Search

The mechanical and thermal stability equations of asymmetric functionally graded discs subjected to the Pasternak foundation are developed by employing Hamilton’s energy principle based on the first-order shear theory. The material properties are temperature-dependent and vary according to power-law and exponentially in thickness and radial direction, respectively. Accordingly, the temperatu re is also varying in both directions. Using the well-developed differential quadrature method, stability equations are discretized along with the boundary conditions, leading to a complete algebraic linear equations system. The validation of results is performed to certify the results. Numerical and illustrative results are presented to study the effect of elastic foundation parameters, graded indexes, nodal lines, and boundary conditions on thermal and mechanical buckling. Also, the impact of compressive in-plane force on thermal buckling and thermal environment on mechanical buckling is presented. [ABSTRACT FROM AUTHOR]

Analysis and numerical results for the axisymmetric vibrations of non-uniform two-dimensional functionally graded circular plates subjected to two-directional temperature distribution are presented on the basis of the exact neutral surface and Mindlin plate theory. The mechanical properties of the plate material are supposed to be temperature-dependent and graded in thickness as well as in radial direction. Based on the thermal boundary conditions, a classical solution of the two-directional heat conduction equation is obtained by the separation of variables method. Equations for thermoelastic equilibrium and axisymmetric motion of the plate are derived in the framework of Hamilton's principle. The numerical solution of these equations is carried out by the generalized differential quadrature method to compute the thermally induced displacements and natural frequencies using MATLAB. The lowest three values are reported as the frequency parameter for the first three modes of clamped and simply-supported plates. To show the influence of the exact neutral surface, taper parameters, material graded index, heterogeneity and density parameter, numerical results are presented. Mode shapes are plotted for the specified plates. [ABSTRACT FROM AUTHOR]

Up to now, no studies have been yet reported to study the mechanical behaviors of three-dimensional functionally graded graphene platelets reinforced composite (FG-GPLRC) open-type panel. In this paper, the free vibration of FG-GPLRC open-type panel under multi-directional initially stressed using three-dimensional poroelasticity theory is investigated for the first time. Weight fraction of graphene open-type panel is assumed to be distributed either uniformly or functionally graded (FG) along the radial direction. Modified Halpin–Tsai model is used to compute effective Young's modulus, whereas effective Poisson's ratio and mass density are computed using the rule of mixture. State-space differential equations are derived from the governing equation of motion and constitutive relations in cylindrical co-ordinates. The accuracy of the obtained formulation is validated by comparing the numerical results with those reported in the available literature as well as with the finite-element modeling. The influences of several importance parameters, such as various directional initial stress, compressibility coefficient, porosity, and various type of sandwich open-type cylindrical panel, are investigated on the frequency of the structures. The results of the present study can be served as benchmarks for future mechanical analysis of cylindrical FG-GPLRC structures. [ABSTRACT FROM AUTHOR]

In this paper, analytical and numerical solutions are presented for computing mechanical displacements and stresses in a thick-walled cylindrical made of functionally graded materials (FGMs) under mechanical and thermal loadings. The elastic modulus and thermal conductivity are assumed to vary in the radial direction, and the Poisson's ratio is assumed constant. Navier's ordinary second-order differential equation derived from the mechanical equilibrium equation was solved to obtain the exact solution of the displacement and stress distributions. Furthermore and in order to validate the accuracy of the analytical solution, a numerical model was construct using the finite element method. Very good agreement has been found between the analytical formulation and the predictions of numerical simulation which confirms the accuracy of the model in the case of a thick-walled tube made of FGM under steady state temperature distribution and a mechanical loading. These results clarify the influence of the thermal field, non-homogeneity parameter and internal pressure on the thermo-elastic response of the functionally graded cylindrical vessel. [ABSTRACT FROM AUTHOR]

The present article investigates the axisymmetric vibrations of non-uniform bi-directional functionally graded rings under two-dimensional temperature distribution on the basis of first-order shear deformation theory. The linear variation of thickness along the radial direction is controlled by a taper parameter. The temperature-dependent mechanical properties are assumed to be graded in thickness as well as radial direction. The separation of variables method is applied to obtain the classical solution of two-dimensional heat conduction equation by imposing the thermal boundary conditions. The governing differential equations of thermoelastic equilibrium and axisymmetric motion together with boundary conditions are extracted from Hamilton's principle. The quadrature technique is used to obtain the frequency equations and then the lowest three roots of these equations are calculated by MATLAB. After validating the results for the present approach, numerical results are given to analyze the effects of thermal environment, taper parameter, volume fraction index, heterogeneity and density parameters on the frequency parameter. Mode shapes for the specified rings are illustrated. • Axisymmetric free vibration analysis is presented for moderately thick FG rings. • Two-dimensional material and temperature variation are obtained and used. • Linear variation of thickness is assumed. • Generalized DQM and HDQM is employed to solve the developed mathematical model. [ABSTRACT FROM AUTHOR]

In this article, the size-dependent thermal buckling analysis of nonuniform functionally graded asymmetric circular and annular nanodiscs is presented on the basis of Kirchhoff's plate theory, Eringen's nonlocal elasticity theory, and physical neutral plane. For the first time, the nonlocal regularity conditions and boundary conditions are obtained for the asymmetric discs. The thickness of the nanodiscs is assumed to be varying linearly and parabolically in the radial direction. The Power-law model is adopted to compute the temperature-independent effective mechanical properties of the functionally graded materials (FGMs). The size-dependent stability equation is obtained from Euler-Lagrange's equation which is derived from Hamilton's principle. This equation and corresponding boundary conditions are discretized by the differential quadrature method (DQM) and provide an eigenvalue problem. The numerical value of the lowest eigenvalue is reported as a critical temperature difference on the surfaces of the nanodiscs. The effects of various parameters such as nonlocal parameter, volume fraction index, nodal lines, and taper parameters for thickness variations are studied. • Asymmetric thermal stability analysis is presented for FG circular and annular nanodisc. • Non-local regularity and boundary conditions are obtained. • Linear and parabolic thickness variation is assumed. • Differential quadrature method is employed to solve the mathematical model. [ABSTRACT FROM AUTHOR]

In the current study, the stability of a functionally graded annular plate reinforced with a limited content of graphene platelets (FG-GPLRC) resting on a two-parameter elastic foundation is investigated. The structure is under the coincident effect of radial compressive forces and inertial load due to angular velocity. It is considered that the GPL nanofillers are randomly oriented, and their weight fraction varies with a layer-wise pattern through the thickness direction. The equivalent Young's modulus and other material properties of the annular FG-GPLRC plate are evaluated by utilizing the Halpin–Tsai micromechanics rule. It is considered that the plate is resting on a two-parameter elastic foundation. The governing equations are extracted based on the first-order shear deformation theory (FSDT) and the von-Kármán type of geometric nonlinearity. Applying the virtual work principle and the adjacent equilibrium standard, the plate's equations of stability are established. The derived governing equations are solved using a combined analytical–numerical (TE-GDQ) method, including trigonometric expansion in the circumferential direction and the generalized differential quadratures method through the radial direction. Comprehensive novel numerical results is derived to evaluate the effect of weight fraction of nanoparticles, the type of FGM, geometric dimensions, various boundary conditions, and surrounding elastic foundation on the buckling behavior of the plate. • Mechanical and rotating bifurcation stability of annular plates reinforced with GPL. • GDQ method to obtain the response of governing equilibrium equations. • Second-order correlation homogenization technique to extract effective properties. • FSDT and von-Karman nonlinear relations to obtain the equilibrium equations. • The adjacent equilibrium criterion to distinguish the primary and secondary. [ABSTRACT FROM AUTHOR]