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Geometrically non-linear thermally induced vibrations of functionally graded material (FGM) joined spherical-conical shells are analyzed in the current research. Thermo-mechanical properties of the shells are assumed to be temperature and position dependent. The system of joined spherical-conical shells is subjected to thermal shock on the ceramic-rich surface, whereas the metal-rich one is kept at reference temperature. The one-dimensional transient heat conduction equation is established and solved via the generalized differential quadrature (GDQ) and Crank-Nicolson methods. This equation is non-linear since the thermo-mechanical properties of the shells are temperature dependent. The total functional of the shells is obtained under the assumptions of uncoupled thermoelasticity laws, first order shear deformation shell theory, and the von Kármán type of geometrical non-linearity. Non-linear coupled equations of motion are solved via the iterative Picard method accompanied with the β-Newmark time approximation technique. Numerical results are well-validated with the available data for the case of single FGM spherical shell. Parametric studies are conducted to examine the influences of conical and spherical shell geometries, material composition, temperature dependence, in-plane and out-of-plane mechanical boundary conditions, various configuration of conical/spherical shell system, and thermal boundary conditions. It is highlighted that thermally induced vibrations indeed exists. [ABSTRACT FROM AUTHOR]

Present investigation deals with the response of a piezoelectric hollow sphere that is subjected to sudden thermal shock. Loading and boundary conditions are assumed to be symmetric so the response of the sphere is also considered to be symmetric. The governing equations of the vessel are obtained which are three in number. These equations include the equation of motion, the energy equation and the Maxwell equation. The energy equation is established in the framework of single relaxation time theory of Lord and Shulman. The established equations are written in terms of temperature change, radial displacement, and electric potential. These equations are provided in a dimensionless presentation for the sake of generality. After that with the aid of the generalized differential quadrature method, the established equations are discreted. Also Newmark time marching scheme is applied to trace the radial displacement, electric potential, and temperature change in time domain. Novel numerical results are then provided to explore the propagation and reflection of electrical, thermal and mechanical waves in a hollow sphere. It is shown that temperature wave propagates with finite speed within the framework of the Lord–Shulman theory. [ABSTRACT FROM AUTHOR]

An investigation is performed in this research to study the response of doubly curved shells subjected to rapid surface heating. Doubly curved shell is made from a composite laminated media where each layer is reinforced with graphene platelets (GPLs). Also each layer may have different amount of GPLs which results in a piecewise functionally graded graphene platelet reinforced composite (FG-GPLRC) shell. The elasticity modulus of the shell is estimated by means of the Halpin-Tsai rule where the size of the reinforcements is also included. It should be noted that mass density, thermal expansion coefficient, Poisson's ratio and specific heat are evaluated using the simple rule of mixture approach. The one-dimension transient heat conduction equation is established and solved for each layer of the composite media. The continuity of the temperature change and heat flux are also considered between the layers. After that, time dependent thermal moment and thermal force are evaluated and inserted into the equations of motion of the structure. First order shear deformation theory of shells and Donnell kinematics are applied to establish the basic equations of the shell. With the aid of the Ritz method and Chebyshev polynomials as the basic functions, the matrix representation of the motion equations of the doubly curved shallow shells subjected to rapid surface heating are established. These equations are traced in time using the Newmark time marching scheme. Results of this study are compared with the available data in the open literature. After that novel results are provided for vibrations induced by rapid surface heating in FG-GPLRC doubly curved shells. [ABSTRACT FROM AUTHOR]

The present study examines the geometrically non-linear dynamic response of hermetic capsule construction made of functionally graded materials subjected to thermal shock. The Voigt and Toloukian models are used to derive the material properties, where dependence of the properties to position and temperature is included. The one-dimensional transient heat transfer equation is established. The Crank-Nicholson approximation and Picard's iterative method are used to solve this nonlinear equation using the GDQ numerical method in accordance with the temperature dependence of the material properties. After obtaining the temperature distribution along the thickness, it is possible to determine the thermal force and moment. Using the first-order shear theory to calculate the displacement field and the von Kármán form of geometry non-linearity, the equations of motion are determined. The Newton-Raphson iterative approach and the β -Newmark time estimate approach are used to solve the non-linear coupled equations of motion. The influencing factors on the reaction of the structure, such as the radius of the sphere and the length of the cylinder, the power law index, and the shell thickness are determined after the equations, techniques, and findings are validated. [ABSTRACT FROM AUTHOR]

This paper mainly focuses on the dynamic response of composite beams reinforced with graphene platelets subjected to a moving load. The governing equations of motion of the beam are obtained by using a quasi-3D theory which takes the through-the-thickness shear strains and thickness stretching effects into account. By employing the Halpin–Tsai micro-mechanical rule, which captures the dimensions of the reinforcement, the elastic modulus of reinforced composite is evaluated. A moving load with constant magnitude and velocity, which moves on the free surface of the beam is assumed. In order to discretize the governing equations and obtain a set of ordinary time-dependent equations, the Navier solution which is proper for simply-supported boundary conditions is used. Since the governing equations are time-dependent, a Newmark algorithm is used to acquire the temporal evolution of displacements in FG-GPLRC beams. To be assured of the accuracy of results, simple cases are compared with other data in the open literature, initially. After that, novel results are presented to investigate different factors regarding natural frequencies and dynamic deflection of composite beams reinforced with graphene platelets. It is indicated that the adopted theory has sufficient accuracy to estimate the natural frequencies and dynamic response of arbitrary thick FG-GPLRC beams. [ABSTRACT FROM AUTHOR]

Current investigation deals with the forced vibration response of a composite laminated plate which is reinforced with graphene platelets (GPLs). The weight fraction of GPLs in each layer may be different which results in a piecewise functionally graded (FG) media. The elastic properties of the composite media are obtained using the Halpin-Tsai approach. The motion equations of the plate are established with the aid of the Ritz method where the shape functions are presented using the Chebyshev polynomials. The time dependent system of equations is solved using the Newmark time marching scheme. The established system of equations may be used for the dynamic response of an FG-GPL reinforced composite rectangular plate which is subjected to a moving load with arbitrary path and velocity. Numerical results are given to show the influence of boundary conditions, GPL weight fraction and GPL distribution profile on the dynamic response of the plate. It is shown that, with increasing the weight fraction of the GPLs, the dynamic deflections in the plate decrease. Also with introduction of a proper pattern where the surfaces at top and bottom have the highest weight fraction of GPLs, the dynamic deflection of the plate may be decreased significantly. [ABSTRACT FROM AUTHOR]

In this research, development and solution of the generalized magneto-thermoelastic response of a layer based on both Lord–Shulman and Green–Lindsay theories are reported. To this end, the Maxwell electromagnetism equations are reduced to one-dimensional space. The Lorentz force is applied to obtain the magnetic body force and extract the effect of the magnetic field effect on the equation of motion of the layer. The heat conduction equation is also established for the one-dimensional layer using both the Lord–Shulman and Green–Lindsay theories. The established equations are four in number in terms of displacement, temperature change, induced magnetic field and electric field. Equations are reformulated in a dimensionless presentation where the speed of waves is also changed. Using the generalized differential quadrature method, the established dimensionless equations are discreted and provided in a matrix representation. Next, using Newmark time marching scheme, equations are traced in time. At first results of this study are compared with the available data in the open literature. After that novel results are given for a layer. It is shown that under both of the mentioned theories, temperature propagates with finite speed where the speed of wave may be obtained using the relaxation times. [ABSTRACT FROM AUTHOR]

Current investigation deals with the nonlinear generalized thermoelasticity of a functionally graded material (FGM) layer. It is assumed that the elasticity modulus, thermal conductivity, thermal expansion coefficient, mass density and specific heat capacity follow the exponential type of property distribution while the thermal relaxation time is assumed to be constant for the FGM layer. The governing motion and energy equations for the layer are obtained under the assumptions of Lord and Shulman with a single relaxation time. The energy equation is kept in its nonlinear form and the assumption made in the previous investigations to linearize the energy equation is not performed in the current research. Two coupled equations are presented in a dimensionless presentation and solved by means of the generalized differential quadrature and Newmark time marching method. Numerical results of this study are validated for the case of homogeneous layer. After that, novel numerical results are provided to investigate the response of a layer subjected to thermal shock. As expected, the exponential index of the FGM layer, boundary conditions, coupling parameter, relaxation time and nonlinearity are all major factors on the response of the thermally affected layer. It is verified that under thermally nonlinear analysis the magnitudes of stress and displacement are underestimated. Also, temperature and displacement enhance as the exponential index of the FGM layer increases. [ABSTRACT FROM AUTHOR]

The present study deals with the free vibration analysis of composite laminated doubly curved shells which are reinforced with graphene platelets. The weight fraction of graphene platelets in each layer of the composite medium may be different which leads to a functionally graded graphene platelet-reinforced medium. The elastic modulus of the composite medium is obtained using the Halpin–Tsai approach which captures the size effects of the reinforcements. Using the first-order shear deformation shell theory and Sanders kinematic assumptions, the total strain and potential energies of the shell are established. The shape functions of the essential variables are estimated by means of Chebyshev polynomials which are suitable for arbitrary combinations of in-plane and out-of-plane boundary conditions. The results of the present study are well-validated with the available data in the open literature. After that, novel results are given to discuss the effects of different parameters on the frequencies and mode shapes of functionally graded graphene platelet-reinforced composite shells. It is shown that increasing the amount of graphene platelets in the shell results in higher frequencies. Also, among the introduced functionally graded patterns, the FG-X pattern leads to higher frequencies. [ABSTRACT FROM AUTHOR]

This study proposes a numerical solution for the coupled thermomechanical response of a rotating annular disk which is subjected to the combined action of thermal and mechanical loads. The annular disk is isotropic and homogeneous with constant thickness. With the aid of the generalized thermoelasticity theory of Lord and Shulman, which includes one relaxation time and avoids the propagation on thermal waves with infinite speed, the energy and motion equations of the disk are extracted. These equations are then transformed to a dimensionless presentation. The developed governing equations are discretized by means of the generalized differential quadrature method. The time-dependent coupled system of equations are traced in time with the aid of the Newmark time marching scheme. Numerical results are given to explore the effect of rotating speed on propagation of temperature, radial displacement and stress waves. It is shown that magnitude of displacement and stress waves is highly dependent to rotation speed, however the magnitude of temperature wave seems to be independent of rotating speed. [ABSTRACT FROM AUTHOR]

This research investigates the free vibration of a rotating annular microplate under the flexoelectric effect. Initially, the Kirchhoff plate theory assumptions are used to express the displacement fields. After considering the displacement field, strains and their gradients are derived and substituted into the electric enthalpy and kinetic energy expressions. Subsequently, by applying Hamilton’s principle to the aforementioned equations, the electric and mechanical equations are computed. To derive the equations of motion, initially, the polarization vectors and their gradients are derived from the electric equations and associated boundary conditions. Subsequently, these are incorporated into the mechanical equations, which also encompass electric components. It is notable that by removing the time-dependent terms from the in-plane equations of motion, the static displacement due to rotation at each speed is obtained. After deriving the equations of motion and boundary conditions, these equations are non-dimensionalized using non-dimensionalizing relations. In the next step, Hamilton’s principle is used to discretize the equations and boundary conditions. Consequently, by applying the generalized differential quadrature method and extracting the stiffness and mass matrices resulting from the transverse equation of motion and boundary conditions, the natural transverse frequency of the rotating annular microplate under the flexoelectric effect is calculated. The results of this research are useful for promoting the use of rotating annular microplants under flexoelectric effect for microelectromechanical systems designers with high efficiency. [ABSTRACT FROM AUTHOR]

The response of a disk made from a heterogeneous material within the framework of Lord-Shulman theory is investigated in this article. The theory admits a single relaxation time to avoid the infinite speed of temperature wave. It is assumed that all of the thermomechanical properties except for Poisson ratio and thermal relaxation time vary exponentially through the radial direction of the disk. Two coupled equations, namely, the axisymmetric equation of motion and the energy equation are obtained for the disk. The energy equation is kept in the nonlinear form and the linearization of the previous investigations is not performed in this work. These two equations are provided in a dimensionless presentation. After that, using the generalized differential quadrature method, a system of nonlinear algebraic equations is established. Following the β − Newmark time marching method, the temporal evolution of radial displacement and temperature at the nodal points of the disk are obtained. Comparison study is given to assure the validity of the proposed solution method. After that, novel numerical results are given to discuss the effects of involved parameter. It is shown that, under the nonlinear analysis, the magnitudes of radial and hoop stresses and radial displacement are underestimated. [ABSTRACT FROM AUTHOR]

Free vibration response of a joined shell system including cylindrical and spherical shells is analyzed in this research. It is assumed that the system of joined shell is made from a functionally graded material (FGM). Properties of the shells are assumed to be graded through the thickness. Both shells are unified in thickness. To capture the effects of through-the-thickness shear deformations and rotary inertias, first-order shear deformation theory of shells is used. The Donnell type of kinematic assumptions is adopted to establish the general equations of motion and the associated boundary and continuity conditions with the aid of Hamilton's principle. The resulting system of equations is discretized using the semi-analytical generalized differential quadrature method. Considering the clamped and free boundary conditions for the end of the cylindrical shell and intersection continuity conditions, an eigenvalue problem is established to examine the vibration frequencies of the joined shell. After proving the efficiency and validity of the present method for the case of thin isotropic homogeneous joined shells, some parametric studies are carried out for the system of combined moderately thick cylindrical–spherical shell system. Novel results are provided for the case of FGM joined shells to explore the influence of power-law index and geometric properties. [ABSTRACT FROM AUTHOR]

The response of a long hollow cylindrical vessel made from a piezoelectric material is considered in the present investigation. The piezoelectric vessel is subjected to a thermal shock on one surface. The generalized piezo-thermo-elasticity formulation of Lord and Shulman is adopted which contains a single relaxation time to consider the finite speed of temperature wave propagation. The response of the cylinder is assumed to be axi-symmetric. Three coupled equations are established as the governing equations, which are the equation of motion, the energy equation and the Maxwell equation. These equations are transformed into the dimensionless ones. With the aid of the generalized differential quadrature method, these equations are discretized in the radial direction. After that, with the aid of the Newmark time marching scheme, the temporal evolutions of the thermo-electro-elastic parameters are obtained. Novel numerical results are presented to obtain the response of the cylinder subjected to a thermal shock using the Lord and Shulman theory of thermoelasticity. [ABSTRACT FROM AUTHOR]

Current investigation deals with the generalized thermoelastic response of a finite hollow disk made of a piezoelectric material. The constitutive equations of the piezoelectric media are reduced to a two dimensional plane-stress state. To capture the finite speed of temperature wave, the single relaxation time theory of Lord and Shulman is used. Three coupled differential equations in terms of radial displacement, electric potential, and temperature change are obtained. These equations are written in a dimensionless presentation. With the aid of the differential quadrature method (DQM) a time-dependent algebraic system of equations is extracted. The Newmark time marching scheme is applied to trace the temporal evolution of temperature change, electric potential, radial displacement, stresses, and electric displacement. Numerical results demonstrate that radial displacement and temperature waves propagate with finite speed while the electric potential propagates with infinite speed. [ABSTRACT FROM AUTHOR]

A nonuniform rational B-spline isogeometric finite element formulation is presented in this research to analyze the thermal buckling behavior of composite laminated skew plates reinforced by graphene platelets. Formulation is based on the first-order shear deformation plate theory. It is assumed that each layer of the composite laminated plate may have different volume fraction of graphene platelets leading to a through-the-thickness piecewise functionally graded medium. The equivalent properties of the plate are obtained by means of the Halpin–Tsai rule. The developed solution method may be used for arbitrary combinations of boundary conditions. The accuracy of the developed formulation is depicted via comparison studies with respect to the available data in the open literature. Novel numerical results are also given to show the effects of volume fraction of graphene platelets, distributed patterns of graphene platelets, and geometric characteristics of the skew plate. [ABSTRACT FROM AUTHOR]

Considering the uncoupled thermoelasticity assumptions, a thermally induced vibration analysis for functionally graded material (FGM) conical shells is performed in this research. Thermo-mechanical properties of the conical shell are assumed to be temperature and position dependent. The conical shell is under rapid heating with various cases of thermal loads on the outer surface, whereas the opposite surface is kept at reference temperature or thermally insulated. Since the ratio of thickness to radius is much smaller than one, the transient heat conduction equation, for simplicity, may be established and solved for one-dimensional condition. Assuming temperature-dependent material properties, the heat conduction equation is nonlinear and should be solved using a numerical method. A hybrid generalized differential quadrature (GDQ) and Crank–Nicolson method is used to obtain the temperature distribution in thickness direction, respectively. Based on the first-order shear deformation theory and geometrically nonlinear assumptions, the equations of motion are obtained applying the Hamilton principle. Discretization of the equations of motion in the space domain and boundary conditions is performed by applying the GDQ method, and then, the system of highly nonlinear coupled ordinary differential equations is solved by the iterative Newmark time-marching scheme and well-known Newton–Raphson method. Since the thermally induced vibration of the conical shells is not reported in the literature, the results are compared with the case of a circular plate. Also, studies of the FGM conical shells for various types of boundary conditions, functionally graded patterns, and thermal loads are provided. The effects of temperature dependency, geometrical nonlinearity, semi-vertex angle, shell length, and shell thickness upon the deflections of the conical shells are investigated. [ABSTRACT FROM AUTHOR]

In the present research, thermally induced vibration of shallow spherical shells made of functionally graded materials is investigated. The thermomechanical properties of the FGM media are assumed to be temperature dependent. Based on the uncoupled thermoelasticity theory, the one-dimensional heat conduction equation is established. The top and bottom surfaces of the shell are subjected to several types of rapid heating boundary condition. Because of the temperature dependency of the material properties, solution of nonlinear heat conduction equation needs a numerical method. In the first step, generalized differential quadrature method (GDQM) is applied to discretize the heat conduction equation across the shell thickness. Afterward, the governing system of time-dependent ordinary differential equations is solved using the successive Crank-Nicolson scheme. The obtained thermal force and thermal moment resultants at each time step are applied to the equations of motion. The axisymmetric equations of motion, using the first-order shear deformation theory (FSDT) based on the Kármán type of geometrical nonlinearity, are derived with the aid of the Hamilton principle. Using the harmonic differential quadrature method, shell domain is divided into a number of nodal points, and differential equations are turned into a system of ordinary differential equations. To obtain the displacement components at any time, time marching scheme based on the Newmark method is implemented. The obtained highly nonlinear algebraic equations are solved by means of the Newton-Raphson method. Comparison studies are performed to validate the formulation and solution method of the present research. Various examples are illustrated to discuss the influences of effective parameters such as power law index in the FGM formulation, thickness of the shell, temperature dependency, shell opening angle, in-plane boundary conditions, type of thermal boundary conditions, and geometrical nonlinearity on thermally induced response of the FGM shell under thermal shock. [ABSTRACT FROM AUTHOR]

In the present research, the response of a one-dimensional piezoelectric layer is investigated using the generalized thermoelasticity theory of Lord and Shulman. The layer is subjected to thermal shock on one surface. Three coupled equations, namely, motion equation, energy equation and Maxwell equation in terms of displacement, temperature, and electric potential are established. Using the proper transformation, the mentioned equations are given in a dimensionless form. These equations are discretized by means of the generalized differential quadrature method and traced in time by means of the Newmark time marching scheme. Numerical examples are provided to show the propagation and reflection of thermal, mechanical and electrical waves in a layer. It is shown that under the Lord and Shulman theory, temperature propagates with a finite speed, similar to mechanical displacement wave. However, the electric displacement and potential propagate with infinite speed. [ABSTRACT FROM AUTHOR]

Based on the nonlinear dynamic analysis, thermally induced vibrations of the FGM shallow arches subjected to different sudden thermal loads are studied. Temperature and position dependence of the material properties are taken into account. Based on the uncoupled thermoelasticity assumptions, The non-linear one-dimensional transient heat conduction equation is solved numerically by a hybrid iterative GDQ method and Crank-Nicolson time marching scheme. A first order shear deformation arch theory (FSDT) is also combined with the von Kármán type of geometrical non-linearity and the Donnell kinematic assumption to obtain the equations of motion employing the Hamilton principle. Discretization of the highly coupled non-linear equations of motion is done by using the GDQ method in the arch domain. The solution of the system of the ordinary differential equations is established by means of a hybrid iterative Picard-Newmark scheme. Comparison is also made with the existing results for the case of isotropic homogeneous shallow arches, where good agreement is obtained. Also, parametric studies are proposed to show the effects of temperature dependency, geometrical non-linearity, arch thickness, power law index, and the type of thermal-mechanical boundary conditions upon the arch deflection. [ABSTRACT FROM AUTHOR]

Abstract Natural frequencies of circular deep arches made of functionally graded materials (FGMs) with general boundary conditions are obtained in this research based on the unconstrained higher-order shear deformation theory taking into account the depth change, complete effects of shear deformation, and rotary inertia. The material properties are assumed to vary continuously through the thickness direction of the arch. Displacement field within the arch is obtained through expansion up to an arbitrary order. Governing differential equations of the in-plane vibration are derived using Hamilton's principle. These equations are solved numerically utilizing the differential quadrature method (DQM) formulation. In order to illustrate the validity and accuracy of the presented results, results are compared with the available data in the open literature. Afterwards, novel numerical results are given for free vibration behaviour of the FGM deep arches with various boundary conditions. Highlights • Displacement of the arch is estimated by means of a higher order theory up to an arbitrary order. • Different types of boundary conditions are covered in this research. • GDQ method is used to solve the governing equations. • Properties are distributed across the depth of the arch using a power law function. [ABSTRACT FROM AUTHOR]

Abstract In the present research, buckling analysis of composite laminated conical shells reinforced with graphene sheets is investigated. Graphene sheets as reinforcements are distributed in each lamina. Volume fraction of graphene in each layer may be different which results in a piecewise functionally graded conical shell. First order shear deformation shell theory, Donnell kinematic assumptions and von Kármán type of geometrical non-linearity are used to establish the governing equations of the conical shell and the associated boundary conditions. The pre-buckling forces of the shell are obtained employing a membrane analysis. The linear stability equations are developed using the adjacent equilibrium criterion. These equations are discreted by means of the generalised differential quadratures across the shell length and Fourier expansion through the circumferential direction. An eigenvalue problem is obtained which yields the critical buckling pressure of the conical shell in thermal environment and the circumferential mode number at the onset of buckling. Comparison studies are provided for graphene reinforced and conventional composite laminated cylindrical shells and also isotropic conical shells with and without thermal environment. Afterwards parametric studies are given for buckling of functionally graded graphene reinforced composite laminated conical shells in thermal environment with different boundary conditions. It is shown that, temperature elevation decreases the critical buckling pressures of the conical shell significantly. Also buckling pressure of the shell may be enhanced through a piecewise functionally graded distribution of volume fraction of reinforcements. [ABSTRACT FROM AUTHOR]

Abstract Present research aims to analyze the nonlinear bending response of the functionally graded material curved tube subjected to the uniform lateral pressure. The effect of thermal environment is also included. Properties of the arch are distributed through the radial direction using a power law function. Thermomechanical properties of the media are assumed to be temperature dependent. The governing nonlinear equilibrium equations of the arch are obtained by means of the von Kármán assumption and a higher order shear deformation tube theory which satisfies the traction free boundary conditions on the inner and outer surfaces of the tube. The three coupled nonlinear equations of the tube are reduced to new two ones in a dimensionless presentation. These two equations are solved using the two step perturbation technique for pin ended and clamped ended boundary conditions. Closed form and accurate expressions are provided to estimate the deflection of the arch as a function of the thermal and mechanical load parameters. Numerical results are provided to explore the effect of different parameters such as the power law index of the FGM tube, boundary conditions of the tube, thermal environment, and three geometrical parameters. Highlights • A two step perturbation technique is used to obtain the response of an FGM curved tube under thermo-mechanical load. • A higher order tube model is used which satisfies the traction free boundary conditions on the surfaces of the tube. • Temperature dependency of the constituents is included into the formulation. • Closed form expressions are given to estimate the deflections of clamped and pinned tubes. [ABSTRACT FROM AUTHOR]

The analysis of large amplitude thermally induced vibrations of a shallow curved beam is considered in this article. The beam is made from an isotropic homogeneous material. One surface of the arch is subjected to rapid surface heating while the other surface is kept at reference temperature. The temperature profile is evaluated by means of the 1D heat conduction equation across the thickness of the beam. The thermally induced moments and forces are evaluated from the temperature profile. These resultants are inserted into the equations of motion of the arch. To establish the equations of motion, kinematic assumptions of a shallow arch with considerations of the von Kármán type of geometrical nonlinearity, Euler-Bernoulli beam assumptions, and linear stress-strain-temperature law are employed. The equations of motion are discreted using the conventional polynomial Ritz formulation. The resulting equations are nonlinear and at each time step the Newton-Raphson technique is used to obtain the solution. The equations of motion of the arch are traced in time domain using the Newmark time marching scheme, which results in the temporal evolution of lateral displacement at arbitrary point of the arch. Numerical results are provided to explore the effects of different parameters. It is shown that thermally induced vibrations indeed exist especially for thin arches. As the beam becomes thicker or shorter, the thermally induced vibrations fade up and for sufficiently thick arches, quasi-static and dynamic responses of the arch become identical. [ABSTRACT FROM AUTHOR]

Present research investigates the thermal postbuckling of sandwich plates containing a stiff core and two thin carbon nanotube reinforced composite (CNTRC) face sheets. Properties of the core, carbon nanotubes (CNTs) and polymeric matrix of the faces are assumed to be temperature-dependent. It is assumed that CNTs as reinforcements may be distributed according to a functionally graded pattern. Plate is formulated based on the first-order shear deformation theory and von Kármán type of geometrical nonlinearity. The governing equations are obtained by the energy method with the aid of the Conventional Ritz method. Shape functions of the Ritz method are estimated according to the Chebyshev polynomials. A set of nonlinear eigenvalue equations is achieved. The obtained equations are homogeneous, coupled, and nonlinear in terms of both displacements and temperature. A successive displacement control strategy is implemented to trace the thermal postbuckling equilibrium path of the plate. It is shown that, with increasing the volume fraction of CNT, critical buckling temperature of sandwich plate increases and postbuckling deflection decreases. Furthermore, through a functionally graded distribution of volume fraction of CNTs across the thickness, critical buckling temperature of the sandwich plate may be enhanced and thermal postbuckling deflection may be alleviated. [ABSTRACT FROM AUTHOR]

Present research deals with the geometrically nonlinear bending of a long cylindrical panel made of a through-the-thickness functionally graded material subjected to thermal load. A panel under the action of uniform temperature rise loading is considered. Formulation of the shell is based on the third-order shear deformation shell theory, where the first-order shear deformation and classical shell theory may be extracted as special cases. Thermomechanical properties of the shell are assumed to be temperature dependent and are estimated according to a power law function across the shell thickness. Also, it is assumed that shell is in contact with an elastic foundation which acts in tension as well as in compression. The nonlinear governing equations of the shell are obtained using the von Kármán type of geometrical nonlinearity. The obtained governing equations are solved for two cases, i.e., simply supported shells and clamped shells. The developed equations are solved using a two-step perturbation technique. Accurate closed-form expressions are provided to obtain the mid-span deflection of the shell as a function of temperature elevation. Numerical results are provided to analyze the effects of power law exponent, boundary conditions, temperature dependency, side to radius ratio, and side to thickness ratio. [ABSTRACT FROM AUTHOR]

The present investigation deals with the large amplitude response of shallow thick circular arches subjected to thermal, mechanical, or thermomechanical loads. The structure is resting on a three-parameter elastic foundation containing the Winkler springs, the shear Pasternak layer, and hardening nonlinear springs. The arch is made of a through-the-thickness functionally graded material. Except for Poisson’s ratio, the other properties of the arch are assumed to be temperature and position dependent. Each property is estimated according to the rule of mixtures in terms of the volume fraction of the constituents. The case of uniform temperature rise and uniform radial lateral load is considered. The governing equations of the arch are obtained with the aid of the third-order shear deformation arch theory and the von Kármán type of geometrical nonlinearity. The developed coupled and nonlinear equilibrium equations are solved using the two-step perturbation technique for the case of simply supported arches. Closed-form expressions are developed for nonlinear bending equilibrium path of shallow arches under thermal and mechanical loads. Results are provided for different power law indices, geometrical parameters, and the foundation stiffness. [ABSTRACT FROM AUTHOR]

The present research considers the free vibration characteristics of a joined shell system that consists of three segments. The joined shell system contains two conical shells at the ends and a cylindrical shell at the middle. All shell elements are made from isotropic homogeneous material. The shell elements are unified in thickness. With the aid of the first-order shear deformation shell theory and the Donnell type of kinematic assumptions, the equations of motion of a conical shell and the associated boundary conditions are obtained. These equations are valid for each segment. The obtained equations are then discreted using the generalised differential quadratures (GDQ) method. Applying the intersection continuity conditions for displacements, rotations, forces, and moments between two adjacent shells, and also boundary conditions at the ends of the joined shell system, a set of homogeneous equations is obtained, which governs the free vibration motion of the joined shell. Comparisons are made with the available data in the open literature for the case of thin conical-cylindrical-conical shells with special types of geometry or boundary conditions. Afterwards, numerical results are provided for moderately thick shells with different geometrical and boundary conditions. [ABSTRACT FROM AUTHOR]

In This article, nonlinear thermally induced vibrations of temperature-dependent functionally graded material (FGM) deep spherical shells are analyzed. One surface of the shell is kept at the reference temperature while the other one is subjected to rapid surface heating. Based on the theory of uncoupled thermoelasticity, the one-dimensional heat conduction equation across the thickness of the shell is developed and solved using the combined Crank–Nicolson method and the central finite difference method. The temperature profile obtained from the numerical solution of the heat conduction equation is used to calculate the thermal forces and the thermally induced bending moment to insert into the equations of motion of the shell. Under the assumptions of the first-order shear deformation theory (FSDT), uncoupled thermoelasticity laws, the von Kármán type of geometrical nonlinearity, and employing the Hamilton principle the axisymmetric equations of motion are obtained. The conventional multi-term polynomial Ritz method is used to discretize the governing nonlinear equations of motion. To convert the differential equations of motion into algebraic equations in each time step, the β -Newmark time marching scheme is used, and the obtained equations are solved with the help of the Newton–Raphson linearization method. In some cases, the dynamic buckling temperature is detected using the Budiansky criterion. Various numerical results are presented to analyze the effects of different parameters such as the opening angle of the shell, the thickness of the shell, and the power law index of the material composition rule. • Dynamic Snapping of FGM Spherical Shell is investigated Under Thermal Shock. • Thermally Induced Vibration Phenomenon is Explored. • Deep Shell Theory is Applied. • Material Properties are Position and Temperature Dependent. [ABSTRACT FROM AUTHOR]

Present research deals with the shear buckling behaviour of composite skew plates reinforced with aligned single walled carbon nanotubes (CNTs). Distribution of CNTs across the thickness of the skew plate are assumed to be uniform or functionally graded. Two different types of shear loads are considered. The case of rectangular shear which produces pure shear and the case of skew shear which results in a combined uniform shear and uniaxial tension/compression. Suitable for moderately thick plates, first order shear deformation plate theory is used to estimate the displacement field of the plate. The equivalent properties of the composite media are obtained by means of the refined rule of mixtures approach which contains efficiency parameters to capture the size dependent properties of the CNTs. With the aid of the Hamilton principle, transformation of the orthogonal coordinate system to an oblique one and the conventional Ritz method whose shape functions are constructed according to the Gram–Schmidt process, the stability equations of the plate are established and solved for two different types of loading, namely rectangular and skew shear loads. As shown, through introduction of a proper functionally graded pattern, i.e., FG-X pattern, the buckling load of the plate may be increased, significantly. [ABSTRACT FROM AUTHOR]

In the present research, dynamic buckling of a shallow arch subjected to transient type of thermal loading is investigated following the Budiansky–Hutchinson criterion. Arch is subjected to thermal shock on one surface while the other surface is kept at reference temperature. Transient heat conduction equation across the arch thickness is established and solved analytically. The induced bending moment and compressive thermal force are obtained and inserted into the equations of motion of the arch. To model the arch, classical arch theory suitable for thin arches is employed. The von Kármán type of strain-displacement relation suitable for small strains and large deformations is used. The governing nonlinear equations of motion are presented as the coupled nonlinear algebraic equations. These equations are established using the conventional Ritz method, where the shape functions are constructed employing the polynomial functions. The resulting equations are solved by means of the Newmark time marching scheme and the Newton–Raphson linearization technique. By means of the Budiansky criterion, critical thermal shock parameters are distinguished. Dynamic buckling temperatures are also verified using the phase-plane presentation, also known as the Hoff–Hsu criterion. It is verified that the shallow arches may undergo dynamic snap-through type of motion under rapid surface heating when certain geometrical constrains are met. [ABSTRACT FROM AUTHOR]

Present study proposes a nonlinear formulation to study the large amplitude free vibration of composite laminated plates reinforced by graphene sheets. Volume fraction of graphene sheets as reinforcements may be different in the layers. Material properties of the constituents are assumed to be temperature dependent. Properties of the composite media are obtained using a refined Halpin–Tsai approach where the auxiliary parameters are included into the formulation to capture the size dependency of the nanocomposite media. With the aid of third order shear deformation plate theory and the von Kármán type of kinematic assumptions, the basic governing equations of the plate are established. Afterwards, a non-uniform rational B-spline (NURBS) based isogeometric finite element method is used to study the large amplitude free vibration response of the graphene reinforced composite plates in thermal environment. Large amplitude frequencies as a function of centre point deflection are provided for different functionally graded patterns, aspect ratios, side to thickness ratios and boundary conditions. [ABSTRACT FROM AUTHOR]

A thermal postbuckling analysis for composite laminated plates reinforced with graphene sheets is performed in this research. All of the thermomechanical properties of the composite media are assumed to be temperature dependent. Volume fraction of the graphene in each layer is assumed to be different which results in a piecewise functionally graded plate. Based on the third order shear deformation plate theory of Reddy, the total strain energy of the plate is obtained. Composite laminated plate is assumed to be under uniform temperature rise. Properties of the graphene reinforced composite media are estimated by means of a refined Haptin-Tsai approach which contains efficiency parameters to capture the size dependency of the constituents. Afterwards, a non-uniform rational B-spline (NURBS) based isogeometric finite element method is implemented to study the thermal postbuckling response of the graphene reinforced composite laminated plates. Thermally induced postbuckling curves of the composite plate reinforced by graphene are provided for different functionally graded patterns, aspect ratios, side to thickness ratios and boundary conditions. It is shown that, FG-X pattern of graphene reinforcement results in the highest critical buckling temperature and the lowest postbuckling deflection. [ABSTRACT FROM AUTHOR]

In this investigation, the asymmetrical buckling behaviour of FGM annular plates resting on partial Winkler-type elastic foundation under uniform temperature elevation is investigated. Material properties of the plate are assumed to be temperature dependent. Each property of the plate is graded across the thickness direction using a power law function. First order shear deformation plate theory and von Kármán type of geometrical nonlinearity are used to obtain the equilibrium equations and the associated boundary conditions. Prebuckling deformations and stresses of the plate are obtained considering the deflection-less conditions. Only plates which are clamped on both inner and outer edges are considered. Applying the adjacent equilibrium criterion, the linearised stability equations are obtained. The governing equations are divided into two sets. The first set, which is associated with the in-contact region and the second set which is related to contact-less region. The resulting equations are solved using a hybrid method, including the analytical trigonometric functions through the circumferential direction and generalised differential quadratures method through the radial direction. The resulting system of eigenvalue problem is solved iteratively to obtain the critical conditions of the plate, the associated circumferential mode number and buckled shape of the plate. Benchmark results are given in tabular and graphical presentations dealing with critical buckling temperature and buckled shape of the plate. Numerical results are given to explore the effects of elastic foundation, foundation radius, plate thickness, plate hole size, and power law index of the graded plate. It is shown that, stiffness foundation, and radius of foundation may change the buckled shape of the plate in both circumferential and radial directions. Furthermore, as the stiffness of the foundation or radius of foundation increases, critical buckling temperature of the plate enhances. [ABSTRACT FROM AUTHOR]

Present investigation deals with the thermal postbuckling behaviour of a composite laminated beam where graphene is used as reinforcement of each lamina. The composite laminated beam may be piecewise functionally graded by changing the volume fraction of graphene in each lamina. Mechanical properties in each layer are obtained according to the modified Halpin-Tsai approach which contains efficiency parameters to capture the size dependency of the nanocomposite properties. Thermomechanical properties of the matrix and reinforcements are assumed to be temperature dependent. Beam is resting on an elastic foundation which acts in compression as well as in tension. The first order shear deformation beam theory and von Kármán type of geometrical nonlinearity are used as the basic assumptions to establish the total strain energy of the system. Beam is subjected to uniform temperature elevation. With the aid of conventional Ritz method and the simple polynomials as the basic functions, the matrix representation of the governing equations is derived. The adopted solution method may be used for arbitrary combinations of boundary conditions. The obtained system of equations is nonlinear in terms of both temperature and displacements. An iterative displacement control strategy is proposed to extract the thermal postbuckling curves of the beam resting on a conventional elastic foundation. Numerical results are given to discuss the effects of graphene distribution, stacking sequence, boundary conditions, side to thickness ratio and foundation stiffness on critical buckling temperature and thermal postbuckling equilibrium path of the beam. It is shown that, through a piecewise functionally graded distribution of graphene in matrix, critical buckling temperature may be enhanced significantly and thermal postbuckling deflection may be alleviated. [ABSTRACT FROM AUTHOR]

Present research aims to analyse the thermal buckling response of composite laminated plates reinforced with graphene sheets. Volume fraction of graphene in each layer may be different which results in a piecewise functionally graded material. All of the thermomechanical properties of the matrix and graphene sheets are assumed to be temperature dependent. A micromechanical approach is used to estimate the thermomechanical properties of the composite media. Using the first order shear deformation plate theory, the strain energy of the plate and the work done by the thermally induced prebuckling forces are obtained. Afterwards, a non-uniform rational B-spline (NURBS) based isogeometric finite element method is used to study the thermal buckling response of the graphene reinforced composite plates. A detailed study is provided to investigate the effects of boundary conditions, functionally graded pattern, aspect ratio and side to thickness ratio of the plate. [ABSTRACT FROM AUTHOR]

Free vibration analysis of a joined shell system composed of two conical shells is analysed in this research. It is assumed that the system of joined shell is made from a linearly elastic isotropic homogeneous material. Both shells are unified in thickness. To capture the through-the-thickness shear deformations and rotary inertias, first order theory of shells is accompanied with the Donnell type of kinematic assumptions to establish the general motion equations and the associated boundary and continuity conditions with the aid of Hamilton's principle. The resulted system of equations are discreted using the semi-analytical generalised differential quadrature (GDQ) method. Considering various types of boundary conditions for the shell ends and intersection continuity conditions, an eigenvalue problem is established to examine the vibration frequencies as well as the associated mode shapes. After proving the efficiency and validity of the present method for the case of thin isotropic homogeneous joined shells, some parametric studies are carried out for the system of combined moderately thick conical-conical. [ABSTRACT FROM AUTHOR]

Free vibration behaviour of a shear deformable conical shell with intermediate ring support is analysed in this research. It is assumed that the conical shell is made from a linearly elastic isotropic homogeneous material. To capture the through-the-thickness shear deformations and rotary inertia effects, first order shear deformation theory of shells accompanied with the Donnell type of kinematic assumptions are adopted to establish the general equations of motion and the associated boundary conditions with the aid of Hamilton's principle. The resulting system of equations are discreted using the semi-analytical generalised differential quadratures (GDQ) method. The shell is divided into two sections, where the continuity conditions are satisfied at the ring position. Considering various types of boundary conditions for the shell ends and continuity conditions at the ring position, an eigenvalue problem is established to examine the natural frequencies of the shell reinforced with an intermediate ring support. After proving the efficiency and validity of the present method for the case of thin isotropic homogeneous cylindrical shell with intermediate ring support, parametric studies are carried out for the case of shear deformable conical shells with intermediate ring support. [ABSTRACT FROM AUTHOR]

Forced vibration response of a conical panel subjected to the action of a moving load is investigated in the current research. Panel is made from a carbon nanotube (CNT) reinforced composite where the CNTs as reinforcements are distributed either uniformly or functionally graded across the panel thickness. Panel is formulated using the first order shear deformation shell theory and the Donnell kinematic assumptions. It is subjected to a moving load whose path and velocity are both arbitrary. The properties of the composite media are estimated according to a refined rule of mixtures approach. The governing equations of motion of the shell are obtained according to the Ritz method where the shape functions are obtained according to the Gram-Schmidt process. The developed equations with the aid of Ritz method are transformed into time-dependent ordinary differential equations whose solution is traced in time by means of the Newmark time marching scheme. Numerical results are provided to explore the influences of semi-vertex and opening angles of the cone, geometrical parameters and also CNT characteristics of the shell. It is shown that, dynamic deflection of the shell decreases significantly with the introduction of FG-X pattern of CNTs. Furthermore, enrichment of the matrix with more CNTs alleviates the dynamic deflection of the conical shell. [ABSTRACT FROM AUTHOR]

In this investigation, the asymmetrical buckling behavior of isotropic homogeneous annular plates resting on a partial Winkler-type elastic foundation under uniform temperature elevation is investigated. First-order shear deformation plate theory is used to obtain the governing equations and the associated boundary conditions. Prebuckling deformations and stresses of the plate are obtained under the solution of a plane stress formulation, neglecting the rotations and lateral deflection. Applying the adjacent equilibrium criterion, the linearized stability equations are obtained. The governing equations are divided into two sets. The first set, which is associated with the in-contact region, and the second set, which is related to contact-less region. The resulting equations are solved using a hybrid method, including the analytical trigonometric functions through the circumferential direction and generalized differential quadratures method through the radial direction. The resulting system of eigenvalue problem is solved to obtain the critical conditions of the plate and the associated circumferential mode number. Benchmark results are given in tabular and graphical presentations for combinations of simply supported and clamped types of boundary conditions. Numerical results are given to explore the effects of elastic foundation, foundation radius, plate thickness, plate hole size, and the boundary conditions. [ABSTRACT FROM PUBLISHER]

The present research deals with the nonaxisymmetric buckling behaviour of isotropic homogeneous annular plates subjected to simultaneous effects of uniform temperature rise and constant angular speed. First-order shear deformation plate theory is used to obtain the complete set of governing equations and the associated boundary conditions. Pre-buckling deformations and stresses of the plate are obtained using the solution of a plane stress formulation, neglecting the rotations and lateral deflection. Applying the adjacent equilibrium criterion, the linearised stability equations are obtained. The resulting equations are solved using a hybrid method, including the exact trigonometric functions through the circumferential direction and generalised differential quadrature method through the radial direction. The resulting eigenvalue problem is solved to obtain the critical conditions of the plate and the associated circumferential mode number. Numerical results reveal that, only for annular plates with exterior edge clamped, rotation may enhance the critical buckling temperature of a plate under special circumstances. Furthermore, asymmetric stability analysis should be performed to extract the critical state and buckled shape of a rotating annular plate subjected to uniform heating. Otherwise, the critical buckling temperature is overestimated and the buckling pattern is wrongly predicted. [ABSTRACT FROM AUTHOR]

It is known that the distribution of stresses in a rectangular plate is the same as the applied stresses on the boundaries when the loading is uniform or linearly varying. For other types of compressive loads, for instance parabolic compressive loading, the distribution of stresses in the plate is different from the applied loads at the boundaries of the plate. For such conditions, to obtain the buckling loads of the plate, an accurate prebuckling analysis should be performed. The present research aims to obtain the buckling loads and buckling pattern of composite plates reinforced with carbon nanotubes with uniform or functionally graded distribution across the plate thickness. The properties of the composite media are obtained based on a modified rule of mixtures approach with the introduction of efficiency parameters. First-order shear deformation plate theory is used to approximate the plate kinematics. The plate is subjected to uniaxial compressive loads which vary as parabolic functions across the width of the plate. At first, using the Ritz method and Airy stress function formulation, the distribution of stress resultants in the plate domain is obtained as a two-dimensional elasticity formulation. Afterwards, by means of the Chebyshev polynomials as the basic functions of the Ritz solution method, an eigenvalue problem is established to obtain the buckling load and buckling shape of the plate. Comparison studies are provided to assure the accuracy of the presented formulation for isotropic homogeneous and cross-ply laminated plates. Afterwards, parametric studies are performed for composite plates reinforced with carbon nanotubes. [ABSTRACT FROM AUTHOR]

Thermal postbuckling analysis and the axisymmetric static and dynamic snap-through phenomena due to static/sudden uniform lateral pressure in a thermally postbuckled functionally graded material circular plate are performed in this research. Plate is formulated using the first order shear deformation plate theory. Thermo-mechanical properties of the plate are assumed to be temperature dependent where dependency is described according to the higher order Touloukian representation. Two types of temperature loading are considered. Uniform temperature rise and heat conduction across the thickness direction. The one dimensional heat conduction equation in the thickness direction is obtained and discreted via the central finite difference method. The obtained system of equations is nonlinear since the thermal conductivity itself is a function of the unknown nodal temperatures. Using the von-Kármán assumptions, the governing equations of the plate are obtained in a matrix representation with the aid of the conventional Ritz method whose shape functions are developed using the Gram-Schmidt process. At first thermal postbuckling analysis is performed which is a nonlinear problem with respect to both temperature and displacements. Afterwards, response of the bulged thermally postbuckled plate is obtained under the static and dynamic uniform pressure. Snap-through phenomenon may be observed in both static and dynamic loading cases, due to the immovability of the edge of the plate and the initial deflection caused by postbuckling deflection. To capture the snapping phenomenon and trace the path beyond the limit loads, cylindrical arch-length technique is used. In dynamic snap-through analysis, the effect of structural damping is also included. Numerical results of this study reveal that the structure is sensitive to the initial deflection caused by thermal postbuckling load. Increasing the temperature prior to mechanical loads enhances the snap-through intensity and also increases both the upper and lower limit loads. As shown, dynamic snap-through loads are lower than the static ones, however dynamic snap-through intensity is more than the static snap-though intensity. Furthermore, structural damping enhances the dynamic buckling loads of the plate and decreases the dynamic postbuckling deflection of the plate. [ABSTRACT FROM AUTHOR]

Present research deals with the postbuckling problem of carbon nanotube reinforced composite plates subjected to uniform temperature rise loading. Distribution of carbon nanotubes as reinforcements may be uniform or functionally graded. To account for the large deformations of the plate, von-Kármán type of geometrical nonlinearity is included into the formulation. The virtual displacements principle associated with the conventional Ritz formulation whose shape functions are selected as the Chebyshev polynomials is used to obtain the matrix representation of the nonlinear equilibrium equations. The solution method is general and may be used for arbitrary combination of boundary conditions. The postbuckling equilibrium path which is governed by a nonlinear eigenvalue problem is traced using a displacement control strategy. Results of this study are compared with the available data in the open literature for the cases of isotropic homogeneous plates and cross-ply laminated plates. Afterwards numerical results are given for FG-CNTRC plates. It is shown that, FG-X pattern results in higher buckling temperature and also decreases the postbuckling deflection of the plate. Furthermore, this type of composites are eager to exhibit the secondary instability which is designated with a snap-through phenomenon in the post-buckling equilibrium path. [ABSTRACT FROM AUTHOR]

Free vibration characteristics of carbon nanotube reinforced composite spherical panels are studied in the present research. First order shear deformation shell theory and the Sanders kinematics are considered as the basic assumptions. Distribution of carbon nanotubes (CNTs) across the panel thickness may be uniform or functionally graded. Equivalent properties of the media are estimated according to a modified rule of mixtures approach which consists efficiency parameters to capture the size dependency of the properties. Using Hamilton’s principle and the conventional Ritz formulation, the matrix representation of the equations associated with the free vibration motion is obtained. Shape functions of the Ritz method are obtained according to the Gram-Schmidt process. The resulting eigenvalue problem is solved to obtain the frequencies as well as mode-shapes of the spherical panel reinforced with CNTs. Convergence and comparison studies are provided to assure the effectiveness and accuracy of the proposed method. Afterwards, parametric studies are given to explore the effects of volume fraction of CNTs, distribution pattern of CNT, boundary conditions and geometric characteristics of the panel. It is shown that, enrichment of the polymeric matrix with more CNT results in higher frequencies. Furthermore, graded pattern of CNT is an influential factor on frequencies. [ABSTRACT FROM AUTHOR]

Thermoelastic analysis of an isotropic homogeneous layer within the framework of Lord-Shulman theory of generalized thermoelasticty is performed in this research. Two coupled partial differential equations, namely; the energy and equation of motion are established. The energy equation is kept in its original nonlinear form and the assumption made in previous investigations to linearize the energy equation is not established in the present work. The two coupled equations are presented in terms of axial displacement and temperature change. These equations are then transformed into a dimensionless presentation and discretised via the generalized differential quadrature method. The resulting equations are traced in time by means of the well-known β − Newmark time marching scheme and solved iteratively at each time step. After validating the proposed approach and solution method for the case of thermally linear, a set of parametric studies are carried out to explore the effects of thermal shock magnitude, relaxation time, and the coupling parameter. It is shown that thermally nonlinear theory governs when thermal shock is severe, relaxation time is large, or coupling parameter is large. [ABSTRACT FROM AUTHOR]

Shear buckling response of carbon nanotube reinforced composite (CNTRC) rectangular plates in thermal environment is investigated in this research. Distribution of CNTs across the plate thickness may be uniform or graded via a mid-plane symmetric pattern. Properties of the CNTRC plate are obtained using the modified rule of mixtures approach by introduction of efficiency parameters. First order plate theory is adopted to construct the basic equations of the plate. A two-dimensional Ritz formulation with Chebyshev basis polynomials is implemented to obtain the elastic and geometric stiffness matrices of the plate. The proposed solution method may be used for arbitrary in-plane and out-of-plane edge supports. After performing convergence and comparison studies to show the effectiveness and accuracy of the proposed method, parametric studies are conducted to examine the influences of boundary conditions, volume fraction of CNTs, graded pattern of CNTs, thermal environment and plate geometry. It is shown that, shear buckling capacity of the plate may be enhanced through functionally graded distribution of CNTs. Besides, enrichment of matrix with CNTs enhances the shear buckling loads of FG-CNTRC plates. [ABSTRACT FROM AUTHOR]