Showing papers on "Plate theory published in 2022"

Static bending and buckling analysis of bi-directional functionally graded porous plates using an improved first-order shear deformation theory and FEM

Abstract: The static bending and buckling behaviors of bi-directional functionally graded (BFG) plates with porosity are investigated in this paper. An improved first-order shear deformation theory with an assuming parabolic distribution shear stresses is developed to describe the displacement, strain, and stress fields of the plates. The significant novelty of the proposed theory is that the transverse shear stresses equal to zero at two free surfaces of the BFG plates. Therefore, no shear correction factor is required as in other first-order shear deformation theory. A four-node quadrilateral plate element (IMQ4) is developed based on the improved first-order shear deformation theory, mixed finite element method (FEM) and Hamilton's principle for analysis of BFG plates. Several comparison studies are provided to demonstrate the precision and robustness of the proposed plate element IMQ4. Then the proposed plate element, IMQ4, is employed to analyze the bending and buckling responses of the BFG plates. Some new numerical results on the flexural and buckling behaviors of BFG plates are achieved via a deep parametric study.

Influence of the visco-Pasternak foundation parameters on the buckling behavior of a sandwich functional graded ceramic–metal plate in a hygrothermal environment

Abstract: This study presents the buckling response of functionally graded (FG) “sandwich plate” on a viscoelastic foundation and exposed to hygrothermal conditions. An accurate solution is developed using higher-order shear deformation theory (HSDT), with only four unknowns being placed to reach the solution. The displacement fields first utilize an indeterminate integral accompanied by a sinusoidal shape function to simulate the transverse shear deformation theory. The foundation’s mathematical model followed the two-Pasternak coefficient model, with one more term being added to represent the damping effect. The sandwich plate is essentially composed of three layers. This study presented three different FG sandwich plate geometric analytical solutions regarding layer orders and composition. The equations of motion were generated according to Hamilton’s principle. Thereafter, the analytical solution was based on Navier’s principle to solve the buckling temperature of a simply supported FG sandwich plate seated on a viscoelastic foundation. This paper shows a parametric study of the effect of the damping coefficient along with the aspect ratio, moisture condition, power-law index, and temperature variation over the buckling temperature of the FG “sandwich plate” on the viscoelastic foundation. • Effect of visco-Pasternak foundation on buckling response of FG plate is studied. • An efficient analytical approach is developed for buckling analysis. • Original integral shear deformation model has been used. • Influences of geometry, hygrothermal conditions and damping coefficient are explored.

Influence of the visco-Pasternak foundation parameters on the buckling behavior of a sandwich functional graded ceramic–metal plate in a hygrothermal environment

Abstract: This study presents the buckling response of functionally graded (FG) “sandwich plate” on a viscoelastic foundation and exposed to hygrothermal conditions. An accurate solution is developed using higher-order shear deformation theory (HSDT), with only four unknowns being placed to reach the solution. The displacement fields first utilize an indeterminate integral accompanied by a sinusoidal shape function to simulate the transverse shear deformation theory. The foundation’s mathematical model followed the two-Pasternak coefficient model, with one more term being added to represent the damping effect. The sandwich plate is essentially composed of three layers. This study presented three different FG sandwich plate geometric analytical solutions regarding layer orders and composition. The equations of motion were generated according to Hamilton’s principle. Thereafter, the analytical solution was based on Navier’s principle to solve the buckling temperature of a simply supported FG sandwich plate seated on a viscoelastic foundation. This paper shows a parametric study of the effect of the damping coefficient along with the aspect ratio, moisture condition, power-law index, and temperature variation over the buckling temperature of the FG “sandwich plate” on the viscoelastic foundation.

Analytical solutions for nonlinear vibration of porous functionally graded sandwich plate subjected to blast loading

Abstract: This paper presents the nonlinear vibration of porous functionally graded sandwich plate on elastic foundations subjected to blast loading by the analytical approach. The sandwich plate consists of two FGM face sheets and a homogeneous core which is made from metal or ceramic. Two types of porosity distribution, including evenly and unevenly distributed porosity have been considered for sandwich plate. The material properties of sandwich plate are assumed to vary in the thickness direction according to simple power law distribution with a volume fraction index and a porosity coefficient. The blast loading is assumed to be uniformly distributed on the surface of the sandwich plate and modeled by an exponential function. The Reddy’s higher order shear deformation theory with von Kármán type nonlinearity is used to establish governing equations for the vibration of sandwich plate. By applying Galerkin and fourth-order Runge–Kutta methods, the numerical results show the effects of volume fraction index, porosity coefficient, type of porosity distribution, geometrical parameters, elastic foundations and parameters of blast loading on the nonlinear vibration of the sandwich plate. Comparisons are conducted to evaluate the reliability of the obtained results.

Analytical solutions for nonlinear vibration of porous functionally graded sandwich plate subjected to blast loading

Abstract: This paper presents the nonlinear vibration of porous functionally graded sandwich plate on elastic foundations subjected to blast loading by the analytical approach. The sandwich plate consists of two FGM face sheets and a homogeneous core which is made from metal or ceramic. Two types of porosity distribution, including evenly and unevenly distributed porosity have been considered for sandwich plate. The material properties of sandwich plate are assumed to vary in the thickness direction according to simple power law distribution with a volume fraction index and a porosity coefficient. The blast loading is assumed to be uniformly distributed on the surface of the sandwich plate and modeled by an exponential function. The Reddy’s higher order shear deformation theory with von Karman type nonlinearity is used to establish governing equations for the vibration of sandwich plate. By applying Galerkin and fourth-order Runge–Kutta methods, the numerical results show the effects of volume fraction index, porosity coefficient, type of porosity distribution, geometrical parameters, elastic foundations and parameters of blast loading on the nonlinear vibration of the sandwich plate. Comparisons are conducted to evaluate the reliability of the obtained results.

Nonlinear Free Vibration Analysis of In-plane Bi-directional Functionally Graded Plate with Porosities Resting on Elastic Foundations

Abstract: This paper deals with the nonlinear free vibration analysis of in-plane bi-directional functionally graded (IBFG) rectangular plate with porosities which are resting on Winkler–Pasternak elastic foundations. The material properties of the IBFG plate are assumed to be graded along the length and width of the plate according to the power-law distribution, as well as, even and uneven types are taken into account for porosity distributions. Equations of motion are developed by means of Hamilton’s principle and von Karman nonlinearity strain–displacement relations based on classical plate theory (CPT). Afterward, the time-dependent nonlinear equations are derived by applying the Galerkin procedure. The nonlinear frequency is determined by using modified Poincare–Lindstedt method (MPLM). Numerical results are obtained in tabular and graphical form to examine the effects of some system key parameters such as porosity coefficients, distribution patterns, gradient indices, elastic foundation coefficients, aspect ratio and vibration amplitude on the nonlinear frequency of the porous IBFG plate. To validate the analysis, the results of this paper have been compared to the published data and good agreements have been found.

Static buckling analysis and geometrical optimization of magneto-electro-elastic sandwich plate with auxetic honeycomb core

Abstract: The nonlinear static buckling analysis of magneto-electro-elastic sandwich plate on Pasternak-type elastic foundations subjected to the mechanical, thermal, electric and magnetic loadings is presented in this paper. The sandwich plate is composed of an auxetic honeycomb core with negative Poisson’s ratio and two face sheets made of magneto-electro-elastic​ material. The system basic equations are derived based on the Reddy’s higher order shear deformation plate theory taking into account the effect of von Kármán the kinematic nonlinearity and initial imperfection. The form of possible solutions and electric, magnetic potentials are chosen as trigonometric functions based on two cases of boundary conditions. The relationship between axial compressive loading and dimensionless deflection amplitude is determined by using the Galerkin method. For optimization problem, the Bees algorithm is applied to obtain the maximum value of critical buckling load of the sandwich plate which depends on five geometrical and material parameters. The effects of elastic foundations, temperature increment, geometrical parameters and electric and magnetic potentials on the stability characteristics are investigated in numerical results. The accuracy and reliability of present approach is confirmed by comparisons with the existing results in the literature.

Static and vibration response analysis of sigmoid function-based functionally graded piezoelectric non-uniform porous plate

Abstract: This paper has done static and vibration response analysis of the sigmoid functionally graded piezoelectric (S-FGP) tapered plate under thermo-electric load with different even/uneven type porosity. The governing equations of plate motion are derived using first-order shear deformation theory (FSDT) based displacement fields with Hamilton’s principle, and material property distribution is considered as per sigmoid law in the thickness direction of the FGP plate. The obtained governing equations are solved using the higher-order finite element method (FEM) with nine noded interpolation functions with 63 degrees of freedom (DOFs) per element. Convergence and the comparison study have been performed to exhibit the efficacy of the present study. It is observed that parameters like the non-dimensional center deflection, non-dimensional stress, and non-dimensional frequency are decreased as the material gradient index increases. The positive and negative types of electric loading have considerable effects on the pre/post type buckling configuration of the porous S-FGP tapered plate under thermal effect. The present analysis results can be used in the various smart structure application made of porous FGP materials.

Size-Effect Analysis on Vibrational Response of Functionally Graded Annular Nano-Plate Based on Nonlocal Stress-Driven Method

Abstract: Dynamic analysis of functionally graded size-dependent annular nano-plate is the main concern in this study. To obtain the vibrational behavior of this plate, the stress-driven nonlocal integral elasticity, as well the strain gradient theory were used in conjunction with the classical plate theory. The resulting equilibrium equations were solved using the generalized differential quadrature rule (GDQR) and the influences of various parameters such as; size-effect parameter, material heterogeneity index, the aspect ratio of the inner to outer radii, and the effects of different boundary conditions were investigated on the vibrational behavior of the nano-plate, based on different types of boundary conditions. Results indicate that the natural frequencies increase with an increase in the heterogeneity index [Formula: see text] and the increase in size-effect parameter shows a similar effect in both models. Additionally, for the simply supported and free-edge boundary conditions (for both edges), as well as the free and knife-edges, and simply supported-free edges, the strain gradient theory predicts higher values of frequency ratios as [Formula: see text] was increased. Similar results were obtained for the remaining types of boundary conditions, with a higher sensitivity to [Formula: see text], provided the stress-driven model is used. This behavior can be interpreted as the sensitivity of the nano-plate to [Formula: see text] that is manifested by the use of the stress-driven model for the prediction of vibrational behavior of the nano-plate.

Active Vibration Control of Piezoelectric Sandwich Plates

Abstract: This paper deals with the active vibration control of piezoelectric sandwich plate. The structure consists of a substrate plate layer sandwiched between two layers of piezoelectric sensor and actuator. Based on laminate theory and constitutive equation of piezoelectric material, the vibration active control dynamic equation of the sandwich structure is established by using hypothetical mode method and Hamilton principle. The Rayleigh-Ritz method is used to solve it. The form of hypothetical solution is used for approximate solution, which is simple and accurate. The method of this paper is verified by several examples. The parametric studies of the sandwich plate structures are carried out. The results show that applying different boundary conditions and piezoelectric patch positions to the structures have a great influence on the natural frequency. When the driving voltage increases, the deflection of the plate structures increase approximately linearly. The active vibration control studies are investigated as well. The results show that within a certain range, the larger the value of the speed feedback coefficient, the better the active control effect. The positions of the piezoelectric patches affect the effectiveness and cost of active control. When the piezoelectric plate is located at the fixed end, the effect and cost of active control are better than that at the midpoint and free end of the plate.

Exact Three-Dimensional Stability Analysis of Plate Using an Direct Variational Energy Method

Abstract: In this paper, direct variational calculus was put into practical use to analyses the three dimensional (3D) stability of rectangular thick plate which was simply supported at all the four edges (SSSS) under uniformly distributed compressive load. In the analysis, both trigonometric and polynomial displacement functions were used. This was done by formulating the equation of total potential energy for a thick plate using the 3D constitutive relations, from then on, the equation of compatibility was obtained to determine the relationship between the rotations and deflection. In the same way, governing equation was obtained through minimization of the total potential energy functional with respect to deflection. The solution of the governing equation is the function for deflection. Functions for rotations were obtained from deflection function using the solution of compatibility equations. These functions, deflection and rotations were substituted back into the energy functional, from where, through minimizations with respect to displacement coefficients, formulas for analysis were obtained. In the result, the critical buckling loads from the present study are higher than those of refined plate theories with 7.70%, signifying the coarseness of the refined plate theories. This amount of difference cannot be overlooked. However, it is shown that, all the recorded average percentage differences between trigonometric and polynomial approaches used in this work and those of 3D exact elasticity theory is lower than 1.0%, confirming the exactness of the present theory. Thus, the exact 3D plate theory obtained, provides a good solution for the stability analysis of plate and, can be recommended for analysis of any type of rectangular plates under the same loading and boundary condition. Doi: 10.28991/CEJ-2022-08-01-05 Full Text: PDF