Composite Shell Panels Research Articles

Nonlinear free vibration analysis of composite conical shell panel with cluster of delamination in hygrothermal environment

The nonlinear eigenvalue responses of conical composite shell structure with cluster of multiple delaminations are investigated numerically using the displacement-type finite element technique including the influence of the moisture and elevated thermal environment. The governing equation for the free vibrated structure case of the layered conical panel is obtained through a generalization of the principle of virtual displacement. The numerical solutions are obtained through a customized computer code developed via the higher order displacement field model imposing the zero stresses at the top and bottom surfaces of the laminate. The panel model has been discretized using an eight-nodded isoparametric element to maintain the desired C0 continuity and to avoid the mathematical complexity involved in C1-type continuity. A delamination model is developed by accounting single and cluster of delaminations. The delamination is located at centre of the laminates, either in cluster form or segregated over the lamina. The model is developed by considering the laminate is exposed to elevated moisture and temperature environment. The contribution of moisture and temperature effects on delaminated lamina is examined. The solution methodology is validated with published results. Influence of various parameters such as lamination schemes, aspect ratios, support conditions, thickness ratios, curvature ratios and material properties of the linear and nonlinear free vibration frequencies are analysed in detail and presented. The inferences from the study signify the reduction trend of fundamental frequency due to the presence of single/multi-delamination and moisture content.

Nonlinear Vibration and Dynamic Analysis of Functionally Graded Graphene-Reinforced Eccentrically Stiffened Imperfection Composite Cylindrical Shell Panels

Nonlinear Vibration and Dynamic Analysis of Functionally Graded Graphene-Reinforced Eccentrically Stiffened Imperfection Composite Cylindrical Shell Panels

A three-dimensional formulation for levy-type transversely loaded cross-ply shell panels

In this study, a formulation is developed for investigation of three-dimensional edge stresses in cylindrical composite shell panels under distributed transverse loading. The formulation is obtained by employing the Galerkin weak formulation of the equilibrium equations. The obtained governing equations for the panel are solved via an analytical method for Levy-type boundary conditions including free and clamped edges. The presented formulation is capable of prediction of three-dimensional and boundary layer stresses in the composite panels subjected to transverse loading. The edge stresses in free edge, clamped edge and simple edge of transversally loaded cylindrical composite panel are studied. Comparison of numerical results with the available results of exact elasticity solution in the literature confirms the accuracy and the efficiency of the formulation.

An Extended Kantorovich Method Used for Static Solution of an Arbitrarily Edge Supported Sandwich Cylindrical Shell Panel

Exact solution of complex problems like composite shells with arbitrarily supported boundary conditions through analytical three-dimensional (3-D) approach is mathematically challenging. In the present work an analytical 3-D elasticity solution for the static bending problem of a laminated composite cylindrical shell panel having any arbitrary boundary conditions is proposed. The governing Partial Differential Equations (PDE) problems are obtained by the application of the Ressiner-type mixed variational principle in cylindrical coordinate system. The extended Kantrovich method [10] is applied to solve these equations by reducing them to Ordinary Differential Equations (ODE). Further, the set of ODEs corresponding to the radial component & the circumferential components are solved utilizing modified power series method & Pagano’s approach respectively. Through numerical studies of sandwich shell panels it is shown that this method accurately predicts the deflections, stresses, boundary effects and interfacial disruptions being generated of laminate scheme, material property variations and configuration of the shell panel. Crucially, this is achieved with just two or three terms and few iterations, hence attributes faster computation as compared to other numerical techniques.

Hygrothermal effect on vibroacoustic behaviour of higher-order sandwich panel structure with laminated composite face sheets

This article is a study of vibroacoustic behaviour of sandwich shell panels with laminated composite faces under concentrated harmonic loading in a hygrothermal environment by means of a higher-order finite-boundary element model. The system governing equations of the vibrating structure are derived using the higher-order shear deformation shell theory coupled with finite element and boundary element approach. The corrugated composite material properties due to temperature and moisture variation are included in the model macroscopically. The stiffness, mass tensors and modal values of the hygro-thermally stressed vibrating panel are first obtained and the acoustic radiation responses are then computed by solving the Helmholtz wave equation discretized on the structure boundary. The proposed scheme is implemented via a domestic MATLAB program to compute the desired responses. The results for natural frequencies, critical buckling moisture, critical buckling temperature and radiated sound power are found to be more accurate when matched with the available benchmark solutions. Additional numerical simulations are also performed with commercial software to authenticate the correctness of the present model. Finally, numerous numerical experimentations are carried out to reveal the versatility of the present scheme. The influence of hygrothermal conditions, geometrical parameters, support conditions and lamination scheme of the faces on the hygro-thermo-acoustic responses of laminated composite sandwich shell panels are probed and deliberated in detail.

Computation of worst geometric imperfection profiles of composite cylindrical shell panels by minimizing the non-linear buckling load

• Semi-analytical method is used to compute limit point loads of imperfect cylindrical shell panel. • Global imperfection is represented by double Fourier series . • The unknown Fourier coefficients are determined using genetic algorithm which gives the lowest limit point load. • The “worst imperfection” profile is reported for various stacking sequences of laminated composite cylindrical panel. In this article the “most unfavorable” shape of initial geometric imperfection profile for laminated cylindrical shell panel is obtained analytically by minimizing the limit point load. The partial differential equations governing the shell stability problem are reduced to a set of non-linear algebraic equations using Galerkin's technique. The non-linear equilibrium path is traced by employing Newton–Raphson method in conjunction with the Riks approach. A double Fourier series is used to represent the initial geometric imperfection profile for the cylindrical shell panel. The optimum values of these Fourier coefficients are determined by minimizing the limit point load using genetic algorithm. The results are determined for simply supported composite cylindrical shell panel. Numerical results show that more number of terms is needed in Fourier series representation to obtain the “worst” geometric imperfection profile which gives lower limit load compared to single term representation of imperfection. We have incorporated constraints on the shape of imperfection to avoid unrealistic limit point loads (due to imperfection shape) as we have assumed that the imperfection is due to machining/manufactuting.

Dynamic instability characteristic of damped laminated composite conical shell panel under periodic axial compression

The static and dynamic instability behavior of a simply supported damped composite conical shell panels subjected to periodic axial compression is studied. Bolotin method is adopted to trace the boundaries of instability regions. Influences of semi-vertex angles, symmetric and antisymmetric laminate, length to radius ratios, thickness to radius ratios, and static load factors on the instability regions are studied. Moreover, the time history responses and corresponding phase plots from the unstable and stable region are studied to bring out the various features of instability problem such as existence of beats, effect of damping, and forcing frequency on the response.

Stability and vibration analysis of CNT-Reinforced functionally graded laminated composite cylindrical shell panels using semi-analytical approach

The present paper examined the buckling, postbuckling and vibration characteristics of pre-buckled and post-buckled laminated CNT reinforced composite (CNTRC) cylindrical shell panel made up of single walled carbon nanotubes (SWCNTs) and isotropic matrix. The effective material properties of CNTRC panel are computed using extended rule-of mixture (ROM) method. Higher order shear deformation theory (HSDT) with von Kármán type of nonlinearity is adopted to model the CNTRC cylindrical shell panel. Four different boundary conditions are considered. Besides uniform loading, different types of non-uniform in-plane load distribution such as triangular, trapezoidal, parabolic and partial edge loadings are considered. The internal stress distribution within the shell panel due to applied non-uniform loadings is evaluated by prebuckling analysis. Subsequently, via Hamilton's principle the governing partial differential equations of CNTRC laminated cylindrical shell panel are derived. Employing Galerkin's method and by neglecting the inertia terms the partial differential equations are reduced to a set of non-linear algebraic equation for the static problem. However, for dynamic problem the partial differential equations are converted to a set of ordinary differential equations. Beside parametric study the obtained numerical results from the present semi-analytical study illustrates the effects of CNT volume fraction, CNT dispersion profile, non-uniform load distribution and boundary conditions on the stability and vibration characteristics of CNTRC cylindrical panel.

Investigation of thermo-elastic buckling of variable stiffness laminated composite shells using finite element approach based on higher-order theory

Here, the thermo-elastic buckling characteristics of variable stiffness composite shells, viz., cylindrical and spherical shell panels, subjected to uniform/non-uniform thermal fields are investigated based on finite element approach introducing higher-order theory accounting through thickness effect. The variable stiffness in the composite laminate is spatially created introducing curvilinear fibers that continuously changes the fiber orientation within the lamina. The critical buckling temperature is evaluated solving the governing equations developed through the principle of minimization of total potential energy by adopting the eigenvalue approach. To select the appropriate structural model, the thermal buckling of such curved panels subjected to thermal fields are initially examined using different structural theories. To predict the buckling temperature, the thermal stress resultants are firstly evaluated using the displacement fields of pre-buckling of the laminated shells under the assumed temperature. The formulation is tested against considering problems for which analytical/numerical solutions available in the literature. A comprehensive study based on various design factors such as curvilinear fiber angular variation, lay-up, length-to- and radius-to-thickness ratios, and boundary conditions on the thermoelastic stability of laminated composite shell panels is made.

Thermoelastic free vibration response of graphene reinforced laminated composite shells

This article deals with the free vibration analyses of graphene reinforced singly and doubly curved laminated composite shell panels in thermal environment using finite element method. The curved shell panels are mathematically modeled using higher order shear deformation theory (HSDT) while the distortion of the geometry due to thermal loading is manifested through geometric stiffness considering Green Lagrange type of nonlinearity. Four different types of graphene reinforcement configurations are considered in different types of shells (cylindrical, elliptic paraboloid, hyperbolic paraboloid, conoidal and hypar). The extended Halpin–Tsai approach is used to obtain the temperature dependent material properties of the laminated composite shells. Eight noded isoparametric shell elements consisting of seven degrees of freedom per node are considered to discretize the geometry. The accuracy and convergence of the formulation are verified by solving various examples available in the literature. Finally, parametric study is presented to investigate the influence of various parameters on the free vibration response of the graphene reinforced laminated composite shells.

Free edge stress prediction in thick laminated cylindrical shell panel subjected to bending moment

• A Galerkin based Layer-wise formulation is presented for thick composite panel subjected to bending moment. • An analytical solution is presented for governing equations of the panel considering free edge conditions. • Free edge stresses in bending of thick panel with general layer stacking is studied for the first time. • The predictions satisfy the free edge and free surface conditions. • The effect of geometrical parameters and layer stacking are investigated. A thick composite cylindrical shell panel with general layer stacking is studied to investigate the free edge and 3D stresses in the panel which is subjected to pure bending moment. To this aim, a Galerkin based layerwise formulation is presented to discretize the governing equation of the panel to ordinary differential equations. Employing a reduced displacement field for the cylindrical panel, the governing equations for thick panel are developed in terms of displacements and a set of coupled ordinary differential equations is obtained. The governing equations are solved analytically for free edge boundary conditions and applied pure bending moment. The accuracy of numerical results is examined and the distribution of interlaminar and in-plane stresses is studied. The free edge stresses are studied and the effect of radius to thickness ratio, width to thickness ratio and layer stacking on the distribution of stresses is investigated. The focus of numerical results is on the prediction of boundary layer and free edge stress distribution.

Free Vibration Behavior of Carbon Nanotube Reinforced Composite Conical Shell Panel Under Thermal Environment

The free vibration of carbon nanotube reinforced composite conical shell panel is examined under temperature field. In this analysis, single-walled carbon nanotube and poly(m-phenylenevinylene-co-2,5-dioctoxy-pphenylenevinylene) are used as fibre and matrix materials, respectively. The material properties are considered as temperature-dependent. The effective material properties of carbon nanotube reinforced composite panel are evaluated through the extended rule-of-mixture. The finite element model is prepared using commercially available finite element tool ANSYS APDL. An eight node Serendipity shell element (SHELL281) is used to discretize the present conical model. The displacement field is framed in the first-order shear deformation theory with six degrees of freedom. The Block Lanczos eigenvalue extraction method is used to obtain the frequency responses. In order to obtain the appropriate mesh density for the said model, the convergence study is executed for various mesh sizes. The present results are compared and validated with the previously reported results. Finally, the influences of different parameters such as length-to-thickness ratio, volume fraction and temperature on the frequency responses of the carbon nanotube reinforced composite conical shell panel are demonstrated through numerical illustrations. The results reveal that the frequency parameters of conical shell panel enhance with the volume fraction and the length-to-thickness ratio, whereas reduce with the temperature value.

Numerical analysis of acoustic radiation responses of shear deformable laminated composite shell panel in hygrothermal environment

In this article, the vibroacoustic responses of laminated composite curved panels subjected to harmonic point excitation in a combined temperature and moisture environment are investigated numerically using a novel higher-order finite-boundary element model. The hygrothermal dependent composite material properties are incorporated macroscopically in the formulation. The governing equations are derived using the higher-order shear deformation shell theory coupled with finite and boundary element approach. First, the Hamilton's principle is employed to obtain the stiffness, mass tensors and modal values of the vibrating structure subjected to hygrothermal stresses. The acoustic radiation responses are then computed by solving the Helmholtz wave equation discretized on the structure boundary using boundary elements coupled with the structural finite elements. Compared to those reported in open literature, the results for natural frequencies, critical buckling temperature, critical buckling moisture and sound power level values computed using the present scheme are found to be more accurate. The sound power values are also acquired via a simulation model implemented using commercial tools ANSYS and LMS. Virtual Lab and compared with present numerical results. The scheme is further extended to solve numerous numerical examples highlighting the influence of hygrothermal loads, geometry, curvature ratio, modular ratio, support conditions and lamination scheme on the hygro-thermo-acoustic responses of laminated composite shell panels.

Analysis of vibro-acoustic response of un-baffled laminated composite conical shell panel with varying thickness

This article presents the vibro-acoustic modeling and analysis of un-baffled laminated composite conical shell panels with varying thickness subjected to harmonic point load. The variation of thickness is considered to be unidirectional. A simulation model for the vibrating panel is developed using the commercial finite element package (ABAQUS). The natural frequencies are computed and compared with available published values for validation purpose. Then, the modal values are exported to LMS Virtual.Lab environment where an indirect boundary element approach has been adopted to extract the coupled vibro-acoustic responses. The sound power radiated by the vibrating structure computed using the present scheme is compared with the results available in the published literature. A comprehensive study has been performed to highlight the effect of thickness variation, excitation location, lamination scheme and support conditions on the acoustic radiation responses of the laminated conical shell panel. The variation of thickness is observed to greatly influence the mode shapes of the panel thereby influencing the sound radiation characteristics. The stiffness of the panels is affected by the lamination scheme, which in addition to stiffness variation due to varying thickness alters the radiation characteristics of the panels significantly.

Viscoelastic material damping characteristics of carbon nanotubes based functionally graded composite shell structures

This work deals with the study of viscoelastic modeling and vibration analysis of functionally graded nanocomposite shell panels where carbon nanotubes are reinforced in the polymer matrix based on the functionally graded distributions of carbon nanotubes. Five types of grading of carbon nanotubes (such as UD, FGX, FGV, FGO, and FGΛ) in the thickness directions have been considered in order to investigate the vibration damping performance of such composite shell panels. A detailed mathematical formulation for the determination viscoelastic properties is presented. The Mori–Tanaka micromechanics in conjunction with weak interface theory has been developed for the mathematical formulations of the viscoelastic modeling of carbon nanotubes based polymer matrix phase. An eight-noded shell element with five degrees-of-freedom per node has been formulated to study the vibration damping characteristics of various panels made by such functionally graded nanocomposite materials. The shell finite element formulation is based on the transverse shear effects as per the Mindlin’s hypothesis, and stress resultant-type Koiter’s shell theory. Impulse and frequency responses of such structures have been performed to study the effects of various important parameters (such as volume fraction of carbon nanotubes, interfacial condition, agglomeration, temperature, geometries of shell panel) on the dynamic responses. Obtained results demonstrate that quick vibration mitigation may be possible using such carbon nanotubes based proposed composite materials.

Acoustic radiation characteristics of un-baffled laminated composite conical shell panels

This article presents a study on the vibro-acoustic behavior of laminated composite conical shell panels subjected to harmonic point excitation. The shell panel model is developed in the framework of the first order shear deformation theory using commercial software package ABAQUS. Finite element method (FEM) is used to perform the free vibration analysis followed by the acoustic analysis performed using boundary element method (BEM) in LMS Virtual.Lab environment. The natural frequency and the sound power radiated by the panel are computed using the present scheme and validated with the results published in the available literature. The influence of the excitation location, lamination scheme and support conditions on the vibro-acoustic behavior of the laminated composite conical panels is investigated. The excitation location greatly influences the first, second resonant modes. The radiated sound power is found to be increasing with decreasing number of edge constraints.

Viscoelastic modelling and dynamic characteristics of CNTs-CFRP-2DWF composite shell structures

Abstract The carbon nanotubes (CNTs) are well known for its application in the areas of advanced composite materials for their improved elastic properties. The large specific interfacial surface area owing to tiny dimensions of CNTs may greatly escalation the interfacial sliding which may promote the dissipation of energy in a dynamic situation that makes them very ideal for damping applications in engineering structures/systems. The present article investigates the viscoelastic modelling and dynamic responses of the CNTs – based carbon fiber reinforced two dimensional woven fabrics (CNTs-CFRP-2DWF) composite spherical shell panels where CNTs are reinforced in the polymer matrix phase. The Mori – Tanaka (MT) micromechanics in conjunction with weak interface (WI) theory has been developed for the mathematical formulations of the viscoelastic modelling of CNTs-based polymer matrix phase. Further, strength of material (SOM) method has been employed to formulate viscoelastic material behavior of the yarn and finally the viscoelastic properties of the representative unit cell (RUC) is established based on the unit cell method (UCM). An eight-node shell element with five degree of freedom per node has been formulated to study the vibration damping characteristics of spherical shell structures made by CNTs-CFRP-2DWF composite materials. The shell finite element formulation is based on the transverse shear effect as per the Mindlin's hypothesis, and stress resultant-type Koiter's shell theory. Frequency and temperature dependent material properties of such CNTs-CFRP-2DWF composite materials have been obtained and analysed. Impulse and frequency responses of such structures have been performed to study the effects of various important parameters such as volume fraction of CNTs, interfacial condition, agglomeration, temperature, geometries of shell panel on the material properties and such dynamic responses. Obtained results demonstrate that quick vibration mitigation may be possible using such CNTs-CFRP-2DWF composite material which is desirable to overcome the drawbacks of conventional CFRP woven fabric composite materials.

Acoustic radiation and frequency response of higher-order shear deformable multilayered composite doubly curved shell panel – An experimental validation

In this article, the acoustic radiation responses of doubly curved laminated composite shell panels subjected to harmonic excitation are investigated numerically in the framework of the higher-order shear deformation theory. A general mathematical model for the vibrating curved panel has been developed and the cylindrical, spherical, elliptical and hyperboloid shell panel geometries resting on an infinite rigid baffle are considered for analysis. The desired response is computed using an in-house code developed in MATLAB. Firstly, the natural frequencies of the vibrating shell panel are obtained using the present model and validated with data available in the literature with experimental test results. A coupled finite element/boundary element formulation is then used to obtain the acoustic response of the structure. The mean square velocity, radiation efficiency and the sound power radiated are chosen as the acoustic response indicators. The effect of different support conditions, lamination schemes, aspect ratio and geometry of the vibrating doubly curved shell panel on the acoustic radiation behaviour is investigated and discussed in detail. It is observed that the support conditions and the lamination scheme greatly influence the acoustic radiation from the panels. On the other hand, the radiation pattern is quite similar for different geometries with a substantial distinction for flat plate.

Viscoelastic modeling and vibration damping characteristics of hybrid CNTs-CFRP composite shell structures

The present article deals with the viscoelastic modeling and dynamic responses of the carbon nanotubes (CNTs)-based carbon fiber-reinforced polymer (CNTs-CFRP) composite spherical shell panels where CNTs are reinforced in the polymer matrix phase. The Mori–Tanaka micromechanics in conjunction with weak interface theory has been developed for the mathematical formulations of the viscoelastic modeling of CNTs-based polymer matrix phase. Further, the strength of material method has been employed to formulate the viscoelastic material behavior of the homogenized hybrid CNTs-CFRP composite materials. An eight-noded shell element with five degrees of freedom per node has been formulated to study the vibration damping characteristics of spherical shell structures made by CNTs-CFRP composite materials. Frequency- and temperature-dependent material properties of such hybrid composite materials have been obtained and analyzed. Impulse and frequency responses of such structures have been performed to study the effects of various important parameters on the material properties and such dynamic responses. Obtained results demonstrate that quick vibration mitigation may be possible using such CNTs-based proposed composite materials.

Nonlinear bending and snap-through instability analyses of conical shell panels using element free Galerkin method

The nonlinear bending and snap-though instability phenomenon of isotropic and composite conical shell panels are investigated here using the element free Galerkin (EFG) method with moving kriging (MK) shape function. Sanders’ shell theory along with von Kármán strain-displacement assumptions are employed to derive the nonlinear equations of equilibrium, which are solved by modified Riks technique in conjunction with Newton-Raphson method. The convergence and accuracy of the EFG method are examined for the linear and nonlinear bending behavior of conical shell panels. Thereafter, the effect of geometrical parameters on the nonlinear stability characteristics of conical panels is investigated under different loading conditions. New results for linear as well as nonlinear bending behavior of isotropic and laminated conical shell panels, hitherto not found in the literature, are presented for future reference.