Loads In Thermal Environments Research Articles

Free vibration and transient response of initially compressed CNT-reinforced composite plates

This paper investigates the linear free vibration and nonlinear transient response of carbon nanotube (CNT)-reinforced composite plates subjected to pre-existent compressive load in thermal environments. CNTs are reinforced into matrix according to uniform and functionally graded distributions. The properties of constitutive materials are assumed to be temperature-dependent while the effective properties of nanocomposite are determined using an extended rule of mixture. Governing equations are established within the framework of classical plate theory incorporating von Kármán nonlinearity and initial geometrical imperfection. Analytical solutions of deflection and stress function are assumed to satisfy simply supported boundary conditions, and Galerkin method is applied to obtain a time differential equation including both quadratic and cubic nonlinear terms. Fourth-order Runge–Kutta numerical integration scheme is employed to determine dynamical deflection-time response of nanocomposite plates. Numerical analyses are presented to consider the influences of CNT volume fraction, CNT distribution, initial compressive load, geometrical imperfection, elevated temperature and plate geometry on the natural frequencies and nonlinear dynamical response of nanocomposite plates. The study reveals that the natural frequency and dynamical deflection are strongly decreased and increased when initial compressive load is increased, respectively. Numerical results also find that the natural frequencies are enhanced and dynamical deflection is dropped as a result of increase in volume percentage of CNTs, respectively.

Modeling and solution of eigenvalue problems of laminated cylindrical shells consisting of nanocomposite plies in thermal environments

This work is dedicated to the modeling and solution of eigenvalue problems within shear deformation theory (SDT) of laminated cylindrical shells containing nanocomposite plies subjected to axial compressive load in thermal environments. In this study, the shear deformation theory for homogeneous laminated shells is extended to laminated shells consisting of functionally graded (FG) nanocomposite layers. The nanocomposite plies of laminated cylindrical shells (LCSs) are arranged in a piecewise FG distribution along the thickness direction. Temperature-dependent material properties of FG-nanocomposite plies are estimated through a micromechanical model, and CNT efficiency parameters are calibrated based on polymer material properties obtained from molecular dynamics simulations. After mathematical modeling, second-order time-dependent and fourth-order coordinate-dependent partial differential equations are derived within SDT, and a closed-form solution for the dimensionless frequency parameter and critical axial load is obtained for first time. After the accuracy of the applied methodology is confirmed by numerical comparisons, the unique influences of ply models, the number and sequence of plies and the temperature on the critical axial load and vibration frequency parameter within SDT and Kirchhoff–Love theory (KLT) are presented with numerical examples.

Nonlinear transient response of magneto-electro-elastic cylindrical shells with initial geometric imperfection

Exploring the nonlinear mechanical behaviors of structures under external excitation is significant. This article, for the first time, attempts to demonstrate the transient response of imperfect magneto-electro-elastic (MEE) cylindrical shells under pulse load in thermal environment by time history curves and phase trajectories. Using Love's thin shell theory and Maxwell's equations, expressions for displacement-, electric-, and magnetic- fields are obtained. Combining Hamiltonian principle and Galerkin method, the nonlinear dynamic equations of cylindrical shells are derived, and Runge-Kutta method is employed to solve the whole problem. Subsequently, the transient responses under various parameters including BaTiO3 vol fraction, geometric imperfection, electrical potential, magnetic potential, prestress, viscoelastic foundation, positive phase duration, damping coefficient, maximum blast load, geometrical parameter, temperature variation and various pulse loads are presented in numerical analysis in the forms of time history curves and phase trajectories. Finally, the conclusion advocates that the BaTiO3 vol fraction, geometric imperfection and dimensions of cylindrical shells have significant impacts on the transient response.

A new analytical approach to the nonlinear buckling and postbuckling behavior of functionally graded graphene reinforced composite laminated cylindrical, parabolic, and half‐sinusoid shallow imperfect panels

AbstractThis paper presents and analyzes the nonlinear buckling responses of three types of shallow imperfect panels (cylindrical panel, parabolic panel, and half‐sinusoid panel) made from functionally graded graphene reinforced composite (FG‐GRC) on nonlinear elastic foundations subjected to axial compressive load in thermal environments. The nonlinear governing equations are formulated on Reddy's higher‐order shear deformation shell theory (HSDST) and take into account von Karman‐type nonlinearity. A new approximation technique to determine the stress function in average sense is developed and Galerkin's method is used to obtain the algebraically nonlinear equation system. Then, the simple calculation process can be used to solve the obtained equation systems, and the formulations to calculate the critical buckling loads and postbuckling load‐deflection curves are expressed in explicit form. The results can be flexibly applied to FG‐GRC panels with different curvatures in engineering designs. The effects of panel types, geometrical parameters, temperature increase, initial imperfection, and nonlinear elastic foundations on the critical buckling loads and postbuckling curves of cylindrical, parabolic, and half‐sinusoid FG‐GRC panels are discussed in numerical results. Numerical results also show a small disadvantage in the load‐carrying capacity of cylindrical panels compared to parabolic panels and half‐sinusoid shallow panels.Highlights Postbuckling of cylindrical, parabolic, and half‐sinusoid panels are studied. The panels are made of functionally graded graphene reinforced composite. Reddy's higher‐order shear deformation shell theory is applied. A new approximation technique to determine the stress function is developed. Critical buckling loads and postbuckling expressions are explicitly obtained.

Bending Analysis of Asymmetric Functionally Graded Material Sandwich Plates in Thermal Environments

This paper investigates the bending of asymmetric functionally graded material (FGM) sandwich plates subjected to thermo-mechanical loads in thermal environments. In this paper, a thermo-mechanical analysis model for asymmetric FGM sandwich plates is proposed, which contains only four control equations and four unknown variables. The governing equation is obtained through refined shear theory and the principle of virtual work, and the Navier method is used to solve it. Numerical examples of simply supported FGM sandwich plates under thermo-mechanical loads are given to verify the accuracy of the model. Finally, detailed studies are conducted on the bending of asymmetric FGM sandwich plates under thermo-mechanical loads, exploring the effects of various parameter changes on their bending behavior, and providing strong guidance for the application of asymmetric FGM sandwich plates in industrial production practice.

Post-buckling behavior of rectangular multilayer FG-GPLRC plate with initial geometric defects subjected to non-uniform in-plane compression loads in thermal environment

A semi-analytical method is established to investigate post-buckling behavior of functionally graded graphene platelets reinforced composite (FG-GPLRC) plate with initial geometric defects under non-uniform in-plane compression loads. Buckling governing equations are derived base on a new unified framework of transverse shear deformation plate theory, and the reliability and accuracy of proposed method are validated. Parametric studies are systematically performed for the first time to elaborate the effects of GPLs, structural characteristics, initial geometric defects, loading cases and thermal environment on post-buckling behavior of FG-GPLRC plate. This article can provide theoretical guidance for the design and optimization of FG-GPLRC plate.

Nonlinear buckling of higher-order shear deformable stiffened FG-GRC laminated plates with nonlinear elastic foundation subjected to combined loads

The nonlinear postbuckling analysis of functionally graded graphene reinforced composite (FG-GRC) plates taking into account the nonlinear effect of elastic foundation subjected to external pressure and axial compression load in thermal environment is analytically examined in this paper. Assuming that the FG-GRC laminated plates are stiffened by FG-GRC laminated stiffener system resting on a three-parameter nonlinear elastic foundation. The higher-order shear deformation plate theory (HSDPT) with the geometrical nonlinearities of von Kármán is applied to establish the basic formulations. Moreover, the smeared stiffener technique is successfully improved for the higher-order shear deformable anisotropic stiffener system by using a homogeneous model of the laminated beam. Galerkin's method is used to achieve the expressions of critical buckling loads and postbuckling load-deflection curves in explicit form. The numerical values display the influences of nonlinear elastic foundation, temperature, laminated stiffeners, material, and geometrical features on nonlinear responses of plates.

Nonlinear pyrocoupled dynamic response of functionally graded magnetoelectroelastic plates under blast loading in thermal environment

The nonlinear dynamic response of magnetoelectroelastic (MEE) functionally graded plates (MEEFG) subjected to blast loads and operating in a temperature environment is examined in this study. The goal of this research is to investigate the impact of pyrocoupling along with the blast loads on the coupled nonlinear behavior of smart MEEFG plates. The material properties of MEEFG plates are calculated using the well-known modified power law. The kinematics of the plate is supposed to follow Reddy's higher-order shear deformation theory (HSDT). Also, von-Karman's equations are used to bring nonlinearity into the model. The blast loads are calculated using an exponential function and are expected to be dispersed evenly across the plate's surface. The principle of virtual work is used to develop the governing equations using finite element (FE) methods, which is then solved using the direct iterative technique. The numerical examples are offered to show how gradient patterns, gradient index, and blast loading parameters affect the nonlinear dynamic response.

Mechanical buckling analysis of thick FGM toroidal shell segments with porosities using Reddy’s higher order shear deformation theory

An analytical investigation on buckling behavior of thick functionally graded shells with nearly cylindrical shapes and porosities under mechanical loads is presented in this paper. Loading conditions considered are that axial compressive load, lateral pressure and combined mechanical loads in thermal environments. Porosities are evenly or unevenly distributed within the shell. Governing equations are established based on a higher order shear deformation theory taking into account interaction between the shell and surrounding elastic medium. Two-term form of deflection is assumed to satisfy simply supported boundary conditions and Galerkin method is applied to derive closed-form results of buckling loads.

Nonlinear pyrocoupled deflection of viscoelastic sandwich shell with CNT reinforced magneto-electro-elastic facing subjected to electromagnetic loads in thermal environment

Nonlinear pyrocoupled deflection of viscoelastic sandwich shell with CNT reinforced magneto-electro-elastic facing subjected to electromagnetic loads in thermal environment

Nonlinear buckling analysis of stiffened FG-GRC laminated cylindrical shells subjected to axial compressive load in thermal environment

The main aim of this paper is to investigate the postbuckling and buckling of functionally graded graphene-reinforced composite (FG-GRC) laminated cylindrical shells strengthened by stiffeners under axial compression with the uniform temperature change effect. The stiffener design option for FG-GRC cylindrical shells under axial compression is presented and a suitably smeared stiffener technique for GRC laminated stiffener system is developed. Basing on the von Kármán Donnell shell theory, the Galerkin’s procedure, and the three-term solution of deflection, the explicit forms of critical buckling and expression of load-deflection postbuckling curves relation are obtained. Effects of the GRC laminated stiffeners, the environment temperature, the graphene-reinforced parameters on the compressed buckling behavior are validated.

Dynamic buckling of functionally graded multilayer graphene nanocomposite annular plate under different boundary conditions in thermal environment

This paper deals with dynamic stability of functionally graded (FG) nanocomposite annular plate reinforced with graphene platelets (GPLs) subjected to a periodic radial compressive load in thermal environment. On the basis of modified Halpin–Tsai micromechanics model, the effective elastic modulus of structure is estimated. Taking into consideration of the first-order shear deformation theory, the governing motion equations are obtained via the Hamilton’s principle. Afterward, the partial differential motion equations are discretized into a system of Mathieu–Hill equations by utilizing generalized differential quadrature method. Furthermore, the Bolotin’s technique is applied to determine the principle unstable zone of functionally graded graphene platelet reinforced composite (FG-GPLRC) annular plate. The accuracy and validity of current study are examined by comparing the fundamental natural frequencies of structure with those published in available literature. Eventually, to investigate the influences of number of layers, GPLs patterns and their geometric, boundary conditions, geometrical parameters of structure, static load factor, and temperature change on the DIRs of FG-GPLRC multilayer annular plate, different parametric studies are performed.

Parametric instability of functionally graded carbon nanotube-reinforced hybrid composite plates in thermal environments

This paper studies the parametric instability of hybrid nanocomposite plates under an arbitrary periodic load in thermal environments. The hybrid nanocomposite plate is a three-layer board. It has metal layers on both surfaces and one core reinforced with functionally graded (FG) carbon nanotubes (CNTs). The Galerkin method with a reduced eigenfunction transformation is applied to establish the governing equations of motion. According to the Bolotin method, a set of Mathieu-type differential equations is formed to determine dynamic instability regions and dynamic instability index (DII). The in-plane periodic stress is taken to be a combination of pulsating axial and bending stresses in the example problems. The effects of the layer thickness ratio, CNTs volume fraction, CNTs distribution type, temperature, bending stress, static and dynamic load on the dynamic instability of hybrid nanocomposite plates are investigated and discussed.

Buckling of shear deformable FG‐CNTRC cylindrical shells and toroidal shell segments under mechanical loads in thermal environments

AbstractAn analytical study on buckling of carbon nanotube reinforced composite (CNTRC) circular cylindrical shells and toroidal shell segments surrounded by elastic media, exposed to thermal environments and subjected to axial compression and combined mechanical loads is presented in this paper. Carbon nanotubes (CNTs) are reinforced into isotropic matrix through uniform and functionally graded distributions. Material properties of constituents are assumed to be temperature dependent and effective elastic moduli of CNTRC are estimated by an extended rule of mixture. Formulations are based on first order shear deformation theory taking into account interaction between the shell and surrounding medium. Two‐term solution of deflection is assumed to satisfy simply supported boundary conditions and Galerkin method is used to obtain closed‐form expressions of buckling loads. Numerical illustrations are given to analyze the effects of CNT volume fraction and distribution patterns, preexisting loads, surrounding elastic media and geometrical parameters on the stability of CNTRC shells. The proposed approach is simple and effective to evaluate buckling loads of moderately thick closed nanocomposite shells under different types of mechanical loads.

Pre- and post-buckling analysis of FG cylindrical nanoshells in thermal environment considering the surface stress effect

An analytical approach is developed to study the pre- and post-buckling responses of circular cylindrical nanoscale shells subjected to lateral and axial loads as well as thermal environment. The effect of surface free energy as one of the key nanoscale effects is considered in the context of Gurtin-Murdoch surface elasticity theory. The nanoshell is made of functionally graded materials (FGMs) whose properties are calculated using power-law functions. The basic formulation is derived according to the classical shell theory together with the von-Karman nonlinear relations. Moreover, the physical neutral plane position is taken into consideration. Using the Ritz energy method, an analytical approach is also proposed to solve the problem. Comprehensive numerical results are presented to investigate the behavior of nanoshell under lateral pressure and axial load in thermal environment, in pre- and post-buckling domains. The influences of various parameters including the surface stress, FGM gradient index, temperature and geometrical parameters on the non-linear critical axial stress/lateral pressure are illustrated.

Nonlinear thermo-mechanical buckling of higher-order shear deformable porous functionally graded material plates reinforced by orthogonal and/or oblique stiffeners

In this paper, an analytical approach for nonlinear buckling and post-buckling behavior of stiffened porous functionally graded plate rested on Pasternak's elastic foundation under mechanical load in thermal environment is presented. The orthogonal and/or oblique stiffeners are attached to the surface of plate and are included in the calculation by improving the Lekhnitskii's smeared stiffener technique in the framework of higher-order shear deformation plate theory. The complex equilibrium and stability equations are established based on the Reddy's higher-order shear deformation plate theory and taken into account the geometrical nonlinearity of von Kármán. The solution forms of displacements satisfying the different boundary conditions are chosen, the stress function method and the Galerkin procedure are used to solve the problem. The good agreements of the present analytical solution are validated by making the comparisons of the present results with other results. In addition, the effects of porosity distribution, stiffener, volume fraction index, thermal environment, elastic foundation… on the critical buckling load and post-buckling response of porous functionally graded material plates are numerically investigated.

Nonlinear buckling and postbuckling of sandwich FGM cylindrical shells reinforced by spiral stiffeners under torsion loads in thermal environment

The main purpose of this paper is the investigation of the nonlinear torsional buckling and postbuckling of sandwich functionally graded cylindrical shells with the von Karman large deflection nonlinearities under thermal effect by an analytical method. The shell skin is reinforced by stringer, circular ring and spiral stiffeners, the material properties of shell skin and stiffeners are assumed to vary continuously through the thickness. The very large effect of spiral stiffeners on the buckling load-carrying capacity of a cylindrical shell in comparison with orthogonal stiffeners is clearly proved in numerical investigations. Based on the Donnell shell theory and the improved smeared stiffener technique for both thermal and mechanical terms of spiral stiffeners, the equilibrium equations of the shell are established in this paper. By using the Galerkin method, the postbuckling curves and critical buckling loads are obtained. The effects of temperature change, stiffeners, material and dimensional parameters on the nonlinear torsional buckling and postbuckling of shell are numerically analyzed.

Magneto-electro-elastic vibration of moderately thick FG annular plates subjected to multi physical loads in thermal environment using GDQ method by considering neutral surface

The vibration analysis of an annular plate made up of functionally graded magneto-electro-elastic materials subjected to multi physical loads is presented. The plate is in thermal environment and temperature is distributed non-uniformly in its thickness direction. In addition, the plate is assumed moderately thick, the material properties vary through the thickness, and the exact neutral surface position is determined and took into account. According to Hamilton’s principle and the first-order shear deformation theory, the governing motion equations are extracted. Numerical results for various boundary conditions are obtained via the generalized differential quadrature method and are validated in simpler states with those of the literature. The effects of different parameters such as material property gradient index, multi physical loads, temperature variations, boundary conditions and geometric specifications of the plate on the natural frequencies and mode shapes are investigated. Temperature changes have little effect on the natural frequencies and the effect of electric potential on them is opposite of magnetic one. In other words, by increasing the magnetic potential, the rigidity of the plate increases too, and the frequency increases. The results of this study are useful to design more efficient sensors and actuators used in the smart or intelligent structures.

Free vibration and nonlinear dynamic response of imperfect nanocomposite FG-CNTRC double curved shallow shells in thermal environment

Analytical solutions for the nonlinear vibration of imperfect functionally graded nanocomposite (FG-CNTRC) double curved shallow shells on elastic foundations subjected to mechanical load in thermal environments are introduced in this paper. The double curved shallow shells are reinforced by single-walled carbon nanotubes (SWCNTs) which are assumed to be graded through the thickness direction according to the different types of linear functions. Motion and compatibility equations are derived using Reddy's higher order shear deformation shell theory and taking into account the effects of initial geometrical imperfection and temperature – dependent properties. The deflection – time curve and the natural frequency are determined by using Galerkin method and fourth – order Runge – Kutta method. The effects geometrical parameters, elastic foundations, initial imperfection, temperature increment, mechanical loads and nanotube volume fraction on the nonlinear thermal vibration of the nanocomposite double curved shallow shells are discussed in numerical results. The accuracy of present approach and theoretical results is verified by some comparisons with the known data in the literature.

A novel approach for nonlinear bending response of macro- and nanoplates with irregular variable thickness under nonuniform loading in thermal environment

A new method has been presented for static analysis of macro- and nano sector plates with variable thickness. The thickness variations are assumed linearly, functionally, and also irregularly. The governing equations have been derived based on the nonlocal modified higher-order shear deformation theory and have been solved applying the semi-analytical polynomial method. The obtained results have been compared with the results of the other relevant articles. The effective parameters on the analysis have been investigated such as the thickness, the size of the plate under uniform and nonuniform loadings, and the boundary conditions including free edges.Communicated by Marco Amabili.