Higher Order Shear Deformation Shell Research Articles

Free-damped vibration analysis of viscoelastic foam-filled FGM anisogrid lattice cylindrical shells

Our aim with this paper is to model and investigate the vibration and damping of a new hybrid composite shell. The considered composite cylindrical shell includes an FGM anisogrid lattice shell perfectly filled with viscoelastic foams. The modeling of the lattice part composed of spiral and hoop ribs is accomplished according to a global continuous standard based on orthotropic deep shells. The distribution pattern of the metal and ceramic constituents along the lattice ribs is specified by a power law. The homogenizations between ceramic and metal phases within the ribs, as well as between the FGM lattice structure and foam, are governed by the rule of mixtures. Based on the transferred Kelvin–Voigt viscoelastic scheme, the dynamic moduli of the foam portion are acquired. Because viscoelastic foam is a soft material, the higher-order shear deformation shell theory is used to estimate the system's displacement components. After emanating the dynamic equations by Hamilton's principle, the Chebyshev collocation-based semi-numerical method is implemented to detect the system's frequencies and loss factors. The comprehensive results show the role of each composite characteristic in the vibration and damping behavior of the defined structure.

Nonlinear continuum thermo-mechanics of the composite thick panel used in concrete ceilings via general expression of the polynomial series theory

Proper concrete vibration is vital to the final quality and durability of concrete structures. There is a lack of objective methods to assess conformance to the requirements of vibration behavior of concrete systems used in various engineering structures. So, in the current work for the first time, nonlinear vibrations of a composite thick panel made of concrete materials are presented. In the current work, the GPLs are used to reinforce the thick concrete panel in the length direction. In the current work, according to the higher-order shear deformation shell theory the effects of the von Kármán strain-displacement kinematic nonlinearity are presented in the constitutive laws of the shell. The nonlinear governing equations for various nonlinear boundary edges are solved via discretization of equations on the space domain, derivation of Duffing-type equations, and Hadamard and Kronecker Products. The results are validated by comparing the current results with deep neural networks (DNN) and open-source results in the literature. For DNN, it is introduced a supervised neural network based on physical information to predict the vibrational behavior of the current system. In this context, data-driven solutions and data-driven discovery are presented to solve the problem of determining nonlinear frequency. Consequently, new results are investigated to show the effects of the Pasternak modulus, Winkler modulus, and the GPLs’ weight fraction on the nonlinear vibrations of concrete panels.

Magneto-electric analysis of higher-order deformable sandwich cylindrical shell

This work presents an analytical framework for magnetoelectroelastic analysis of a higher-order shear deformable sandwich cylindrical shell through a thickness-stretched model and piezomagnetoelasticity relations. The sandwich cylindrical shell is subjected to a combination multifield loadings. Based on the thickness-stretched model, the transverse deflection is decomposed into bending, shear, and stretching parts where the third term is responsible for strain along the thickness direction. The sandwich cylindrical shell is fabricated from an elastic core sandwiched by two piezoelectric/piezomagnetic face-sheets subjected to an electromagnetic environment. The multifield equations are derived using the principle of virtual work. After performing a verification study, the comprehensive numerical results are presented in terms of multifield loading. The results indicate that the radial displacement is significantly improved using the thickness-stretched model.

Nonlinear Resonance of Functionally Graded Porous Circular Cylindrical Shells Reinforced by Graphene Platelet with Initial Imperfections Using Higher-Order Shear Deformation Theory

This paper uses the higher-order shear deformation theory (HOSDT) to analyze the nonlinear resonance of functionally graded graphene platelet-reinforced porous (FG-GPL-RP) circular cylindrical shell with geometrical imperfections subjected to the harmonic transverse loading. The shell considered is surrounded by the elastic Winkler–Pasternak foundation. Based on Hamilton’s principle, the nonlinear governing equations of motion of the imperfect system considered are established using the first-order and various higher-order shear deformation shell theories that contain a unified higher-order displacement field. Four types of porosity and graphene nanoplatelet distribution patterns are considered. The modified Halpin-Tsai scheme and rule of mixture are utilized to calculate the effective properties of FG-GPL-RP materials. Explicit expressions of the nonlinear primary resonance of imperfect FG-GPL-RP cylindrical shells for simply-supported boundary conditions are achieved by the Galerkin technique and method of multiple scales. After verifying the accuracy of the model used and the results obtained, the influences of the geometric parameters, material properties and distribution and imperfection value on the nonlinear primary resonant response of the imperfect FG-GPL-RP circular cylindrical shells are examined in detail.

A couple-stress-based moving Kriging meshfree shell model for axial postbuckling analysis of random checkerboard composite cylindrical microshells

The current investigation intends to devise a couple stress continuum-based moving Kriging meshfree shell model for axial nonlinear buckling and postbuckling responses of random checkerboard composite cylindrical microshells. Accordingly, the graphene nanoplatelet reinforcements are supposed to be randomly dispersed based upon a checkerboard scheme within the resin matrix, the effective material properties of which are estimated based upon a probabilistic method. The modified couple stress continuum elasticity is implemented into the higher-order shear deformation shell theory incorporating geometrical nonlinearity. The established microstructural-dependent shell model is then numerically analyzed via the moving Kriging meshfree technique with the ability to take the essential boundary conditions into account accurately by employing proper moving Kriging shape function. By tracing the postbuckling paths, the snap-through phenomenon is observed. It is found that for a higher graphene nanoplatelet volume fraction, the significance of the stiffening character associated with the rotation gradient tensor increases. Furthermore, for a specific value of graphene nanoplatelet volume fraction, by reducing the length to width aspect ratio of graphene nanoplatelet reinforcements, the role of couple stress size dependency in the critical buckling load and critical shortening of an axially compressed cylindrical microshell becomes more important.

Nonlinear forced vibration of sandwich cylindrical panel with negative Poisson’s ratio auxetic honeycombs core and CNTRC face sheets

Recently, auxetic cellular solids in the forms of honeycombs and carbon nanotube reinforced composite (CNTRC) have great potential in a diverse range of applications. This paper studies the nonlinear free and forced vibration of sandwich cylindrical panel on visco-Pasternak foundations in thermal environment subjected to blast load The sandwich cylindrical panel consists of auxetic honeycombs core layer and two CNTRC face sheets. The Poisson’ ratio of the auxetic core is negative and the material properties of CNTRC face sheets are assumed to continuously vary in the thickness direction according to four different types of linear functions. The blast load is determined from the distance of the center of blast to center of the structure and the mass of explosive materials. The fundamental equations are established based on Reddy’s higher order shear deformation shell theory taking into account the effect of initial imperfection and visco-Pasternak foundations. The Galerkin and Runge–Kutta methods are used to obtain the nonlinear dynamic response and the natural frequency of the sandwich cylindrical panel. The numerical results show the effect of geometrical parameters, visco foundations, initial imperfection, temperature increment, nanotube volume fraction and blast load on the nonlinear vibration characteristics of the sandwich cylindrical panel. The accuracy of present approach and theoretical results is verified by some comparisons with the known data in the literature.

A new shear deformation shell theory for free vibration analysis of FG sandwich shells

In recent years, many researches have been published dealing with the mechanical responses of shells with variable cross-sectional mechanical properties such as sandwich, functionally graded and laminated composites shells. In the present paper, a simple and efficient shear deformation theory is formulated for the free vibration response of functionally graded sandwich shells. The main advantage of this theory is its reduced number of unknowns and their related governing equations and theses tend to be highly compared to others shear deformation shell theories. Two kinds of FG sandwich shells are studied with respect to their geometrical configuration and material properties. The first kind is composed of FG facesheet and homogeneous core and the other is formed by homogeneous facesheet and FG core. The governing equations of motion for the free vibration analysis are obtained using Hamilton's principle. The closed form solutions are sought by using the Navier's method for eigenvalue problems. The accuracy and efficiency of the present theory are established and proved by comparing obtained numerical results with those predicted by other higher order shear deformation shell theories. The influences of various parameters such as material distribution, thickness of the core and the facesheet of sandwich shell and curvature ratios are studied, discussed and reported as significant rate sensitivity to predict the fundamental frequencies of FG sandwich shells.

Nonlinear vibration and dynamic instability analyses of laminated doubly curved panels in thermal environments

Nonlinear dynamic analysis for a shear deformable anisotropic laminated doubly curved panel of rectangular planform resting on elastic foundations is presented. A new panel model of arbitrary curvature and arbitrary fiber stacking sequences but constant thickness is developed and established. The governing equations are based on an extended higher order shear deformation shell theory with von Kármán-type of kinematic nonlinearity and including the anisotropic couplings. The nonlinear deformations and initial deflections of the panel are both taken into account. A two-step perturbation technique combining with the Galerkin method is employed to determine the linear and nonlinear vibration frequencies and forced responses. Nonlinear forced harmonic vibration in a Duffing oscillator for anisotropic laminated doubly curved panel is also investigated and discussed together with the effects of damping and excitation by using multiscale and Melnikov methods. The numerical results are validated for various lamination schemes through a comparison with solutions for free vibration frequencies of saddle (hyperbolic), flat plate, cylindrical and spherical shells available in the literature or obtained by the commercial finite element software. The numerical illustrations concern nonlinear vibration and dynamic response of moderately thick, anisotropic laminated doubly curved panels under different values of panel geometric parameters and mechanical excitation.

Isogeometric analysis for postbuckling of sandwich cylindrical shell panels with graphene platelet reinforced functionally graded porous core

The proposed work investigates for the first time the postbuckling behavior of sandwich cylindrical shell panels with two metallic face layers and a graphene platelet (GPL) reinforced functionally graded porous (FGP) core subjected to central point loads, uniform and non-uniform pressure loadings. Based on a general higher-order shear deformation shell theory and the von Kármán large deflection assumption, the discrete equilibrium equations of the sandwich cylindrical panels are established by the principle of virtual work. The NURBS (non-uniform rational B-spline) based isogeometric analysis (IGA) in conjunction with the modified arc-length method of Crisfield are utilized synthetically to acquire nonlinear load–deflection responses for the panels numerically and both snap-through and snap-back types of instability are captured. Several benchmarks are carried out to verify accuracy and reliability of IGA and arc-length method in present formulation. Parametric studies are performed to demonstrate the influences of weight fraction of the graphene platelet, porosity distribution, porosity coefficient and thickness of the sandwich core on the nonlinear load–deflection responses of the sandwich cylindrical panels. Some complex load–deflection curves of the FGP-GPL cylindrical panels may be useful for future references.

Large-amplitude oscillations of composite conical nanoshells with in-plane heterogeneity including surface stress effect

In the current investigation, a new formulation for nonlinear vibration behaviors of functionally graded (FG) composite conical nanoshells are constructed using Gurtin-Murdoch elasticity theory based on higher-order shear deformation shell theory (HSDFST) framework. Both Voigt and Reuss homogenization procedures are considered for the estimation of the mechanical characteristics of FG materials. Using generalized differential quadrature method (GDQM) together with Galerkin technique, the surface elastic-based nonlinear frequency-responses of FG composite conical nanoshell are obtained. It has been illustrated that the decrease of material property gradient index or transformation of boundary condition from full simply supported to full clamped, surface stress effect on the nonlinear frequency of a FG composite conical nanoshell reduces. Also, decreasing semi-vertex angle increases the frequency ratio of ωNL/ωL which reveals higher geometrical nonlinearity. However, it is seen that surface elasticity effect on the nonlinear vibration behavior of FG composite conical nanoshells is not significant.

Effect of external pressure on the vibration analysis of higher order shear deformable FG-CNTRC spherical panels

The numerical investigation is performed on the vibration of the higher order shear deformable carbon nanotube reinforced composite (CNTRC) spherical panels subjected to the initial external pressure. The functionally graded nanocomposite is reinforced with the non-uniform distribution of CNTs. The problem is formulated following the higher order shear deformation shell theory (HSDT) within the variational differential quadrature numerical approach. For this purpose, the direct discretization of Hamilton’s principle is carried out with the aid of differential quadrature operators. Derivation of the variational formulation of nanocomposite spherical panels based on the HSDT and studying the effects of external pressure on the vibration behavior are the main novel aspects of this research. Several numerical examples are provided to survey the impacts of geometrical and material factors on the vibration of pressurized functionally graded CNTRC spherical panels. It is shown that the internal pressure has the most influence on the vibrational behavior of the thicker panel.

Nonlinear oscillations of composite conical microshells with in-plane heterogeneity based upon a couple stress-based shell model

Abstract The current investigation deals with the nonlinear oscillation response of conical microshells made of a composite material with functional graded (FG) in-plane heterogeneity is studied in the presence of the size dependency. To accomplish this purpose, various types of homogenization schemes including Voigt model, Reuss model, Mori-Tanaka model, and Hashin-Shtrikman bounds model are employed. The size-dependent characteristics are taken into consideration on the basis of the modified couple stress theory of elasticity within the framework of the higher-order shear deformation shell theory. The couple stress-based differential equations of motion are constructed via the Hamilton's principle. An efficient numerical solution methodology adopting generalized differential quadrature (GDQ) method together with the pseudo-arc technique is put to use to obtain the modified couple stress-based nonlinear frequency of homogenized FG composite conical microshells. It is demonstrated that by increasing the value of the maximum shell deflection, the couple stress type of size effect plays more important role in the nonlinear vibration response of FG composite conical microshells. Additionally, it is indicated by changing the boundary conditions from simply supported one to clamped one, the influence of couple stress size dependency decreases.

Couple stress-based nonlinear buckling analysis of hydrostatic pressurized functionally graded composite conical microshells

The present study deals with the size-dependent nonlinear buckling characteristics of conical microshells made of functionally graded (FG) composite materials under uniform hydrostatic pressure based upon the modified couple stress theory of elasticity. Accordingly, a modified couple stress-based shell model within the framework of the higher-order shear deformation shell theory and von Karman geometrical nonlinearity is constructed. Using the virtual work's principle in conjunction with the adjacent equilibrium criterion, the non-classical governing differential equations are established. The material properties of FG composite conical microshells are estimated on the basis of different homogenization schemes. To solve the size-dependent nonlinear problem, the generalized differential quadrature discretization pattern together with the Galerkin technique is employed. It is seen that among various types of homogenization scheme, the Voigt and Reuss models represent, respectively, the overestimated and underestimated critical buckling pressures. Also, it is found that for a FG composite conical microshell with higher semi-vertex angle, the influence of the material property gradient index on the nonlinear critical buckling pressure diminishes. In addition, it is observed that the couple stress size dependency plays more important role in the nonlinear buckling behavior of FG composite conical microshells with lower ratio of R1/h. These patterns are the same for all types of boundary conditions.

Static bending and free vibration analysis of multilayered composite cylindrical and spherical panels reinforced with graphene platelets by using isogeometric analysis method

This study makes an attempt at analyzing numerically the bending and free vibration behavior of multilayered composite cylindrical and spherical panels reinforced with graphene platelets (GPLs). A numerical model for the static and dynamic analyses of the GPL reinforced composite curved panels based on isogeometric analysis (IGA) combined with higher-order shear deformation shell theory is developed for the first time. NURBS (non-uniform rational B-spline) based IGA considered in the present investigation is capable of constructing exactly the complex geometries of the shell-type structures. The cylindrical and spherical panels are fabricated by stacking several layers in which the GPL concentration alters in a layerwise manner to form functionally graded (FG) structure. Uniform, FG-O, FG-X and FG-A types of GPL dispersions are taken into account. The Halpin-Tsai model is adopted to determine the effective modulus of elasticity, whilst the modified rule of mixture is utilized to estimate Poisson’s ratio and the mass density of the nanocompoiste curved panels. The motion equations for the static and dynamic problems are derived from the higher-order shear deformation shell theory established based on the Reddy’s shell theory, and NURBS based isogeometric formulation is made to obtain the central deflections and natural frequencies of the multilayered FG GPL strengthened composite curved panels. The validity of the present IGA method is first evidenced, followed by the illustrative parametric studies to further scrutinize the static and dynamic responses of the nanocomposite cylindrical and spherical panels with the various reinforcement schemes.

Novel study on functionally graded anisotropic doubly curved nanoshells

This work aims at investigating the dispersion of elastic eaves in doubly curved nanoshells. The nonlocal strain gradient theory is adopted in conjunction with a higher-order shear deformation shell theory, to include the size-dependent effects. The nanoshells are made of functionally graded anisotropic materials, whose properties are changed exponentially through the thickness direction. Hamilton’s principle is employed to obtain the governing equations of wave motion which are solved analytically to compute the wave frequencies as well as phase velocities as a function of the wave number. The sensitivity of the wave response is analyzed for the exponential factor, small-scale parameters, geometrical conditions as well as wave number. In addition, the accuracy of modeling the nanoshells with less elastic coefficients compared to the anisotropic model is studied to disregard any kind of complex equations.

On pre-stressed functionally graded anisotropic nanoshell in magnetic field

Elastic bulk wave characteristics of doubly curved nanoshell made of functionally graded (FG) anisotropic material are studied. The effective properties of FG anisotropic material vary along the thickness direction. A higher-order shear deformation shell theory and the Bi-Helmholtz nonlocal strain gradient theory are, respectively, utilized to model the nanoshell as a continuum model and predicting the size-dependent behavior. The Hamiltonian principle is adopted to obtain the governing equations of wave motion. These equations are solved analytically to evaluate the wave characteristics of the nanoshell. Emphasizing the effect of parametric excitation, the influences of small-scale parameters, exponential factor, magnetic field intensity, initial stress, elastic foundation parameters, and wave number are assessed on the wave dispersion response of FG anisotropic nanoshell.

Transient dynamic analysis of laminated shallow spherical shell under low-velocity impact

The impact of transient response laminated shallow shells due to transverse foreign object was investigated analytically and experimentally. The analytical analysis is presented by using the new higher order shear deformation shell theory. The contact force ishassumedhtohbe a known inputhtohthehanalysis. Contact force and transverse deflection of laminated shell have been measured with a piezoelectric force transducer (load cell) and a piezoelectric bending transducer respectively. Laminates made from E-glass polyester and E-glass/carbon/polyester having different thickness and stacking sequences have been used. The analysis can be used to calculate the difference between the transient stresses, displacements, velocities, accelerations and energy observation at the center of laminated shell are plotted as function of time during impact between E-glass/polyester and E-glass/carbon/polyester by MATLAB code at different impact heights to determine whether they have a good resistant ability to impact. Finally, it was compared with the results of an experimental test to verify the accuracy and reliability of the theoretical analysis.

Analyses of nonlinear dynamics of imperfect nanocomposite circular cylindrical shells with swirling annular and internal fluid flow using higher order shear deformation shell theory

The paper focuses on nonlinear dynamical responses of circular cylindrical shell made of carbon nanotubes reinforced polymer conveying to internal and external fluid flow. The fluid flows are assumed incompressible. The governing equations are derived from the Third order shear deformation theory (TSDT), the fluid velocity potential, then using the Galerkin′s technique and the fourth-order Runge-Kutta method to give the characteristics of nonlinear dynamics of fluid-structures interaction. The product of the velocity U.V of the two liquid streams (swirling flow and straight flow) is considered to investigate the stable domain of the structure under the effect of two velocity factors. In addition, the dynamical behaviors as time histories and bifurcation diagram as well as the effects of materials, geometries and the critical velocities of losing stability caused by internal and external flow fluid are scrutinized in the present. The obtained results are also compared and validated with those of other studies and can be used as benchmark solutions for an analytical approach serving in further research.

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.

Nonlinear thermal vibration of carbon nanotube polymer composite elliptical cylindrical shells

This paper investigated the nonlinear vibration and dynamic response of the carbon nanotube polymer composite elliptical cylindrical shells on elastic foundations in thermal environment. The material properties of the nanocomposite elliptical cylindrical shells are assumed to depend on temperature and graded in the thickness direction according to various linear functions. The shell is subjected to the combination of the uniformly distributed transverse load in harmonic form and the uniform temperature rise. The motion and geometrical compatibility equations are derived based on the Reddy’s higher order shear deformation shell theory. The natural frequencies and the deflection amplitude–time curves of the shell are determined by using the Galerkin method and fourth-order Runge–Kutta method. The numerical results show not only the positive influences of carbon nanotube volume fraction and elastic foundations but also the negative influences of initial imperfection and temperature increment on the nonlinear vibration and dynamic response of the carbon nanotube polymer composite elliptical cylindrical shells. The reliability of the present results is verified by comparing with other publications.