Sandwich Conical Shells Research Articles

Crashworthiness of foam filled truncated conical sandwich shells with corrugated cores

Polymeric foam filled truncated metallic conical sandwich shells with corrugated cores were proposed, and their energy absorption characteristics under axial compression were systematically investigated. The types of foam filling include: (i) foam filling inner cavity (FFIC), (ii) foam filling corrugated channel (FFCC), and (iii) foam filling inner cavity and corrugated channel (FFICCC). Test specimens were fabricated by combining the step-by-step molding method with the method of in-situ foam filling. Firstly, the crashworthiness of FFIC, FFCC and FFICCC subjected to axial compression was experimentally characterized. Secondly, numerical simulations with the method of finite elements (FE) were performed, with good agreement achieved between measurements and simulations. Subsequently, based upon the validated FE models, interaction mechanisms between foam filler and metallic shell were explored, and the influences of wall thickness, semi-apical angle and loading speed on energy absorption were quantified. The three different foam filled structures were found to exhibit higher energy absorption than their unfilled counterpart. Particularly, the specific energy absorption (SEA) of the FFCC was higher than that of the unfilled structure, attributed mainly to the participation of all foam fillers in the interaction with metal shells that was rarely found in other types of foam-filled structure.

Mechanical Stability of Eccentrically Stiffened Auxetic Truncated Conical Sandwich Shells Surrounded by Elastic Foundations

Mechanical Stability of Eccentrically Stiffened Auxetic Truncated Conical Sandwich Shells Surrounded by Elastic Foundations

Dynamics of Sandwich Conical Shells with a Discretely Inhomogeneous Core Under Nonstationary Loading

Dynamics of Sandwich Conical Shells with a Discretely Inhomogeneous Core Under Nonstationary Loading

Автоколивання тришарової усіченої конічної оболонки із стільниковим заповнювачем, виготовленим адитивними технологіями

This paper presents a nonlinear mathematical model of self-vibrations of conical sandwich shells with a honeycomb core made by additive technologies. The vibrations of the structure are described by fifteen unknowns. Each layer of the structure is described by five unknowns: three projections of the displacements of the layer middle surface and two rotation angles of the middle surface normal. Displacement continuity conditions at the layer interfaces are used. The higher-order shear theory is used to describe the stress-strain state of the structure. The case of conical sandwich shell ? supersonic gas flow interaction is considered. Due to this interaction, self-vibrations of the shell structure are set up. In their analysis, the geometrical nonlinearity of the structure is accounted for. Motion equations of the structure are derived using the assumed-mode method, which uses the kinetic and the potential energy of the structure. The self-vibrations are represented as eigenmode expansions, which contain a set of generalized coordinates. A system of nonlinear autonomous ordinary differential equations in the generalized coordinates is derived. The self-vibrations are studied using a combination of the shooting technique and the parameter continuation method. Multipliers are calculated to analyze the stability of periodic vibrations and their bifurcations. The dynamic instability of the structure’s trivial equilibrium is studied by numerical simulation. For clamped-clamped and cantilever shells, the properties of their periodic, quasiperiodic, and chaotic motions are analyzed in detail.

Nonlinear supersonic flutter of sandwich truncated conical shell with flexible honeycomb core manufactured by fused deposition modeling

The self-sustained vibrations of sandwich conical shell with a flexible honeycomb core manufactured by fused deposition modeling are studied. The interaction of the sandwich thin-walled structure with supersonic gas flow is analyzed. The geometrical nonlinearity of the shell structure is taken into account to predict the self-sustained vibrations. Vibrations of the structure layer are described by three displacements of the middle surface of each layer and two rotations of the normal to the middle surface. The higher-order shear deformation theory is used to describe the strain–displacement relationships. The self-sustained vibrations of the sandwich conical shell are described by a system of nonlinear ordinary differential equations with respect to the generalized coordinates. The assumed mode method is used to derive the equations.The bifurcations of the nonlinear self-sustained vibrations are analyzed numerically using a continuation technique. Quasi-periodic and chaotic self-sustained vibrations are numerically studied for the shell subjected to different boundary conditions. Numerical results show that the amplitudes of quasi-periodic and chaotic vibrations are significantly larger than the amplitudes of periodic vibrations for this shell.

Study on CNT reinforced functionally graded sandwich conical shell subjected to low-velocity impact under thermal environment

In the present work, low-velocity impact behavior of pre-twisted carbon nanotubes (CNTs) reinforced functionally graded (FG) sandwich conical shell panels is studied using finite element method. The top and bottom face sheets are reinforced with single-walled CNTs reinforced FG materials with various patterns. The temperature-dependent material properties of the CNTs reinforced functionally graded facings are evaluated using micromechanical models. The dynamic equilibrium equation of the impacted sandwich panel is formulated using Lagrange’s equation. A modified Hertzian contact law is used to evaluate contact force. The solutions of the resulting equations are obtained using Newmark’s time integration method. After validation study of the present method, the effects of the CNTs grading pattern, velocity of the impactor, size of the impactor, CNTs volume fraction, operating temperature, angle of twist, and core-to-facing thickness ratio on the low-velocity impact response of the CNTs reinforced functionally graded sandwich conical shell panel are studied in detail. Numerical results show that increasing the volume fraction of CNTs increases the contact force while a lower contact force is predicted at elevated temperatures.

The vibration study of a sandwich conical shell with a saturated FGP core

This paper is provided to analyze the free vibration of a sandwich truncated conical shell with a saturated functionally graded porous (FGP) core and two same homogenous isotropic face sheets. The mechanical behavior of the saturated FGP is assumed based on Biot’s theory, the shell is modeled via the first-order shear deformation theory (FSDT), and the governing equations and boundary conditions are derived utilizing Hamilton’s principle. Three different porosity distribution patterns are studied including one homogenous uniform distribution pattern and two non-homogenous symmetric ones. The porosity parameters in mentioned distribution patterns are regulated to make them the same in the shell’s mass. The equations of motion are solved exactly in the circumferential direction via proper sinusoidal and cosinusoidal functions, and a numerical solution is provided in the meridional direction utilizing the differential quadrature method (DQM). The precision of the model is approved and the influences of several parameters such as circumferential wave number, the thickness of the FGP core, porosity parameter, porosity distribution pattern, the compressibility of the pore fluid, and boundary conditions on the shell’s natural frequencies are investigated. It is shown that the highest natural frequencies usually can be achieved when the larger pores are located close to the shell’s middle surface and in each vibrational mode, there is a special value of the porosity parameter which leads to the lowest natural frequencies. It is deduced that in most cases, natural frequencies decrease by increasing the thickness of the FGP core. In addition, reducing the compressibility of the porefluid a small growth in the natural frequencies can be seen.

Supersonic flutter characteristics of truncated sandwich conical shells with MR core

In this paper, the supersonic flutter characteristics of truncated sandwich conical shells with the magnetorheological (MR) core and isotropic homogeneous host and constraining layers are studied. The mathematical modeling of the shell and the aerodynamic pressure sequentially are performed utilizing the first-order shear deformation theory (FSDT) and the supersonic piston theory incorporating the effects of curvature and aerodynamic damping. The set of the governing equations and associated boundary conditions are derived using Hamilton’s principle. Through an analytical solution in the circumferential direction and a numerical solution in the meridional direction via the differential quadrature method (DQM), a semi-analytical solution is provided for various boundary conditions. After validation of the presented model, the effects of various parameters on the aeroelastic stability regions of the shell are examined such as magnetic field density, semi-vertex angle, length, total thickness, and thickness of the MR core.

Free damped vibration analysis of a truncated sandwich conical shell with a magnetorheological elastomer core

In this paper, free vibration analysis of truncated sandwich conical shells with the magnetorheological (MR) core is investigated. The mathematical modeling of the shell is performed based on the first-order shear deformation theory (FSDT) and the set of the governing equations and associated boundary conditions are derived utilizing Hamilton’s principle. A semi-analytical solution is provided for various boundary conditions through an exact solution in the circumferential direction and a numerical solution in the meridional direction via the differential quadrature method (DQM). After validation of the presented model, the influences of various variables on the natural frequencies and loss factors of the shell are investigated including circumferential wave number, magnetic field density, and geometrical parameters of the shell such as semi-vertex angle, length, total thickness and thickness of the MR core.

Buckling Characteristics of Sandwich Conical Shells with Variable Skin Thickness

In this paper, an analytical solution is presented to study the buckling analysis of the composite sandwich conical shells with variable skin thickness and reinforced with lattice cores. This problem involves the filament wound conical shells, where the skin thickness varies through the length of the shell. First, the reinforced core is converted to a layer by analyzing smeared moments and forces on a unit cell. Next, superimposing the stiffness contribution of the stiffeners with those of the inner and outer shells, the equivalent stiffness of the whole structure is achieved. The power series method based on the first-order shear deformation theory (FSDT) is employed to solve the buckling load of the laminated sandwich conical shell. Numerical solution is conducted to verify analytical results by preparing finite element models. Furthermore, using the analytical model, the impact of several design parameters like buckling load, specific buckling load, stiffener orientation, value of stiffeners angle, lamination angle and semi-vertex angle is investigated, and presented based on the results of this study.

Dynamic behavior of temperature-dependent FG-CNTRC sandwich conical shell under low-velocity impact

Finite element analyses based on higher-order shear deformation theory (HSDT) are presented to study low-velocity impact behavior of pre-twisted sandwich conical shell panels having functionally graded carbon nanotubes-reinforced composite (FG-CNTRC) facings. The temperature-dependent material properties of the FG-CNTRC facings are determined utilizing micromechanical models. The dynamic equilibrium equation of the impacted sandwich panel is formulated using Lagrange’s equation, wherein modified Hertzian contact law is used to evaluate contact force. The solutions of the resulting equations are obtained using Newmark’s time integration method. Finally, the effects of various parameters on the impact response of FG-CNTRC sandwich conical shell panel are analyzed.

The Influence of Variable Shell Thickness on the Vibrational Behavior of Composite Sandwich Conical Shells with Geodesic Lattice Cores

This paper investigates the vibrational behavior of sandwich conical shells with geodesic lattice core and variable skin thicknesses using analytical and numerical approaches. The filament wound conical shell has been considered to have varying skin thickness along the longitudinal direction. The smeared stiffener approach has been used to obtain the equivalent stiffness parameters due to the geodesic lattice core via the force and moment analyses of a unit cell. Superimposing the stiffness contribution of the stiffeners with those due to the inner and outer skins, one can calculate the equivalent stiffness of the whole structure. The equations of motion have been formulated based on the first-order shear deformation theory. The power series method has been implemented for extracting the natural frequencies of vibration. To validate the analytical results, a 3-D finite element model has been provided which is then used to conduct an extensive parametric study. The comparisons indicate an acceptable agreement between the two approaches. Moreover, the effect of variable skin thickness on the natural frequency has been examined. Furthermore, the influences of skin lamination angle, semi-vertex angle of the cone and stiffeners orientation angle have been discussed. The obtained results can be used for future relevant researches.

Investigation on the free vibration behavior of sandwich conical shells with reinforced cores

The free vibration behavior of sandwich conical shells with reinforced cores is investigated in the present study using experimental, analytical, and numerical methods. A new effective smeared method is employed to superimpose the stiffness contribution of skins with those of the stiffener in order to achieve equivalent stiffness of the whole structure. The stiffeners are also considered as a beam to support shear forces and bending moments in addition to the axial forces. Using Donnell’s shell theory and Galerkin method, the natural frequencies of the sandwich shell are subsequently derived. To validate analytical results, experimental modal analysis (EMA) is further conducted on the conical sandwich shell. For this purpose, a method is designed for manufacturing specimens through the filament winding process. For more validation, a finite element model (FEM) is built. The results revealed that all the validations were in good agreement with each other. Based on these analyses, the influence of the cross-sectional area of the stiffeners, the semi-vertex angle of the cone, stiffener orientation angle, and the number of stiffeners are investigated as well. The results achieved are novel and can be thus employed as a benchmark for further studies.

Optimization of dynamic properties for laminated multiphase nanocomposite sandwich conical shell in thermal and magnetic conditions

This paper extends an optimization procedure to obtain the optimal dynamic properties of laminated sandwich multiphase nanocomposite truncated conical shell under magneto-hygro-thermal conditions. Based on principle of Hamilton, the equations of motion are obtained and solved by differential quadrature method and Bolotin's methods for obtaining the dynamic stability region. Based on particle swarm optimization and harmony search algorithms, a novel hybrid optimization method basis HS and PSO is proposed to enhance the performance and convergence of optimum dynamic conditions in this problem. By applying the hybrid optimization algorithm namely as HS-PSO, the volume percent of CNT and carbon fiber, number of laminas, cone semi vertex angle and moisture changes are optimized and the effects of magnetic field and temperature are shown on the dynamic stability of system. The result illustrates that proposed PSO-HS method with same conditions by other optimization methods as harmony memory size (number of particles) of 5 and total iterations of 100 shows the superior convergence performance compare to HS and PSO algorithms.

Thermoelastic free vibration of rotating pretwisted sandwich conical shell panels with functionally graded carbon nanotube-reinforced composite face sheets using higher-order shear deformation theory

This article presents a numerical investigation on the free vibration characteristics of rotating pretwisted sandwich conical shell panels with two functionally graded carbon nanotube-reinforced composite (FG-CNTRC) face sheets and a homogeneous core in uniform thermal environments. The carbon nanotubes are considered to be aligned with the span length and distributed either uniformly or functionally graded along the thickness of the sandwich conical shell panel. The material properties of FG-CNTRC face sheets and homogenous core are assumed to be temperature-dependent and computed employing micromechanics models. The shallow conical shell is modeled using finite element method within a framework of the higher-order shear deformation theory. Lagrange’s equation of motion is employed to derive the dynamic equilibrium equations of sandwich conical shell panels rotating at moderate rotational speeds wherein Coriolis effect is neglected. Computer codes are developed on the basis of present mathematical formulation to determine the natural frequencies of the sandwich conical panels. Convergence and comparison studies are performed to examine the consistency and accurateness of the present formulation. The numerical results are presented to analyze the effects of various parameters on the natural frequencies of the pretwisted FG-CNTRC sandwich conical shell panels under different thermal conditions.

Vibration of two types of porous FG sandwich conical shellwith different boundary conditions

In this paper, in various boundary conditions, the vibration behavior of the two types of porous FG truncated conical sandwich shells is investigated based on the improved high order sandwich shells theory. Two types of porosity are considered in the power law rule to model the FGM properties. In the first type, FG face sheets cover a homogeneous core, and in the second one, the FG core is covered by the homogeneous face sheets. All materials are temperature dependent. By utilizing the Hamilton's energy principle, using the nonlinear von Karman strains in the layers and considering the in-plane stresses and thermal stresses in the core and the face sheets, the governing equations are obtained. A Galerkin method is used to solve the equations with clamped-clamped, clamped-free, and free-free boundary conditions. To validate the results, a FEM software is used and some results are validated with the results in the literatures. Also, Some geometrical parameters, temperature variations and porosity effects are studied. By increasing the length to thickness ratio, temperature, the semi-vertex angle and the radius to thickness ratio, the fundamental frequency parameter decreases in all boundary conditions. In both types of sandwiches for both porosity distributions, by increasing the porosity volume fraction, the fundamental frequency parameters increase. Frequency variation of type-II is lower than type-I in the thermal conditions. And the fundamental frequencies of the clamped-clamped (CC) and clamped-free (C-F) boundary conditions have the highest and lowest values, respectively.

Study on dynamic instability characteristics of functionally graded material sandwich conical shells with arbitrary boundary conditions

This paper presents analytical studies on the dynamic instability of functionally graded material (FGM) sandwich conical shell subjected to time dependent periodic parametric axial and lateral load. In the analysis, four kinds of sandwich distributions, including FGM core and isotropic skins, and isotropic core and FGM skins are considered and the power law distribution is employed to estimate the volume of the constituents. The arbitrary boundary conditions of the FGM sandwich conical shell are achieved by using the artificial spring boundary. The governing equations of conical shell subjected to parametric excitation are established by the Hamilton’s principle considering first order shear deformation shell theory. Then the Mathieu-Hill equations describing the parametric stability of conical shell are obtained by generalized differential quadrature (GDQ) method, and the Bolotin’s method is utilized to obtain the first-order approximations of principal instability regions of shell structure. By comparing the numerical results with the existing solutions in open literature, the validity of the proposed theoretical model is verified. Finally, the influences of sandwich distribution types, gradient indexes, skin-core-skin ratio and load forms on the dynamic stability of FGM sandwich conical shell have been investigated.

Free vibration of rotating pretwisted FG-GRC sandwich conical shells in thermal environment using HSDT

The free vibration behavior of rotating pretwisted sandwich conical shell panels with functionally graded graphene-reinforced composite (FG-GRC) face sheets and homogenous core is investigated in uniform thermal environment using finite element method in conjunction with a higher-order shear deformation theory (HSDT). The volume fraction distribution of the graphene in the face sheets is considered to be uniform or layer-wise functionally graded across its thickness. The temperature-dependent effective elastic moduli of the FG-GRC face sheets are computed employing the refined Halpin-Tsai model, while the effective Poison’s ratio, density, and thermal expansion coefficients are obtained using the mixture-rule. The effects of non-linearity arising out of the initial stresses due to thermal and centrifugal loads are incorporated via geometric stiffness based on Green-Lagrange’s strains. The governing equations for sandwich conical shell panels are derived using Lagrange’s equation of motion at moderate rotational speeds. The influence of graphene distribution patterns on the fundamental frequencies of FG-GRC sandwich conical shells under different thermal conditions is studied with emphasis on triggering parameters like pretwist angle, cone length-to-thickness ratio, core-to-face sheets thickness ratio, and dimensionless rotational speed.

The stability of composite conical shells covered by carbon nanotube-reinforced coatings under external pressures

In this study, the stability of sandwich conical shells covered by functionally graded and uniform distributed carbon nanotube-reinforced composite coatings under external pressures is carried out. The mechanical properties of the carbon nanotube and matrix are assumed to be graded through the thickness of the coatings via three types of grading rule. The basic relationships and stability equations of sandwich conical shells reinforced by carbon nanotubes are obtained employing the modified Donnell-type shell theory and generalized first-order shear deformation theory. The Galerkin procedure is employed to define expressions for the external buckling pressures. For the accuracy of the proposed formulation, the results are compared with the results that are published in the literature. It follows a systematic study aimed at checking the sensitivity of the structural response to the type of pattern and the volume fraction of carbon nanotubes in the composite coatings.

Vibration Analysis of Different Types of Porous FG Conical Sandwich Shells in Various Thermal Surroundings

Vibration behavior of different types of porous functionally graded (FG) conical sandwich shells are investigated based on a modified high order sandwich shells theory for the first time. Sandwich shell includes FG face sheets covering a homogeneous core and the second one includes homogeneous face sheets and a FG core. Power law rule modified by considering two types of porosity distributions is used to model the functionally graded materials. All materials are temperature dependent and uniform, linear and nonlinear temperature distributions are used to model the effect of the temperature variation in the sandwiches. Governing equations are obtained by the Hamilton's energy principle and solved with Galerkin method. To verify the results, they are compared with ones achieved by finite element method obtained by Abaqus software for special cases with the results in literatures.