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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]

This research examines the application of finite strain theory to the generalized coupled thermoelasticity of isotropic 1D structures. The energy equation is derived based on the Lord-Shulman theorem to adapt to the temperature behavior of the structure due to rapid heating. Furthermore, the thermally nonlinear concept is utilized because the variation between the structure temperature and the reference temperature compared to the reference temperature cannot be overlooked. The nonlinear theory of finite strain is employed in the equation of motion, which is ideal for large deformations and rotations in the configuration. The second Piola-Kirchhoff stress and the Green-Lagrangian strains are applied in the formulation. Two nonlinear coupled partial differential equations of energy and dynamic are displayed in nondimensional version for better interpretation. Next, these equations are turned into discrete ordinary differential time-dependent equations through the generalized differential quadrature method. Newmark time marching integration methods and Picard iterative algorithm solve the resulting nonlinear equations. After validating the results with available papers, the effect of various nonlinearities, boundary conditions, and other parameters on the temporal evolution and wave propagation of deformation, temperature, and stress is investigated. It is demonstrated that the effect of nonlinear terms remarkably depends on the material type. The authors also show that utilizing the nonlinear formulation can change the wavefront speed of displacement, temperature, and stress in the domain. • Coupled thermoelasticity based on the finite strain and thermally nonlinear theories. • Lord-Shulman second-sound concept to formulate the energy equation. • Hybrid GDQ, Newmark, and Picard methods to solve nonlinear PDEs. [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]