Shells In Thermal Environments Research Articles

An analytical method for free vibration analysis of multi‐directional functionally graded porous doubly‐curved shells in thermal environment with various boundary conditions

This paper uses the analytical method with arbitrary boundary conditions to model and analyze the free vibrations of multi‐directionally functionally graded porous (MFGP) doubly‐curved shallow shells resting on the Pasternak foundation in a temperature environment. It is anticipated that all mechanical parameters, except Poisson's ratio, will change in the direction of length, width, and thickness. To comprehensively describe the shell's displacement, strain, and stress fields, a modified first‐order shear deformation theory (FSDT) with an assumption of cosine distribution shear stresses has been developed. The fact that the enhanced FSDT theory does not require the use of shear correction and that the shear stress at the two free faces of the shells is zero are two of the theory's most significant advantages. Using Hamilton's principle and improved FSDT, one may get the governing equation for free vibration analysis of MFGP doubly‐curved shallow shells. The Galerkin approach is proposed to solve the governing equation of MFGP doubly‐curved shallow shells with various boundary conditions. The trustworthiness of the article is evaluated via its publication in the article model's several special cases. From this point on, a collection of findings about the natural frequency of MFGP doubly‐curved shallow shells is identified and shown in the form of tables and graphs. The results provided in this manuscript can be used as a benchmark solution for further studies as far as the vibration behavior of the MFGP doubly‐curved shallow shells is concerned.

Linear finite element formulation for free vibration and buckling analyses of multi-directional FGP doubly curved shallow shells in thermal environment

ABSTRACT This paper presents the free vibration and buckling analyses of multi-directional functionally graded porous doubly curved shallow shells resting on Pasternak elastic foundations in a thermal environment. For the first time, a linear finite element formulation using the refined high-order shear deformation theory, combined with the Hermitian function, is developed to compute the vibration and buckling behaviour of doubly curved shallow shells. Mechanical properties of MFGP material change according to the length, width and thickness directions and the porosity distribution including even and uneven. The doubly curved shallow shell is operated in uniform, linear and non-linear temperature environments. The convergence and accuracy of the proposed method are verified by comparing numerical results with published works. In addition, a comprehensive numerical investigation was carried out to evaluate the influence of parameters on the natural frequency and critical buckling behaviour of MFGP doubly curved shallow shells.

Analyzing the nonlinear torsional buckling and post-buckling of ES-FG porous cylindrical shells in thermal environment using FSDT in terms of the displacement components

The main aim of this paper is to investigate the nonlinear buckling and post-buckling of eccentrically stiffened sandwich functionally graded porous (FGP) cylindrical shells surrounded by elastic foundations in thermal environments and under torsional load by analytical approach in terms of the displacement components. The shells are reinforced by eccentric rings and stringers attached to the inside and material properties of face sheets and stiffeners are assumed to be continuously graded in the thickness direction. The sandwich cylindrical shell is composed of FG porous core and two FG layer coating. Based on the first order shear deformation theory (FSDT) with von Kármán geometrical nonlinearity and smeared stiffeners technique, the governing equations are derived. Using Galerkin method, the closed form to find critical torsional load and post-buckling load-deflection curves are obtained. The effects of porosity parameters, the thickness of the porous core, temperature, stiffener, foundation, material and dimensional parameters are analyzed.

Nonlinear free vibrational behavior of temperature-dependent two-directional functionally graded truncated cone-like shells in thermal environment

This article investigates nonlinear free vibrations of temperature-dependent two-directional functionally graded (TDTDFG) cone-like shells in thermal environment. The structure material is a combination of ceramic and metal with temperature-dependent mechanical characteristics varying continuously in the thickness and longitudinal directions. Initially, the thermomechanical dynamic equations of the system are modeled based on the first-order shear deformation theory (FSDT) and the strain-displacement relations of von Kármán. Afterward, the final governing equation for the structure’s transverse motion is obtained using the Galerkin discretization method. Finally, the governing equation is solved using improved Lindstedt-Poincaré method as an analytical technique, resulting in an equation for calculating the nonlinear frequencies of the shell. To validate the research’s results, the system frequencies are calculated under different conditions and compared with the results of previous studies. After ensuring the accuracy of the results, a parametric study is performed to evaluate the effects of various parameters on the linear and nonlinear frequencies of the TDTDFG cone-like shell in thermal environment. The results of this study have demonstrated that gradient indices, geometric ratios, and thermal environment have a significant influence on the nonlinear vibration behavior of structures.

An Investigation of Free Vibration Characteristics of a DFG-CNTRC Thin Laminated Shell in Thermal Environment

A dynamic model of dual-functional gradient carbon nanotube-reinforced composite (DFG-CNTRC) laminated shell in a thermal gradient environment is established. The carbon nanotubes (CNTs) are supposed to be FG distribution in the functionally graded material (FGM) consisting of metal and ceramic components, and its traveling wave vibration in thermal gradient environment environments is studied. The temperature between the internal and external sides of laminated shell varies linearly. Considering the impact of the thermal environment on material properties, the orthogonal polynomials are used as admissible function, and the vibration differential equation of the DFG-CNTRC laminated shell is obtained by using the Rayleigh–Ritz method. First-order shear deformation theory (FSDT) and artificial spring technique are applied to establish a general model of free vibration of rotating DFG-CNTRC laminated shells under arbitrary boundary in the thermal gradient environment. The effects of rotational speed, the environmental temperature, the thickness of the middle layer, and volume fraction of CNTs on the traveling waves are discussed.

Free vibration response of rotating pretwisted porous exponential and sigmoid functionally graded conical shells in thermal environment

A finite element method is used to analyze the free vibration of rotating functionally graded (FG) porous conical shell in thermal environment. Exponential and sigmoid laws are used for grading the FG conical shell in the presence of even and uneven porosity distributions. The one-dimensional Fourier heat conduction equation is used to calculate the nonlinear temperature distribution across the thickness of the shell. The parametric studies reveal that the porosity volume fraction has a significant impact on natural frequency. Centrifugal stiffening, which manifests as a geometrical stiffness matrix, causes rotational speed to enhance the natural frequency of the FG shell.

Vibration of hybrid eccentrically stiffened sandwich auxetic double curved shallow shells in thermal environment

Adding stiffeners or forming a sandwich structure are two ways to reduce unnecessary risks or costs for structures made of advanced materials. Through the proposal of a hybrid sandwich shell model consisting of three layers: Functionally graded graphene platelets reinforced composite layer (FG-GPL), Auxetic core layer, and Functionally graded material layer (FGM) with reinforcement stiffeners, this study presents an analytical solution to illustrate the significant effects of geometrical and material parameters as well as stiffeners on the vibration of sandwich double-curved shallow shells (SDCS shells) subjected to blast loading in a temperature environment and visco-Pasternak medium. The results demonstrate that the shell with stiffener has a higher load-carrying capacity compared to a non-stiffener case and the combination of material layers in a hybrid shell has significant advantages over a homogeneous shell, even under blast load. These findings have practical implications for expanding the application fields of sandwich structures by synthesizing the benefits of each material layer.

Nonlinear primary resonance of axially moving functionally graded cylindrical shells in thermal environment

Based on Love’s thin shell theory, an effort is made to investigate the nonlinear primary resonance response of axially moving functionally graded materials (FGM) cylindrical shells subjected to external excitations in thermal environment. Two kinds of temperature fields, namely, uniform temperature rise and heat conduction, are considered. The effective material properties of the FGM cylindrical shells are temperature-dependent. The equations of motion are derived using Euler-Lagrange principle and solved by multiple scale method, in which the cylindrical shell with four clamped edges is considered. Finally, the effects of different influencing factors on the nonlinear resonance response are discussed.

Free and forced vibration analysis of thin-walled cylindrical shells with arbitrary boundaries in steady thermal environment

This paper presents a method for predicting the free and forced vibration behavior of open and closed cylindrical shells in the steady-state thermal environment. The vibration characteristics of cylindrical shells in thermal environment are studied by considering the changes of the thermal strain in the cylindrical shell and the material properties caused by temperature rise. Based on Spectral-Geometry Method (SGM), the displacement functions of cylindrical shell are expressed as the improved Fourier series. The potential energy and kinetic energy of the cylindrical shell are obtained based on the first-order shear deformation theory (FSDT). Three sets of linear springs and one set of rotating springs are used to simulate arbitrary boundaries of the cylindrical shell, and the circumferential coupling springs are used to ensure the continuity of circumferential boundaries of the shell. The accuracy of the present method is verified by comparing with results derived by the finite element method (FEM), and a comprehensive parametric analysis was performed.

Meshless Chebyshev RPIM Solution for Free Vibration of Rotating Cross-Ply Laminated Combined Cylindrical-Conical Shells in Thermal Environment.

This paper provides a numerical solution to the vibration of a rotating cross-ply laminated combined conical-cylindrical shell in the thermal environment. Its numerical discrete solution method uses the meshless method. The combined shell assumed the temperature independence of material property is divided to the fundamental conical and cylindrical shell substructures, and the theoretical formulation for each substructure is derived based on the first order shear deformation theory (FSDT) and Hamilton’s principle. The effects of the initial hoop tension and temperature change are considered through the kinetic energy reflecting the effects of centrifugal and Coriolis forces and additional strain energy by the nonlinear part of the Green–Lagrange strains. The substructures are then assembled according to the continuity conditions. The boundary and continuity conditions are simulated by introducing artificial virtual spring technology. The displacement component in the theoretical formulation is approximated using a meshless Chebyshev-RPIM shape function. The reliability of the method is verified by comparing with mature and reliable results. The free vibration characteristics of the rotating combined conical-cylindrical shell structure under various sizes, speeds and temperatures are given by numerical examples.

Nonlinear dynamic analysis of porous eccentrically stiffened double curved shallow auxetic shells in thermal environments

In this paper, an analytical approach is proposed to investigate the nonlinear dynamic analysis of porous eccentrically stiffened (PES) double curved shallow auxetic shells with negative Poisson’s ratio (NPR) subjected to blast, mechanical and thermal loads resting on Visco-Pasternak foundation model. The three-layer double curved shallow shell consists of auxetic honeycombs core layer with NPR integrated, isotropic homogeneous materials at the top and bottom of surfaces. Besides, the outer surfaces of the system reinforced by PES are made of functionally graded materials (FGM) and auxetic shells are placed in thermal environments. Combining with the first-order shear deformation theory and Von-Karman strains, governing equations for nonlinear dynamic response of PES double curved shallow auxetic shells in thermal environments are derived. Then, the stress function and Galerkin methods are proposed to obtain the result equations: fundamental frequency, dynamic response, and frequency–amplitude relation. Compared with the published literature, the feasibility and accuracy of the proposed analysis approach are validated. Finally, the effects of stiffeners, Poisson’s ratio, cell inclined angle, mechanical, thermal and blast loads, elastic foundations, boundary conditions, geometrical parameters of auxetic honeycombs core and shell on the nonlinear dynamic response of PES double curved shallow auxetic shells in thermal environments are also carried out in the paper.

Nonlinear parametric vibration of imperfect SSMFG cylindrical shells in thermal environment including internal and subharmonic resonances

The nonlinear vibration behavior of the spiral stiffened multilayer functionally graded (SSMFG) cylindrical shells with initial imperfection exposed to axial parametric and external excitation in the thermal environment is presented in this paper using a semi-analytical method. The distribution of temperature and material constitutive of the stiffeners along the direction of thickness is assumed. The cylindrical shell consists of three layers, the interior and exterior layer is respectively rich metal and ceramic, and the middle layer is functionally graded material (FGM). Using the smeared stiffeners technique, von Kármán equations, and the Galerkin method, the nonlinear vibration problem has been solved. Then, utilizing the multiple scales method, the nonlinear vibration behavior of the system is examined. The resonant case, including internal parametric resonance among three modes and subharmonic resonance of order one-half, is considered. The results show that although the trend of all figures is approximately like together, but the maximum amplitude vibration of the internal SSMFG cylindrical shell with the angle of stiffeners and the external SSMFG cylindrical shell with the angle of stiffeners is more than others.

Nonlinear vibration characteristics of fibre reinforced composite cylindrical shells in thermal environment

In this paper, an analytical model for fiber reinforced polymer composite cylindrical shells (FRPCCSs) accounting for material and geometric nonlinearities and thermal effect is proposed, which is capable of predicting natural frequencies, damping ratios, and resonant responses under different excitation amplitudes and temperatures. Firstly, the nonlinear Young's and shear moduli and loss factors of fiber reinforced polymer composites considering amplitude and temperature dependent properties are represented based on the Jones-Nelson nonlinear material theory, complex modulus principle, together with polynomial fitting technique. Then, the equations of motion for FRPCCSs are derived accounting for nonlinear strain–displacement relations of the von Kármán type. The procedure of determining fitting coefficients for nonlinear Young's and shear moduli and loss factors is also presented in details. Following theoretical studies, a series of thermal vibration experiments on two shell specimens made of CF120 carbon/epoxy composites are carried out to validate the proposed modeling approach as well as evaluating nonlinear vibrations of FRPCCSs experimentally. It has been found that the first three natural frequencies of composite shell specimens are initially decreased and then increased along with the increase of excitation amplitude. This variation trend becomes more significant at high temperature with the maximum variation degree of 8.2%. Meanwhile, the corresponding damping ratios and resonant responses of FRPCCSs show upward trends as the excitation amplitude and environmental temperature increase. Compared to excitation amplitude, environmental temperature has more significant effect on the damping performance of FRPCCSs, of which the relative variation degree is up to 300.5% as the temperature raises from 20 to 200 °C.

Investigation on compression-springback behavior of metal semi-cylindrical shell in thermal environment

The elastic-plastic deformation of materials provides limited displacement for metal gaskets, so as to ensure the sealing performance of flanges. In order to study the sealing performance of a novel metal gasket with a convex structure of a semi-cylindrical shell between two flanges, the compression-springback behavior of semi-cylindrical shell is investigated. By introducing the rebound and anti-coupled system consisting of the compressed body and the resilient body, meanwhile based on von Kármán nonlinear theory and Mises yield criterion, the incremental thermo-elastoplastic stress-strain constitutive relation of the semi-cylindrical shell is theoretically derived. Utilizing the finite difference method in space domain and nonlinear term iteration technique, the plastic stage problem including the semi-cylindrical shell and the sheet with flattening single-corrugated structure is solved. The influence factors of material properties, temperature, geometrical parameters of semi-cylindrical shells and cyclic loads are considered. Results show that the compression-springback behavior of nickel-based alloy is better than that of stainless steel in thermal environment, while the compression-springback behavior of stainless steel is closed to that of nickel-based alloy at room temperature. The width of semi-cylindrical shell and depth of base material significantly affect the compression-springback behavior of stainless steel. In addition, the cyclic load can cause the plastic hardening of stainless steel.

Numerical forced vibration analysis of compositionally gradient porous cylindrical microshells under moving load and thermal environment

By using differential quadrature method (DQM), forced vibrational behavior of a porous functionally graded (FG) cylindrical scale-dependent shell in thermal environment and under a moving point load having constant velocity has been researched. Within the micro-size shell, porosities exist with even or uneven distributions. Accordingly, the material properties of the micro-size shell rely on porosities and may be defined utilizing refined power-law functions. Strain gradients have been incorporated because of the existence of size effects at micro scale. Established governing equations based on first-order shell theory have been arranged in Laplace form. Next, time responses of the micro-size shell have been calculated accomplishing inverse Laplace transform technique together with differential quadrature method (DQM). It may be understood that forced vibrational behaviors of micro-size shells are dependent on the load speed, strain gradient factor, pore volume, material gradation and temperature variation.

A new structure study: Vibrational analyses of FGM convex-concave shells subjected to electro-thermal-mechanical loads surrounded by Pasternak foundation

A new structure that has just been found in this present, named to the convex-concave shell. Based on the change of radius according to the sine or cosine function, a type of rotating circular shell made of functionally graded materials (FGM) has appeared and been investigated in the paper. Characteristics of dynamics of the FGM convex-concave shell in thermal environment and surrounded by the elastic medium are analyzed by an analytical approach. The piezoelectric layers are bonded in the internal and external surfaces of the shells. By using the classical thin shell theory, Von Karman-Donnell geometrical nonlinearity assumption, the governing equations are established and the Galerkin's method is applied to investigate the nonlinear dynamical behaviors of the shells. The numerical results are calculated and validated to the previous literatures of the cylindrical shells-a special case of this structure. In addition, Finite Element Analysis (FEA) is also used to compare with these of the convex-concave shells in two types I and II. The effects of the electro-thermal environment, geometrical parameters and the elastic foundation are scrutinized by the numerical and 2D and 3D graphical results. The achieved results of the structure promise to contribute greatly to significant applications of aerospace, civil and mechanical engineering.

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

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

Dynamic instability analysis of porous FGM conical shells subjected to parametric excitation in thermal environment within FSDT

The conical shell structure is prone to dynamic instability when subjected to time dependent periodic axial loads and it can cause structural damage. Based on that this paper presents an accurate and semi-analytical method for investigation the dynamic instability of porous functionally graded material (PFGM) conical shell in thermal environment. In the analysis, three common types of PFGM conical shells, namely, uniform, symmetric and asymmetric distribution are considered assuming that material properties are related to temperature. The governing equations of conical shell subjected to parametric excitation are established by the Hamilton's principle considering first order shear deformation theory. Then the Mathieu-Hill equations describing the parametric stability of conical shell are obtained by generalized differential quadrature (GDQ) method, and the Bolotin's method is utilized to obtain the first-order approximations of principal instability regions of shell structure. By comparing the numerical results with the existing solutions in open literature, the validity of the proposed theoretical model is verified. Finally, the influences of porosity distribution type, gradient index, radius-to-thickness ratio, porosity volume fraction and temperature fields on the dynamic stability of PFGM conical shell have been investigated, wherein for different porosity distribution types, the UPD type is more sensitive to gradient index as compared to other three types, while the SPD has the minimum relative width.

Nonlinear forced vibrations analysis of imperfect stiffened FG doubly curved shallow shell in thermal environment using multiple scales method

This study investigates the non-linear vibrations of stiffened imperfect functionally graded double-curved shallow shells, as rested on nonlinear elastic foundations. The shells are exposed to external harmonic excitation and are placed in the thermal situations. The modeling of shells is derived according to the classical shell theory and the non-linear geometric von Kármán relationships. It is considered that the distribution of material properties changes along the thickness direction based on a power law index. The smeared stiffener technique is considered to model the stiffened shells. An approximation, according to Galerkin’s approach, is utilized to reduction of the shell governing equations into the non-linear coupled ordinary differential relations. The ODE equations are analytically solved and analyzed through the perturbation methodology for investigating the resonance behavior of shells. Simulation results are reported to examine the influences of stiffeners, initial imperfection, foundation coefficients, thermal environment, and geometrical characteristics on the non-linear primary resonance response of doubly curved shallow shells. Also, the nonlinear dynamic behaviors are analyzed by numerical methods through the bifurcation diagrams, and the nonlinear dynamical behaviors of the shell for different value of parameters are examined.

Nonlinear Torsional Buckling of Functionally Graded Carbon Nanotube Orthogonally Reinforced Composite Cylindrical Shells in Thermal Environment

This paper deals with the nonlinear large deflection torsional buckling of functionally graded carbon nanotube (CNT) orthogonally reinforced composite cylindrical shells surrounded by Pasternak’s elastic foundations with the thermal effect. The shell is made by two layers where the polymeric matrix is reinforced by the CNTs in longitudinal and circumferential directions for outer and inner layers, respectively. The stability equation system is obtained by combining the Donnell’s shell theory, von Kármán nonlinearity terms, the circumferential condition in average sense and three-state solution form of deflection. The critical torsional buckling load, postbuckling load-deflection and the load-end shortening expressions are obtained by applying the Galerkin procedure. The effects of temperature change, foundation parameters, geometrical properties and CNT distribution law on the nonlinear behavior of cylindrical shell are numerically predicted. Especially, the effect of orthogonal reinforcement in comparison with longitudinal and circumferential reinforcement on the torsional buckling behavior of shells is observed.