Curved Shell Panels Research Articles

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.

Thermoelastic flexural analysis of FG-CNT doubly curved shell panel

PurposeThe purpose of this paper is to develop a general mathematical model for the evaluation of the theoretical flexural responses of the functionally graded carbon nanotube-reinforced composite doubly curved shell panel using higher-order shear deformation theory with thermal load. It is well-known that functionally graded materials are a multidimensional problem, and the present numerical model is also capable of solving the flexural behaviour of different shell panel made up of carbon nanotube-reinforced composite with adequate accuracy in the absence of experimentation.Design/methodology/approachIn this current paper, the responses of the single-walled carbon nanotube-reinforced composite panel is computed numerically using the proposed generalised higher-order mathematical model through a homemade computer code developed in MATLAB. The desired flexural responses are computed numerically using the variational method.FindingsThe validity and the convergence behaviour of the present higher-order model indicate the necessity for the analysis of multidimensional structure under the combined loading condition. The effect of various design parameters on the flexural behaviour of functionally graded carbon nanotube doubly curved shell panel are examined to highlight the applicability of the presently proposed higher-order model under thermal environment.Originality/valueIn this paper, for the first time, the static behaviour of functionally graded carbon nanotube-reinforced composite doubly curved shell panel is analysed using higher-order shear deformation theory. The properties of carbon nanotube and the matrix material are considered to be temperature dependent. The present model is so general that it is capable of solving various geometries from single curve to doubly curved panel, including the flat panel.

A numerical study on the nonlinear behavior of corner supported flat and curved panels

The nonlinear behavior of corner supported plates and curved shell panels is investigated here using the first-order shear deformation theory based on Marguerre’s membrane strains for shallow shells and von Karman’s nonlinearity. The nonlinear differential equations are transformed into a set of nonlinear algebraic equations by using the element-free Galerkin method. The moving kriging shape function with two different types of correlation formulae (Gaussian and quartic spline) is employed here. After studying the effectiveness of the method, a detailed parametric study is conducted to examine the effect of support size on the displacements and bending moments of corner supported rectangular plates. Thereafter, the numerical study is extended to the nonlinear bending and stability behaviors of corner supported shallow cylindrical and spherical shell panels.

Analysis of Smart Composite Shell Structures Including Vibration and Control Systems

Analytical investigation is carried out to analysis the effect of smart material (Piezoelectric actuators) embedded through the shell structures. Experimentally, piezoelectric actuators and sensors are used to control the transverse displacements by suppression the excessive vibration on the output response. The smart materials are inserted into the composite layers and affected by electrical signals. Three cases are included in this research, the static analysis, natural vibration, and vibration control. Theory of doubly-curved is coupled with the magnetostricitive material (smart structure). Static equations are solved simultaneously to determine the Nondimensional center deflection versus radius-to-side ratio of doubly-curved shell panel under uniformly distributed load for many layers 120o/90o,0o/90o/0o,0o/90o/0o/90o,……..> . The natural vibration is also taken into account to obtain the Nondimensional fundamental frequencies versus radius-to-side length ratio of doubly curved shell panel. The embedded magnetostrictive layers are taken into account to detect the effect of smart material on vibration control. The eigen value problem are solved to get the real and imaginary parts of the damped motion. Different results are obtained in this work to describe the natural vibration versus time for various values of 12R/a> . Other results are dedicated to determine the effects of embedded smart material on the transverse displaced with respect to time for various layers.

VIBRATION ANALYSIS OF CROSS-PLY LAMINATED COMPOSITE DOUBLY CURVED SHALLOW SHELL PANELS WITH STIFFENERS

In this paper, the analytical solution for the cross-ply laminated composite double curved shell panels with stiffeners is presented. Based on the smeared stiffeners technique and the first shear deformation theory (FSDT), the motion equations are derived by applying the Hamilton’s principle. The Navier’s solution for the simply supported boundary condition for all edges is presented. The numerical results are verified with the known results in the literature. The effects of the number of stiffeners, dimensions of stiffeners, and lamination scheme of cross-ply laminated composite doubly curved shell panels on the natural fundamental frequencies are investigated.

Nonlinear thermoelastic frequency analysis of functionally graded CNT-reinforced single/doubly curved shallow shell panels by FEM

ABSTRACTIn this article, the nonlinear vibration frequencies of functionally graded carbon nanotube-reinforced composite doubly curved shell panels under elevated thermal environment are numerically investigated using finite element method. The doubly curved carbon nanotube-reinforced shell panel has been modeled mathematically using higher-order kinematics theory and Green–Lagrange geometrical nonlinear strains. The properties of the individual constituents of the graded composite are assumed to be temperature dependent. In addition, the properties of the media are obtained based on the modified rule of mixture. The carbon nanotubes are dispersed nonuniformly through the thickness direction. The large deformation kinematic effects on the structural responses are counted by including all the nonlinear higher-order terms in the formulation. The desired nonlinear responses are computed numerically using our in-house computer code in conjunction with the direct iterative scheme. The convergence and the accuracy of the present numerical model have been checked by solving various numerical examples. Nonlinear mechanical responses were affected by several other design parameters and explored numerically for the thickness ratios, volume fractions, temperature loading, type of geometries, and type of grading under the uniform thermal environment.

Static and vibration analysis of cross-ply laminated composite doubly curved shallow shell panels with stiffeners resting on Winkler\u2013Pasternak elastic foundations

In this paper, the analytical solution for static and vibration analysis the cross-ply laminated composite doubly curved shell panels with stiffeners resting on Winkler–Pasternak elastic foundation is presented. Based on the first-order shear deformation theory, using the smeared stiffeners technique, the motion equations are derived by applying the Hamilton’s principle. The Navier’s solution for shell panel with the simply supported boundary condition at all edges is presented. The accuracy of the present results is compared with those in the existing literature and shows good achievement. The effects of the number of stiffeners, stiffener’s height-to-width ratio, and number of layers of cross-ply laminated composite shell panels on the fundamental frequencies and deflections of stiffened shell with and without the elastic foundation are investigated.

Nonlinear Free Vibration Analysis of Laminated Carbon/Epoxy Curved Panels

Nonlinear frequency responses of the laminated carbon/epoxy composite curved shell panels have been investigated numerically and validated with in-house experimentation. The nonlinear responses have been computed numerically via customised computer code developed in MATLAB environment with the help of current mathematical model in conjunction with the direct iterative method. The mathematical model of the layered composite structure derived using various shear deformable kinematic models (two higher-order theories) in association with Green-Lagrange nonlinear strains. The current model includes all the nonlinear higher-order strain terms in the formulation to achieve generality. Further, the modal test has been conducted experimentally to evaluate the desired frequency values and are extracted via the transformed signals using fast Fourier transform technique. In addition, the results are computed using the simulation model developed in commercial finite element package (ANSYS) via batch input technique. Finally, numerical examples are solved for different geometrical configurations and discussed the effects of other design parameters (thickness ratio, curvature ratio and constraint condition) on the fundamental linear and nonlinear frequency responses in details.

Nonlinear Transient Finite-Element Analysis of Delaminated Composite Shallow Shell Panels

The nonlinear transient behavior of the delaminated composite curved shell panel under different kinds of mechanical loading is investigated in this analysis. The delaminated shell panel model is developed mathematically using two higher-order midplane theories in conjunction with the Green–Langrage type of geometrical nonlinear strains including all the nonlinear higher-order terms. Further, the desired nonlinear responses are computed numerically with the help of a unique computer code developed in the MATLAB® environment. The nonlinear numerical responses are computed using Newmark’s time integration scheme together with the direct iterative method in conjunction with finite-element steps. Further, the convergence behavior of the present numerical results is checked. In addition, the validity of the present numerical responses is shown by comparing the results with those of the available published literature. Finally, the role of the size, location, and position of delamination as well as the effects of different design parameters (curvature ratio, aspect ratio, modular ratio, shell configuration, and constraint condition) on the nonlinear transient responses are computed through a wide variety of numerical examples and discussed in detail.

Thermal free vibration behavior of FG‐CNT reinforced sandwich curved panel using finite element method

In this article, the vibration characteristics of carbon nanotube reinforced sandwich curved shell panel are investigated under the elevated thermal environment. The sandwich panel component (face and core layer) properties are assumed to be temperature‐dependent including various distribution of the carbon nanotube for the face sheets of the sandwich structure. The sandwich structural behavior has been modeled mathematically using the higher‐order shear deformation theory. The governing differential equation of motion of the free vibrated sandwich panel is obtained using the classical Hamilton's principle and transformed to the set of algebraic form with the help of suitable finite element steps. Further, fundamental frequencies of the curved sandwich shell panel are obtained numerically by means of a generalized computer code developed in MATLAB with the help of the present higher‐order mathematical model. The accuracy and the stability of the present numerical results have been checked through the proper convergence test. The model is again extended to work out the frequency responses for few more cases and compared with those available published results including the simulation responses (ANSYS). Finally, a wide variety of numerical examples have been solved for various design parameters (volume fraction of CNT, core to face thickness ratios, length to thickness ratios, aspect ratios, support conditions, curvature ratios, and types of grading) of CNT sandwich curved panel and underlined their effects in details under the uniform thermal load. POLYM. COMPOS., 39:2751–2764, 2018. © 2016 Society of Plastics Engineers

Thermal buckling behaviour of shear deformable functionally graded single/doubly curved shell panel with TD and TID properties

In this article, the buckling responses of functionally graded curved (spherical, cylindrical, hyperbolic and elliptical) shell panels under elevated temperature load are investigated numerically using finite element steps. The effective material properties of the functionally graded shell panel are evaluated using Voigt

Numerical investigation of nonlinear thermomechanical deflection of functionally graded CNT reinforced doubly curved composite shell panel under different mechanical loads

In this present study, the geometrical nonlinear static behaviour of the functionally graded carbon nanotube reinforced doubly curved shell panel is investigated under uniform thermal environment. The material properties of the carbon nanotube and matrix are assumed to be graded through the thickness of panel via four types of grading rule. The mathematical model of nanotube graded composite panel is derived using Green-Lagrange type geometrical nonlinearity in the framework of the higher-order kinematics. In addition, thermal environment dependent properties of the individual constituent (carbon nanotube and matrix material) are considered in the present investigation to achieve the generality. Further, the motion equation of equilibrium is obtained by minimizing the total energy functional and discretized with the help of suitable isoparametric finite element steps. The necessary large deflection values are worked out numerically through a generic MATLAB computer code in conjunction with developed nonlinear higher-order model and the direct iterative method. Lastly, the effects of different geometrical and material parameter (aspect ratios, support conditions, thickness ratios, volume fractions, temperature load and type of grading) on the linear and nonlinear deflection behaviour of functionally graded carbon nanotube reinforced composite doubly curved shell panel are examined and discussed in details.

Effect of different temperature load on thermal postbuckling behaviour of functionally graded shallow curved shell panels

This article investigated numerically the postbuckling load parameter of the functionally graded shell panels under uniform and non-uniform thermal environment using nonlinear finite element method. The shell structure is assumed to be under three different thermal fields (uniform, linear and nonlinear temperature) across the panel thickness including the temperature dependent properties of each constituent. The effective material properties of the graded structure are evaluated using micromechanical rule (Voigt type) in association with the power-law distribution of the material constituent. Further, the graded shell panel model is evaluated mathematically based on the higher-order mid-plane theory and Green-Lagrange nonlinear strain deformation relations. The excess thermal distortion of the panel has been included by taking all the nonlinear higher-order strains. The equation of graded structure under the in-plane thermal load is derived by minimizing the total potential energy expression. The desired postbuckling load parameters are computed numerically with the help of a suitable MATLAB code using the present nonlinear finite element model in conjunction with the direct iterative method. The accuracy of the proposed numerical solutions have been checked initially and extended to show the significance of the proposed complex mathematical by solving various numerical examples for different geometrical and material parameters.

Nonlinear Flexural Analysis of Laminated Composite Panel Under Hygro-Thermo-Mechanical Loading — A Micromechanical Approach

In this paper, the geometrically nonlinear transverse bending behavior of the shear deformable laminated composite spherical shell panel under hygro-thermo-mechanical loading is investigated. The laminated composite panel model has been developed mathematically based on the higher-order shear deformation theory and Green–Lagrange nonlinear strain kinematics. The material model is introduced through the micromechanical approach explicitly in terms of the matrix properties, the fiber properties, and the fiber volume fractions. Theoretical formulation is developed based on the hygrothermal dependent composite material properties to evaluate the corrugated behavior of the laminated structure. In addition to that, all the nonlinear higher-order terms arising in the strain displacement relation are included in the present formulation for accurate prediction of the flexural behavior. The desired nonlinear governing equations are obtained using the variational method and discretized with the help of suitable finite element steps. The desired responses are computed by solving the nonlinear equations numerically using the direct iterative method. The convergence behavior of the developed nonlinear numerical model has been checked and validated by comparing the responses with those available published literature. Finally, the effect of hygrothermal environment, geometrical and material parameters and the support conditions on the transverse bending behavior of the laminated composite curved shell panel have been highlighted by solving different numerical examples.

Frequency analysis of doubly curved functionally graded carbon nanotube-reinforced composite panels

Vibration characteristics of moderately thick doubly curved functionally graded composite panels reinforced by carbon nanotube are analyzed. Here, special cases of doubly curved shell panels such as spherical, cylindrical and hyperbolic paraboloid panels and five different distributions of carbon nanotubes through the thickness direction are considered. By utilizing the modified rule of mixture, mechanical properties are estimated. The equations of motion are derived via the first-order shear deformation theory, and non-dimensional frequencies are obtained by the use of Galerkin’s method. The suggested model is justified by a good agreement between the results given by present model and available data in the literature. The influences of volume fraction of carbon nanotubes, thickness ratio, aspect ratio, curvature ratio, and shallowness ratio on the frequencies of moderately thick doubly curved nanocomposite shell panels are also examined. Furthermore, the effect of various boundary conditions on the frequency analysis of doubly curved nanocomposite panels is studied, and the corresponding mode shapes are depicted.

Thermal buckling and vibration analysis of laminated composite curved shell panel

Purpose – The purpose of this paper is to develop a general mathematical model for laminated curved structure of different geometries using higher-order shear deformation theory to evaluate in-plane and out of plane shear stress and strains correctly. Subsequently, the model has to be validated by comparing the responses with developed simulation model (ANSYS) as well as available published literature. It is also proposed to analyse thermal buckling load parameter of laminated structures using Green–Lagrange type non-linear strains for excess thermal distortion under uniform temperature loading. Design/methodology/approach – Laminated structures known for their flexibility as compared to conventional material and the deformation behaviour are greatly affected due to combined thermal/aerodynamic environment. The vibration/buckling behaviour of shell structures are very different than that of the plate structures due to their curvature effect. To model the exact behaviour of laminated structures mathematica...

Geometrical nonlinear free vibration analysis of laminated composite doubly curved shell panels embedded with piezoelectric layers

The nonlinear free vibration behaviour of laminated composite single/doubly curved shell panel embedded with the piezoelectric layer is investigated numerically in this article. For the analysis purpose, a general nonlinear mathematical model has been developed using higher-order shear deformation theory and Green-Lagrange nonlinearity including the quadratic variation of the electric potential across the thickness due to the piezoelectric layer. In order to capture the exact flexure of the shear deformable panel, all the nonlinear higher order terms are included in the present model. The nonlinear governing equation of free vibrated shell panel is derived using Hamilton’s principle and discretised through suitable finite element steps. The desired nonlinear responses are computed numerically using the direct iterative method. The developed nonlinear numerical model has been validated by comparing the responses with that to available published literature. Finally, the efficacy and applicability of the present nonlinear model has been checked by solving few numerical examples for different geometrical parameters (stacking sequence, thickness ratio, aspect ratio, curvature ratio, different support constraints and amplitude ratio) and number of piezo layers and discussed in details.

Closed-form Solution for Freely Vibrating Functionally Graded Thick Doubly Curved Panel-A New Generic Approach

TODAY, DOUBLE CURVATURE SHELL PANELS ARE THE MAIN PARTS OF EACH DESIGN BECAUSE THEIR GEOMETRICAL CHARACTERISTICS PROVIDE HIGH STRENGTH TO WEIGHT RATIO, AERODYNAMIC FORM AND BEAUTY FOR THE STRUCTURES SUCH AS BOATS, SUBMARINES, AUTOMOBILES AND BUILDINGS. ALSO, FUNCTIONALLY GRADED MATERIALS WHICH PRESENT MULTIPLE PROPERTIES SUCH AS HIGH MECHANICAL AND HEAT RESISTANT, SIMULTANEOUSLY, HAVE ATTRACTED DESIGNERS. SO, AS THE FIRST STEP OF ANY DYNAMIC ANALYSIS, THIS PAPER CONCENTRATES ON PRESENTING A HIGH PRECISION AND RELIABLE METHOD FOR FREE VIBRATION ANALYSIS OF FUNCTIONALLY GRADED DOUBLY CURVED SHELL PANELS. TO THIS END, PANEL IS MODELED BASED ON THIRD ORDER SHEAR DEFORMATION THEORY AND BOTH OF THE DONNELL AND SANDERS STRAIN-DISPLACEMENT RELATIONS. A NEW SET OF POTENTIAL FUNCTIONS AND AUXILIARY VARIABLES ARE PROPOSED TO PRESENT AN EXACT LEVY-TYPE CLOSE-FORM SOLUTION FOR VIBRATING FG PANEL. THE VALIDITY AND ACCURACY OF PRESENT METHOD ARE CONFIRMED BY COMPARING RESULTS WITH LITERATURE AND FINITE ELEMENT METHOD. ALSO, EFFECT OF VARIOUS PARAMETERS ON NATURAL FREQUENCIES ARE STUDIED WHICH ARE HELPFUL FOR DESIGNERS.

Thermoelastic analysis of functionally graded doubly curved shell panels using nonlinear finite element method

In this article, large amplitude flexural behaviour of functionally graded doubly curved shell panel is investigated numerically under the thermomechanical load. The nonlinear mathematical model of doubly curved shell panel is developed first time based on higher-order shear deformation theory and Green–Lagrange geometrical nonlinearity. In order to achieve the exact flexure of the structure, all the nonlinear higher order terms are included in the mathematical model. The effective material properties of functionally graded material (metal/ceramic) have been obtained based on Voigt’s micromechanical model. The continuous gradation of metal and ceramic is achieved through the power-law distribution. The governing equation of the panel structure is obtained using the variational principle and a direct iterative method is employed to compute the desired responses numerically. The convergence behaviour of the proposed numerical analysis has been checked and validated through different comparisons to that available literature. Wide variety of examples is solved to reveal the effect of different geometrical parameters, material properties, constraint conditions and thermal and/or mechanical loads on the linear and nonlinear flexural behaviour of functionally graded curved panels.

Nonlinear free vibration analysis of laminated composite doubly curved shell panel in hygrothermal environment

In this article, the geometrical nonlinear free vibration behaviour of shear deformable laminated composite single/doubly curved shell panel in hygrothermal environment is investigated. A general nonlinear mathematical model of laminated composite doubly curved shallow shell panel has been developed based on the higher order shear deformation theory and Green-Lagrange geometric nonlinear kinematics. All the nonlinear higher order terms have been included in the present mathematical model to achieve a realistic case. In addition to that, the composite material properties are considered as temperature and moisture dependent through hygro-thermo-elastic constitutive relations. The governing equation of laminated composite curved panel is obtained using Hamilton’s principle and discretised using nonlinear finite element steps. The desired responses are computed numerically using a direct iterative method. The convergence behaviour of present numerical model has been checked and validated by comparing the responses with those available published results. The effect of different geometrical and/or material parameters on nonlinear vibration behaviour of laminated composite doubly curved shell panel under hygrothermal environment is computed and discussed in detail.