Characterization of the vibration, stability and static responses of graphene-reinforced sandwich plates under mechanical and thermal loadings using the refined shear deformation plate theory

An analytical investigation was carried out to assess the free vibration, buckling and deformation responses of simply-supported sandwich plates. The plates constructed with graphene-reinforced polymer composite (GRPC) face sheets and are subjected to mechanical and thermal loadings while being simply-supported or resting on different types of elastic foundation. The temperature-dependent material properties of the face sheets are estimated by employing the modified Halpin-Tsai micromechanical model. The governing differential equations of the system are established based on the refined shear deformation plate theory and solved analytically using the Navier method. The validation of the formulation is carried out through comparisons of the calculated natural frequencies, thermal buckling capacities and maximum deflections of the sandwich plates with those evaluated by the available solutions in the literature. Numerical case studies are considered to examine the influences of the core to face sheet thickness ratio, temperature variation, Winkler- and Pasternak-types foundation, as well as the volume fraction of graphene on the response of the plates. It will be explicitly demonstrated that the vibration, stability and deflection responses of the sandwich plates become significantly affected by the aforementioned parameters.

Static Bending Analysis of Auxetic Plate by FEM and a New Third-Order Shear Deformation Plate Theory

In this paper, a finite element method (FEM) and a new third-order shear deformation plate theory are proposed to investigate a static bending model of auxetic plates with negative Poisson’s ratio. The three – layer sandwich plate is consisted of auxetic honeycombs core layer with negative Poisson’s ratio integrated, isotropic homogeneous materials at the top and bottom of surfaces. A displacement-based finite element formulation associated with a novel third-order shear deformation plate theory without any requirement of shear correction factors is thus developed. The results show the effects of geometrical parameters, boundary conditions, uniform transverse pressure on the static bending of auxetic plates with negative Poisson’s ratio. Numerical examples are solved, then compared with the published literatures to validate the feasibility and accuracy of proposed analysis method. Keywords: Static bending; New third-order shear deformation plate theory; Auxetic material.

Applying isogeometric approach for free vibration, mechanical, and thermal buckling analyses of functionally graded variable-thickness blades

This article presents free vibration and buckling analyses of functionally graded blades with variable thickness subjected to mechanical and thermal loading using isogeometric analysis as a powerful numerical method. The proposed method is based on deployment of Hamilton’s principle to the two-dimensional kinematics of blades. The governing equations are derived in the context of a modified form of higher order shear deformation plate theory that merely needs C0-continuity (C0-higher order shear deformation plate theory). Without the necessity of defining a shear correction factor, the theory can accurately predict the solution for different thickness-to-length ratios. The numerical predictions for the buckling loads and natural frequencies are successfully compared with the available solutions in the published articles and in the lack of relevant results, finite element analysis using ANSYS is used for verification of the model. The effects of variable thickness and aspect ratio on the natural frequencies and mode shapes known as the frequencies loci veering phenomena are assessed for the first time, which is an important design factor for the blades. The proposed method uses non-uniform rational B-spline element, which is able to approximate linear and nonlinear thickness distribution and the couple modes with an excellent numerical consistency. The influences of aspect ratio, thickness variation, taper ratio, volume fraction exponent, and boundary conditions on the free vibration and buckling of variable-thickness functionally graded blades are also examined.

Free Vibration Analysis of Simply Supported P-FGM Nanoplate Using a Nonlocal Four Variables Shear Deformation Plate Theory

This paper shows an analysis of the free vibration of functionally graded simply supported nanoplate. The nonlocal four variables shear deformation plate theory is used to predict the free vibration frequencies of functionally graded nanoplate simply supported using non-local elasticity theory with the introduction of small-scale effects. The effect of the material properties, thickness-length ratio, aspect ratio, the exponent of the power law, the vibration mode is presented, the current solutions are compared to those obtained by other researchers. Equilibrium equations are obtained using the virtual displacements principle. P-FGM Power law is used to have a distribution of material properties that vary across the thickness. The results are in good agreement with those of the literature.