Composite Conical Shells Research Articles

Static and free vibration analysis of functionally graded conical shells reinforced by carbon nanotubes

This study investigates the static and free vibration behavior of rotating functionally graded (FG) truncated conical shells reinforced by carbon nanotubes (CNTs) with a gradual distribution of the volume fraction through the thickness. CNTs are here selected as reinforcement, because of their noteworthy physical and chemical properties, together with their ability to enhance the mechanical properties of the whole composite structure. A two-parameter agglomeration model is considered to describe the micromechanics of such particles, which tend to agglomerate into spherical regions when scattered in a polymer matrix. From the macro-mechanical point of view, the conical structures are characterized by a gradual variation of their mechanical properties along the thickness direction, since different distributions are explored to describe the volume fraction of the reinforcing phase. The governing equations of motion for the rotating truncated composite conical shells are derived and solved numerically by means of the Generalized Differential Quadrature (GDQ) method combined with the third-order shear deformation theory (TSDT) in small deformations. The GDQ approach has recently emerged as a very promising numerical tool to solve complex problems without passing through any variational formulation, but solving directly the equations of motion in a strong form. In this paper, a parametric study based on the GDQ is systematically performed to exploit the effect of some geometry parameters, i.e. the length, the radius, the thickness and the semi-vertex angle of the cone, as well as the different distribution of CNTs along the thickness, on the frequency at different circumferential wave numbers and rotating speeds. A convergence study of the numerical results is also made in terms of deflection and stress distributions of the structure, which proves the efficiency of the GDQ approach, also for coarse mesh discretizations in the meridional direction.

An exact analysis for transient anisotropic heat conduction in truncated composite conical shells

This paper presents an exact analytical solution for transient anisotropic heat conduction in a truncated composite conical shell for the first time. The fibers of composite conical shell are winded around the body in any arbitrary direction. Heat convection between the ambient fluid flow and composite conical shell is modeled and the exact solution of heat conduction equation is obtained by combining two popular analytical methods. First, by means of an integral transform in angular direction, the heat conduction equation is transformed and after that the transferred heat equation is solved using separation of variables method. Eventually, an inverse transformation is used in order to achieve the final exact solution of heat conduction equation. Validation of the present analytical solution is performed by comparing the analytical results with the solution of second order finite different method. Besides, the capability of present solution in solving the industrial cases is tested. The present solution is applicable in some industrial cases such as cooling pin fins and aeronautical instruments.

First-ply Failure Analysis of Delaminated Rotating Composite Conical Shells: A Finite Element Approach

The present analysis evaluates the first-ply failure load of delaminated composite conical shells. Single and multiple delamination is considered across the thickness of the conical shell. The dynamic equilibrium equation considers only moderate rotational speeds for which Coriolis effect is neglected. Convergence studies are performed in respect of mesh sizes, and comparisons of the present solutions and those reported in open literature are provided to verify the accuracy of the present finite element formulation. Computer codes are developed to obtain the numerical results for the failure loads of delaminated composite conical shells. The first-ply failure load considering different failure criteria namely Maximum stress (independent), Tsai-Hill, Tsai-Wu-Hahn and Tsai-Hill-Hoffman are evaluated. The variation of the failure loads with the position of delamination across the thickness as well as along longitudinal direction are illustrated and presented.

Investigation of the Free Vibrations of Composite Anisogrid Lattice Conical Shells Formed by Geodesically Spiral and Circumferential Ribs

This paper focuses on the dynamic behavior of composite anisogrid lattice conical shells. Lattice composite conical shell consists of composite helical and circumferential ribs and thin outer skin. The free vibration analysis of anisogrid composite lattice conical shell is presented. A smeared method is employed to calculate the variable coefficients of stiffness of conical shell and more close to the realistic applications. The lattice part of conical shell is modeled as a beam, so in addition to the axial loads, ribs endure shear loads and bending moments. The first-order shear deformation shell theory is used to account for the effects of transverse shear deformations and rotary inertia. The current results are verified with 3D finite element model of conical shell by ANSYS Software and those reported in the literature. Some special cases as influences of geometric parameters of lattice part of shell, effects of boundary conditions and circumferential wave number on natural frequencies of the shell are discussed. It was concluded that employment of the smear method could be recommended for determining the coefficients of stiffness of the composite lattice conical shells with outer skin. Also increasing the vertex angle of cone increases the natural frequencies of conical shell.

Buckling analysis of moderately thick FG carbon nanotube reinforced composite conical shells under axial compression by DQM

ABSTRACTA semi-analytical method is presented to study the buckling of moderately thick carbon nanotube reinforced composite conical shells under axial compression. Material properties are assumed to be graded across the shell thickness. In order to derive the equilibrium equations of the shell, first-order shear deformation theory is used. Then, the partial differential equations are transformed to algebraic type by using the differential quadrature method. To validate the results obtained in this study, comparisons are made with the outcomes of previous studies. Finally, the effects of the geometry of the shell, circumferential mode number, volume fraction of the carbon nanotube, and boundary conditions are studied.

Low-velocity Impact Response of Delaminated Composite Conical Shells in Hygrothermal Environment due to Time-delay

This paper presents a finite element based method to investigate the hygrothermal effects on the transient dynamic response of delaminated composite conical shells with initial twist impacted at arbitrary locations by multiple spherical impactors at a predefined time-delay. An eight-noded shell element has been used in the present analysis based on the Mindlin's theory. The multi-point constraint algorithm is incorporated to ensure the compatibility of deformation and equilibrium of resultant forces and moments at the delamination crack front. The indentation laws of Hertz are implemented to compute the contact force and displacement arising from each impact on specific locations of the cantilevered conical shell. Results are presented to depict the influence of important parameters like, temperature, moisture concentration, twist angle, size of delamination and time-delay on the impact response of delaminated composite conical shells.

Investigation of the vibration of lattice composite conical shells formed by geodesic helical ribs

In this paper free linear vibration of lattice composite conical shells will be investigated. Lattice composite conical shell consists of composite helical ribs and thin outer skin. A smeared method is employed to obtain the variable coefficients of stiffness of conical shell. The ribs are modeled as a beam and in addition to the axial loads, endure shear loads and bending moments. Therefore, theoretical formulations are based on first-order shear deformation theory of shell. For verification of the obtained results, comparison is made with those available in open literature. Also, using FEM software the 3D finite element model of composite lattice conical shell is built and analyzed. Comparing results of analytical and numerical analyses show a good agreement between them. Some special cases as variation of geometric parameters of lattice part, effect of the boundary conditions and influence of the circumferential wave numbers on the natural frequencies of the conical shell are studied. It is concluded, when mass and the geometrical ratio of the composite lattice conical shell do not change, increment the semi vertex angle of cone leads to increase the natural frequencies. Moreover for shell thicknesses greater than a specific value, the presence of the lattice structure has not significant effect on the natural frequencies. The obtained results have novelty and can be used for further and future researches.

Buckling analysis of composite panels and shells with different material properties by discrete singular convolution (DSC) method

The main purpose of this study is to give a numerical solution for static buckling problem of circular cylindrical panels, conical panels, conical shells and circular cylindrical shells under axial load. Isotropic, laminated composite, functionally graded material (FGM) and carbon nanotube (CNT) reinforced functionally graded cases are taken into consideration. By using the Donnell’s shell theory and first-order shear deformation (FSDT) shell theory, the related equations have been obtained for buckling phenomena of shells. Then, the method of discrete singular convolution (DSC) based on the Shannon’s kernel is applied for the solution of these equations. Convergence and comparison studies are carried out to check the validity and accuracy of the DSC method. The effects of shell geometric quantities and material properties on buckling are examined and results are presented for isotropic, FGM, CNT reinforced FGM and laminated composite conical and cylindrical shells and panels. Performance and convergence conditions of the method of DSC have also been investigated.

FREE VIBRATION ANALYSIS OF JOINED COMPOSITE CONICAL-CONICAL-CONICAL SHELLS CONTAINING FLUID

ABSTRACT A new continuous element (CE) formulation has been presented in this paper for the vibration analysis of three joined cross-ply composite conical shells containing fluid. The three joined cross-ply composite conical shells containing fluid can be considered as the general case for joined conical-cylindrical-conical, joined cylindrical-conical-cylindrical, joined cylindrical-conical-conical and joined conical-conical-cylindrical shells containing fluid. Governing equations are obtained using thick shell theory of Midlin, taking into account the shear deflection effects. The velocity potential, Bernoulli’s equation and impermeability condition have been applied to the shell-fluid interface to obtain an explicit expression for fuild pressure. The dynamic stiffness matrix has been built from which natural frequencies have been calculated. The appropriate expressions among stress resultants and deformations are extracted as continuity conditions at the joining section. A matlab program is written using the CE formulation in order to validate our model. Numerical results on natural frequencies are compared to those obtained by the finite element method (FEM) and validated with the available results in other investigations. This paper emphasizes advantages of CE model and the effects of the fluid level, semi-vertex angles and lamination sequences on the natural frequencies of joined composite conical-conical-conical shells.

Elastic deformation of fiber-reinforced multi-layered composite conical shell of variable stiffness

Tailoring composite materials by fibers of spatially varying orientation angles has been realized with the advent of automated tow-placing machine. In order to use these variable stiffness composite materials as structural components, their responses to multiple external loads should be investigated. In this study, a truncated composite conical shell structure subjected to inflating pressure and surface shear traction force is considered. A mathematical model that predicts strain and stress distributions on the conical shell is developed. Based on the model, numerical examples are given for various fiber paths defined on the truncated conical shell that is subjected to inflating pressure and spatially varying shear traction force on the inner and outer surfaces, respectively. Numerical examples show that, under these external loads, the meridional strain and stress components are very sensitive to the type of fiber path definitions and value of semi-vertex angle of the cone. Boundary conditions have, also, shown remarkable effects on strain and stress distributions. To verify the adequacy of the mathematical model, the truncated composite conical shell of variable stiffness is simulated using finite element based ABAQUS commercial software.The numerical results obtained through the developed mathematical model and ABAQUS simulations show good agreement.

Mathematical Formulation of Laminated Composite Thick Conical Shells

<span lang="EN-US">The </span><span lang="EN-US">mathematical formulation</span><span lang="EN-US">of thick conical shells using third order shear deformation of thick shell theory are presented. The equations of motion are obtained using Hamilton’s principle. For present analysis, we consider shell's system transverse normal stress, rotary inertia and shear deformation.</span>

Torsional vibration of functionally graded carbon nanotube reinforced conical shells

Abstract The present study deals with the free torsional vibration of a composite conical shell made of a polymeric matrix reinforced with carbon nanotubes (CNTs). Distribution of CNTs across the thickness of the conical shell may be uniform or functionally graded. Five different cases of functionally graded reinforcements are considered. First-order shear deformable shell theory compatible with the Donnell kinematic assumptions is used to establish the motion equations of the shell. These equations are two coupled equations which should be treated as an eigenvalue problem. The generalized differential quadrature method is used to obtain a numerical solution for the torsional frequency parameters and the associated mode shapes of the shell. After validating the results of this study for the cases of isotropic homogeneous cone and annular plates, parametric studies are carried out to analyze the influences of geometrical characteristics of the shell, volume fraction of CNTs, and grading profile of the CNTs. It is shown that volume fraction of CNTs is an important factor with regard to torsional frequencies of the shell; however, grading profile does not change the torsional frequencies significantly.

Investigation on the Geometric Imperfections driven Local Buckling Onset in Composite Conical Shells

Buckling is a critical failure phenomenon for structures, and represents a threat for thin shells subjected to compressive forces. The global buckling load, for a conical structure, depends on the geometry and material properties of the shell, on the stacking sequence, on the type of applied load and on the initial geometric imperfections. Geometric imperfections, occurring inevitably during manufacturing and assembly of thin-walled composite structures, produce a reduction in the carrying load capability with respect to the design value. This is the reason why investigating these defects is of major concern in order to avoid over-conservative design structures. In this paper, the buckling behavior a conical structure with 45° semi-vertical angle is numerically investigated. The initial imperfections are taken into account by using different strategies. At first, the Single Perturbation Load Approach (SPLA), which accounts for defects in the form of a lateral load, normal to the surface, has been adopted. Then, the actual measured defects have been applied to the structure by using the Real Measured Mid-Surface Imperfections (MSI) approach. Investigations on cylindrical shells using the first strategy have already shown the occurrence of a particular phenomenon called “local snap-through”, which represents a preliminary loss of stiffness. In order to better understand this phenomenon for conical shells, both the aforementioned techniques have been used to provide an exhaustive overview of the imperfections sensitiveness in conical composite shells. This study is related to part of the work performed in the frame of the European Union (EU) project DESICOS.

Numerical study on the buckling and vibration of functionally graded carbon nanotube-reinforced composite conical shells under axial loading

Abstract An efficient numerical method within the framework of variational formulation is employed to study the buckling and vibration of axially-compressed functionally graded carbon nanotube-reinforced composite (FG-CNTRC) conical shells. The effective material properties of functionally graded composite conical shell are estimated based on the extended rule of mixture. To derive the governing equations, the matrix form of Hamilton's principle is first presented on the basis of the first order shear deformation theory. Then, employing the generalized differential quadrature (GDQ) method in axial direction and periodic differential operators in circumferential direction, the numerical differential and integral operators are introduced to perform the discretization process. The comparison study is carried out to verify the accuracy and efficiency of the proposed method. Numerical results indicate that the volume fraction and types of distribution of CNTs have considerable effects on the buckling and vibration characteristics of FG-CNTRC conical shells subjected to axial loadings.

Free vibration analysis of conical shells reinforced with agglomerated Carbon Nanotubes

In the present work, a free vibration analysis of Carbon Nanotube-Reinforced Composite (CNTRC) conical shells is performed considering the agglomeration effect of Carbon Nanotubes (CNTs). The material properties of the nanocomposite conical shell are estimated employing the Eshelby-Mori-Tanaka approach based on an equivalent fiber assumption. The numerical results are compared with the experimental data available from the literature. The equations of motion are derived based on the First-order Shear Deformation Theory (FSDT). The Generalized Differential Quadrature (GDQ) technique is originally implemented to solve the governing equations of the problem and to obtain the natural frequencies of the structures, since it has proven to be an efficient and accurate numerical tool. A parametric study is herein developed to investigate the influence of some characteristic parameters on the vibrational behavior of the CNTRC conical shell, e.g. the CNTs volume fraction and agglomeration, or the boundary conditions and geometrical parameters like the thickness to radius ratio. Based on results, it is found that agglomeration of CNTs plays a significant role on the natural frequency of the structure.

Transient response of delaminated composite conical shells due to multiple low velocity impacts in hygrothermal environment

This paper presents a finite element based method to investigate the hygrothermal effects on the transient dynamic response of delaminated composite pretwisted conical shells with initial twist impacted at arbitrary locations by multiple spherical impactors. An eight-noded shell element has been used in the present analysis based on the Mindlin’s theory. The generalized dynamic equilibrium equation is derived from Lagrange’s equation of motion neglecting Coriolis effect for moderate rotational speeds. The multi-point constraint algorithm has been incorporated to ensure the compatibility of deformation and equilibrium of resultant forces and moments at the delamination crack front. The indentation laws as proposed by Hertz have been implemented to compute the contact force and displacement arising from each impact on specific locations of delaminated conical shells already prestressed by residual thermal or moisture strains. Results have been presented to depict the influence of important parameters like, twist angle, size and location of delamination, velocity and mass of the impactors and the time-delay between the impactors on the multiple impact response of delaminated composite conical shells in hygrothermal environment.

Thermal buckling of temperature dependent FG-CNT reinforced composite conical shells

In this research, linear thermal buckling of a composite conical shell made from a polymeric matrix and reinforced with carbon nanotube fibres is investigated. Distribution of reinforcements across the shell thickness is assumed to be uniform or functionally graded. Thermomechanical properties of the constituents are temperature dependent. Under the assumption of first order shear deformation shell theory, Donnell kinematic assumptions and von Kármán type of geometrical nonlinearity, the complete set of equilibrium equations and boundary conditions of the shell are obtained. A linear membrane analysis is carried out to obtain the pre-buckling thermal stresses of the shell. Adjacent equilibrium criterion is implemented to establish the stability equations associated with the buckling state. The resulting equations are discreted by means of trigonometric expansion through the circumferential direction and discrete singular convolution method through the shell length. The established eigenvalue problem is solved iteratively to obtain the critical buckling temperature and critical mode number. Parametric studies are presented to explore the influences of semi-vertex angle, volume fraction of CNTs, distribution pattern of CNTs and boundary conditions. It is shown that, conical shells with intermediate carbon nanotube volume fraction do not have, necessarily, intermediate critical buckling temperature.

Buckling of heterogeneous orthotropic composite conical shells under external pressures within the shear deformation theory

The main objective of this work is to demonstrate a convenient and efficient way to get a closed-form solution for buckling of heterogeneous orthotropic truncated conical shells under external pressures. The first-order shear deformation shell theory (FOSDT) is adopted to formulate the theoretical model. The basic equations of shear deformable heterogeneous orthotropic truncated conical shells are derived using Donnell shell theory. To solve this problem is used an unknown parameter λ in the approximation functions. The partial differential equations are transformed into algebraic equations using unknown λ parameter and Galerkin's method. The expressions for non-dimensional external pressures of heterogeneous orthotropic truncated conical shells are obtained by solving algebraic equations. The parameter λ which is included in the obtained expressions is get from the minimum conditions of the critical external pressures. The accuracy and reliability of the current solutions are validated by numerical examples and comparison with the results available in the literature. The influences of variations of the semi-vertex angle, radius-to-thickness ratio, orthotropy ratio and heterogeneity factor on the non-dimensional critical external pressures of truncated conical shells within the CST and SDT are also discussed.

Vibration and Acoustic Responses of an Orthotropic Composite Conical Shell in a Hygroscopic Environment

The vibration and acoustic radiation for an orthotropic composite conical shell in a hygroscopic environment are explored through the wave propagation approach and Galerkin method. Theoretical results of the natural vibration and far field sound pressure are presented with incremental moisture content. The effects of incremental stiffness and different semi-vertex angle on the acoustic radiation characteristics are studied too. It is found that the natural frequencies decrease with incremental moisture content. The wavenumbers associated with the lowest frequency mode reaches the modal indices corresponding to the lowest buckling mode near the critical buckling moisture content. With the increasing moisture content, a shifting of natural frequencies toward lower frequency band could be observed in lower frequency band of the modal density in constant frequency band. The overall sound pressure level (SPL) decreases generally with the moisture content, but shows a marginal increase near the critical buckling moisture content. The modal density and overall SPL decrease with the incremental stiffness generally, which increases with the decrease of the semi-vertex angle.

Bending characteristics of delaminated cross-ply composite shallow conical shells in hygrothermal environment

In the present study, the influence of temperature and moisture concentration on the bending characteristics of delaminated rotating composite conical shells has been investigated. The shells with initial twist are considered for moderate rotational speeds wherein Coriolis effect is assumed to be absent. The effects of rotary inertia and transverse shear deformation have been incorporated in the present finite element formulation along with the multi-point constraint algorithm for modeling the delamination. Graphical results have been presented depicting the contours of deflection and relative moment along the planform of the conical shell resulting from centrifugal and hygrothermal forces taking into account the influence of twist angle, stacking sequence, rotational speed, and size of delamination present inside the laminate.