandwiched between two FGM skin layers. In this research, we address the impact of geometrical nonlinearity arising from mid-plane stretching, specifically emphasizing the von Kármán geometrical nonlinearity. The results obtained from the proposed method are very agreement with the results in available works in the literature. Moreover, a thorough investigation into the nonlinear transient of FGSS shells is conducted, exploring the complete impact of various input parameters.

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.

Dynamics of Spherical Sandwich Shells with Discrete-Symmetrical Light Core Reinforced with Ribs Under Nonstationary Loads*

Dynamics of Spherical Sandwich Shells with Discrete-Symmetrical Light Core Reinforced with Ribs Under Nonstationary Loads*

Finite Element Modelling for Bending and Vibration Analysis of Composite and Sandwich Spherical Shells

Finite element modelling is used to illustrate the bending and vibration response of composite and sandwich spherical shells. ABAQUS is used to model the shell as a three-dimensional deformable solid part. Composites are modelled using mixed modelling technique. The quadrilateral continuum shell element, which has eight nodes, is used for finite element meshing. For a three-layered composite spherical shell with simply supported boundary conditions, the accuracy of the employed element is first evaluated. After that, three potential end conditions are evaluated for further analysis: cantilever (CFFF), two opposing sides clamped (CFCF), and all sides clamped (CCCC). Bending response is produced by applying two types of pressure loads to the exterior surfaces of composite and sandwich spherical shells: uniformly distributed load (UDL) and sinusoidal load (SINO). For various span to thickness ratios, free vibration response and forced vibration response (Time History) are provided under step pressure (UDL and SINO) loading. The element type being used is found to be quite precise and sturdy.

Vacuum Balloon–A 350-Year-Old Dream

The centuries-old idea of a lighter-than-air vacuum balloon has not materialized yet as such structure needs to be both light enough to float in the air and strong enough to withstand atmospheric pressure. We propose a design of a rigid spherical sandwich shell and demonstrate that it can satisfy these stringent conditions with commercially available materials, such as boron carbide ceramic and aluminum alloy honeycomb. A finite element analysis was employed to demonstrate that buckling can be prevented in the proposed structure. Also discussed are other modes of failure and approaches to manufacturing.

Free and Forced Vibration Characteristics of CNT Reinforced Composite Spherical Sandwich Shell Panels with MR Elastomer Core

In this work, the dynamic behavior of the spherical magnetorheological elastomer (MRE) sandwich shell panel with multiwalled carbon nanotubes (MWCNT) reinforced composite face sheets is studied. The governing differential equation of motion for the (doubly curved) spherical sandwich shell panel is derived based on the Higher-Order Shear Deformation Theory (HSDT) kinematics. In the finite element framework, nine noded iso-parametric elements with nine Degrees of Freedom (DOFs) at each node are considered for solving the numerical problem. The finite element model of the multifunctional MR elastomer core spherical sandwich shell panel is validated against the existing works in terms of natural frequencies on different boundary conditions and magnetic field environment. The influence of MWCNT in the face sheet of the MR elastomer spherical sandwich shell panel is also studied through the structural rigidity. Detailed parametric investigations are performed to study the stiffness and damping characteristics of the shell panel with respect to the magnetic field intensities, thickness ratio, aspect ratio, ply orientation, and boundary conditions on the multifunctional MR elastomer core spherical sandwich shell panel. Also, the transverse vibration study of the MWCNT reinforced spherical sandwich shell with MR elastomer is carried out for different magnetic field intensities and curvatures to assess their effects on the structural performance. This study shows the applicability of the MR elastomer in sandwich shell structure for control of vibration and damping.

Time-depended stress analysis of a sector of the spherical sandwich shell with piezoelectric face sheets and FG-CNT core subjected to blast pressure

A novel Layerwise theory (LT) along with the higher-order shear deformation theory (HSDT) is investigated to determine the stress distribution in a three-layer sector of the spherical sandwich shell with piezoelectric face sheets and functionally graded carbon nanotube (FG-CNT) core. The simply-supported sandwich shell is subjected to the internal blast pressure so that the positive and the negative phases of the pressure are considered. The blast pressure is generated by a 1 Kg TNT hemispherical surface burst detonated. The out-of-shell displacement of the sandwich spherical shell at each layer is assumed to be a quadratic polynomial function of the radial component in addition to a function of the coordinate components within the shell. The nineteen equations of motion are derived by Hamilton's principle and Maxwell's static equations. By solving these nineteen equations, the stress distribution is calculated in the spherical sandwich shell in terms of time.

Numerical Simulation of the Dynamics of Spherical Sandwich Shells Reinforced with Discrete Ribs Under a Shockwave*

The equations of vibrations of a stringer-reinforced spherical sandwich shell under unsteady loading are obtained. In analyzing the elements of the elastic structure, the models of the Timoshenko theory of shells and rods are used. The numerical method for solving the obtained equations is based on the application of the integro-interpolation method for constructing finite-difference schemes for equations with discontinuous coefficients. The problem of the dynamic behavior of a spherical sandwich shell under unsteady loading is solved taking into account the discreteness of the ribs. Numerical results are plotted and analyzed.

On the static and dynamic stability of spherical sandwich shell panels with viscoelastic material core and laminated composite face sheets under uniaxial and biaxial harmonic excitations

The buckling and parametric resonance characteristics of laminated composite spherical sandwich shell panels with viscoelastic material (VEM) core are investigated in the present analysis considering full geometric nonlinearity in the Green–Lagrange sense. The study includes the longitudinal strain and normal strain in the transverse direction along with transverse shear deformation of the VEM core. The core displacements are considered to be varying linearly along the thickness and those of the face sheets follow first-order shear deformation theory. An eight-noded sandwich shell finite element of the serendipity family is adopted to discretize the sandwich shell panel domain. The finite element-based equation of motion is derived using Hamilton’s principle in the form of the Mathieu–Hill-type equation. The dynamic instability regions are obtained by applying Hsu’s criteria-based Saito–Otomi conditions to the transformed equation motion. An in-house finite element-based code is developed in the MATLAB platform to solve the stability problem and to establish the stability regions. A parametric study is carried out to investigate the influence of different system parameters on the critical buckling load and the parametric resonance of the sandwich shell panels. It is noted that an increase in core and constraining layer thicknesses increases the critical buckling load of the sandwich shell panels. The stability boundaries are observed to shift toward a higher-excitation-frequency region in the stability diagram with an increase in constraining layer thickness and a decrease in aspect ratio.

Effect of Reissner’s Parameter on Strain Energies of Spherical Sandwich Shells

With the objective of identifying dominant deformation modes for clamped spherical sandwich shells of different geometries and materials, and especially that of Reissner’s parameter for a shell , the infinitesimal quasi-static deformations are analyzed by using a third-order shear and normal deformable shell theory and the finite element method. For spherical shells subjected to normal tractions on a major surface, the effects are delineated on strain energies (SEs) of the in-plane, out-of-plane, stretching, and bending deformations of the following ratios: span/thickness (); radius of curvature/span (); core to face-sheet thickness (); and face sheet’s elastic modulus along the fiber axis to that of the core (), where . It is found that, for fixed values of other parameters, the proportions of SEs of bending to that of the total deformations, as well as of the transverse normal to that of the transverse shear deformations, increase with an increase in or a decrease in the RPS. For , the SE due to bending deformations of the face sheets equals 29%; and, those due to transverse normal and shear deformations of the core are, respectively, 20 and 5% of the total SE. Thus, one should incorporate transverse normal deformations of the core in the shell theory for such problems. For fixed values of other parameters, the core’s in-plane deformations become more significant than its transverse shear deformations, with an increase in or a decrease in the RPS. The SE of the core’s in-plane deformations equals 30% of the total SE for , suggesting a need to account for in-plane deformations of the core for such shells. The present results provide useful insights into deformation modes for spherical sandwich shells of different Reissner’s parameters.

Static and free vibration analysis of laminated composite and sandwich spherical shells using a generalized higher-order shell theory

In this article, higher-order closed-form solutions are obtained for static bending and free vibration analysis of laminated composite and sandwich spherical shells using a generalized higher-order shell theory. A theory is independent of the choice of shearing stress function (polynomial/non-polynomial) which eventually results in a theoretical unification of most of the classical and higher-order shear deformation theories. The present theory yields an accurate distribution of transverse shear stresses through the shell thickness; therefore, it does not require problem dependent shear correction factor. Governing equations and associated boundary conditions of the theory are derived by employing Hamilton’s principle. Navier type higher-order closed-form solutions are obtained for simply supported boundary conditions. Displacements, stresses and natural frequencies are presented for laminated composite and sandwich plates as well as shallow and deep spherical shells. The results of parabolic, trigonometric, hyperbolic, and exponential models are compared with each other and previously published results to verify the accuracy and efficiency of the present generalized shell theory.

Free vibration study of multilayer sandwich spherical shell panels with viscoelastic core and isotropic/laminated face layers

The present work deals with the free vibration and damping characteristics study of multilayer sandwich spherical shell panels with viscoelastic material core layers and elastic face layers based on first order shear deformation theory. The displacements of the core layers are assumed to vary linearly along the thickness. Longitudinal and transverse deformations of the core layers are taken in to account with the consideration of independent transverse displacements of the elastic layers. The equation of motion is derived using Hamilton's principle in conjunction with the finite element method. Eight number of sandwich shell panels are studied mainly in two groups viz. sandwich panels with laminated base layer and isotropic base layer. Fundamental frequencies and associated system loss factors of different sandwich shell panels are deduced by solving the equation as an eigenvalue problem. The effect of thickness of the constraining layers, thickness of the core layers, viscoelastic material loss factor and aspect ratio on the natural frequencies and system loss factors of the sandwich structures are investigated.

Graded effects of metallic foam cores for spherical sandwich shells subjected to close-in underwater explosion

A fluid model is developed and used in combination with Abaqus/Explicit to investigate the effects of graded foam cores on the loading of a sandwich spherical shell subject to underwater explosion from the inner side, after having validated the modeling technique by reproducing results by other authors. Based on the relation between the core strength and the stiffness of the outer face sheet (OFS), four different situations are considered to discuss the graded effects. It is demonstrated that for the case of relatively strong cores and the OFS with low stiffness or soft cores and the OFS with high stiffness, the core arrangement of low/medium/high (relative density from the inside to the outside) has the best performance to shock loadings which is a consequence of the effects of the fluid–structure interaction and the energy absorption capability; on the other hand, for the case of intermediate core strengths and stiffness of the OFS where the pulling-back force due to the stretching of the OFS is close to the core strength, the configuration of high/medium/low has the best performance due to its higher energy absorption efficiency of the foam and lower transmitted stress.

Dynamic response of spherical sandwich shells with metallic foam core under external air blast loading – Numerical simulation

The dynamic response of spherical sandwich shells with aluminum face sheets and aluminum foam core under external air blast loadings were investigated numerically by employing the LS-DYNA. To calibrate the numerical model, the experiments of cylindrical sandwich shells were modeled. And the numerical results have a good agreement with the experiment data. The calibrated numerical model was used to simulate the dynamic response of spherical sandwich shells subjected to the external air blast loadings. It is found that the spherical sandwich shells have a better performance than that of the cylindrical sandwich shells in resisting the blast loadings. The structural dynamic response process has been divided into three specific stages and the deformation modes have been classified and discussed systematically. According to parametric studies, it is concluded that with the decrease of radius of curvature, increase of the thickness of foam core and face sheets and decrease of blast intensity, the blast-resistance is increasing obviously; keeping the thickness summation of front and back face sheet almost constant, a big thickness of front face sheet will improve the blast-resistance performance. These simulations findings can guide well the theoretical study and optimal design of spherical sandwich structures subjected to external blast loading.

Dynamic response of sandwich spherical shell with graded metallic foam cores subjected to blast loading

Finite element simulations were conducted to investigate the dynamic responses of metallic sandwich spherical shells with graded aluminum foam cores under inner blast loading. The deformation of spherical shells, the energy absorption of each core layer, and the propagation characteristic of stress waves in the foam core layers were analyzed and discussed. The spherical shells exhibited an overall inflation–deformation mode as the foam cores were compressed gradually. The arrangement of the core layers with different relative densities had significant effects on the dynamic plastic responses of the spherical shells. The core layer arrangements of 15%–20%–10% and 20%–15%–10% (relative densities) from inside to outside demonstrate the optimal resistance to blast loading.

An applied model for free radial vibrations of a closed spherical sandwich shell

Free vibrations across the thickness of a closed spherical shell are studied. A finite solution to the one-dimensional (along the radius) wave problem is derived for the shell, which differs from the solution for radial vibrations of a liquid. The solution is used in constructing a model for joint vibrations of three spherical layers. An approximate version of their vibratory motion is suggested, which is based on a shell model with thin stiff layers enveloping a thick soft core layer. The solution to the dynamic problem of free vibrations of the soft core is obtained by the method of separation of variables. The elastic reactions of the thin face layers were taken as boundary conditions, which allowed us to reduce the dynamics of the three layers to a vibratory motion of the midlayer under mixed boundary conditions. A transcendental equation for eigenvalues of the problem on free vibrations is derived and analyzed. A graphic description of the effect of layer thickness and elastic properties on the spectrum of eigenvalues of the mixed boundary problem is represented. Relationships for the main eigenfrequency versus the stiffness of face layers and characteristic geometric parameters of the sandwich shell wall are obtained.

Interaction of a plane progressive sound wave with a functionally graded spherical shell

An exact analysis is carried out to study interaction of a time-harmonic plane progressive sound field with a radially inhomogeneous thick-walled elastic isotropic spherical shell suspended in and filled with compressible ideal fluid mediums. Using the laminated approximation method, a modal state equation with variable coefficients is set up in terms of appropriate displacement and stress functions and their spherical harmonics. Taylor’s expansion theorem is then employed to obtain the solution to the modal state equation ultimately leading to calculation of a global transfer matrix. Numerical example is given for a water-submerged/air-filled Aluminum/Zirconia elastic spherical sandwich shell containing a functionally graded interlayer and subjected to an incident progressive plane sound wave. The mechanical properties of the interlayer are assumed to vary smoothly and continuously across the thickness with the change of volume concentration of its constituents. The effect of incident wave frequency, thickness and compositional gradient of the interlayer on the form function amplitude and the average radiation force acting on the composite shell are examined. Limiting cases are considered and fair agreements with well-known solutions are established.

Shear and Flexural Buckling Modes of a Spherical Sandwich Shell in a Centrosymmetric Temperature Field Inhomogeneous across the Thickness

Problems on buckling modes (BMs) are considered for a spherical sandwich shell with thin isotropic external layers and a transversely soft core of arbitrary thickness in a centrosymmetric temperature field inhomogeneous across the shell thickness. For their statement, the two-dimensional equations of the theory of moderate bending of thin Kirchhoff–Love shells are used for the external layers, with regard for their interaction with the core; for the core, maximum simplified geometrically nonlinear equations of thermoelasticity theory, in which a minimum number of nonlinear summands is retained to correctly describe its pure shear BM, are utilized. An exact analytical solution to the problem on initial centrosymmetric deformation of the shell is found, assuming that the temperature increments in the external layers are constant across their thickness. It is shown that the three-dimensional equations for the core, linearized in the neighborhood of the solution, can be integrated along the radial coordinate and reduced to two two-dimensional differential equations, which supplement the six equations that describe the neutral equilibrium of the external layers. It is established that the system of eight differential equations of stability, upon introduction of new unknowns in the form of scalar and vortical potentials, splits into two uncoupled sets of equations. The first of them has two kinds of solutions, by which the pure shear BM is described at an identical value of the parameter of critical temperature. The second system describes a mixed flexural BM, whose realization, at definite combinations of determining parameters of the shell and over wide ranges of their variation, is possible for critical parameters of temperature by orders of magnitude exceeding the similar parameter of shear BM.