Showing papers on "Plate theory published in 2013"

Isogeometric analysis of functionally graded plates using higher-order shear deformation theory

Abstract: This paper presents a novel and effective formulation based on isogeometric approach (IGA) and higher-order deformation plate theory (HSDT) to study the behavior of functionally graded material (FGM) plates. HSDT model using C1 continuous element is able to improve the accuracy of solution and describe exactly the shear stress distribution without shear correction factors. IGA utilizes the non-uniform rational B-spline (NURBS) functions which allow us to achieve easily the smoothness with arbitrary continuity order. The present method hence fulfills the C1 – requirement of HSDT model. The effective material properties of the FGM plates, which property varies only through the thickness of plate, are calculated using the rule of mixture and the Mori–Tanaka homogenization technique. The static, dynamic and buckling analysis of rectangular and circular plates is investigated for different boundary conditions. Numerical results show high effectiveness of the present formulation.

A size-dependent functionally graded Reddy plate model based on a modified couple stress theory

Abstract: In this paper, a size-dependent model for bending and free vibration of functionally graded Reddy plate is developed The present model accounts for both small scale and shear deformation effects in functionally graded microplates The small scale effects are captured using the modified couple stress theory, while the shear deformation effects are included using the third-order shear deformation theory The equations of motion and boundary conditions are derived from Hamilton’s principle Analytical solutions are obtained for a simply supported plate Numerical examples are presented to illustrate the effects of small scale on the responses of microplates The results reveal that the inclusion of small scale effects results in an increase in plate stiffness, and consequently, leads to a reduction of deflection and an increase in frequency Such small scale effects are significant when the plate thickness is small, but become negligible with increasing plate thickness

A new higher-order shear and normal deformation theory for the static and free vibration analysis of sandwich plates with functionally graded isotropic face sheets:

Abstract: In this paper, a new higher-order shear and normal deformation theory for the bending and free vibration analysis of sandwich plates with functionally graded isotropic face sheets is developed. The number of unknown functions involved in the present theory is only five, as against six or more in case of other shear and normal deformation theories. The theory accounts for hyperbolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factor. The boundary conditions for the plate are assumed to be simply supported in all edges and in the static analysis, the plate is assumed to be subjected to a sinusoidally distributed load. Both symmetric and non-symmetric sandwich plates are considered. The equations of motion are obtained using Hamilton’s principle. Numerical results of present theory are compared with three-dimensional elasticity solutions and other higher-order theories reported in the literature. ...

An exact solution for thermal buckling of annular FGM plates on an elastic medium

Abstract: The buckling of heated functionally graded material (FGM) annular plates on an elastic foundation is studied analytically. A conventional Pasternak-type elastic foundation is assumed to be in contact with plate during deformation, which acts in both compression and tension. The equilibrium equations of an annular-shaped plate are obtained based on the classical plate theory. Each thermo-mechanical property of the plate is assumed to be graded across the thickness direction of plate based on the power law form, while Poisson’s ratio is kept constant. Among all combinations of free, simply-supported, and clamped boundary conditions, existence of bifurcation buckling for various edge supports is examined and stability equations are obtained by means of the adjacent equilibrium criterion. An exact analytical solution is presented to calculate the thermal buckling load by obtaining the eigenvalues of the stability equation. Three types of thermal loading, namely; uniform temperature rise, transversely linear temperature distribution and heat conduction across the thickness type are studied. Effects of thickness to outer radii, inner to outer radii, power law index, elastic foundation coefficient, and thermal loading type on critical buckling temperature of FG plates are presented.

Nonlocal elasticity theory for thermal buckling of nanoplates lying on Winkler–Pasternak elastic substrate medium

Abstract: In the present work, thermal buckling of single-layered graphene sheets lying on an elastic medium is analyzed. For this purpose, the sinusoidal shear deformation plate theory in tandem with the nonlocal continuum theory, which takes the small scale effects into account, is employed. The non-linear stability equations, which contain the reaction of Winkler–Pasternak elastic substrate medium, are derived and then solved analytically for a plate with various boundary conditions and based on various plate theories. Closed form solutions are formulated for three types of thermal loadings as uniform, linear and nonlinear temperature rise through the thickness of the plate. A number of examples are presented to illustrate the numerical results concerned with the buckling temperature response of nanoplates resting on two-parameter elastic foundations. The influences played by transversal shear deformation, plate aspect ratio, side-to-thickness ratio, nonlocal parameter, and elastic foundation parameters are all investigated.

A micro-scale modeling of Kirchhoff plate based on modified strain-gradient elasticity theory

Abstract: A Kirchhoff micro-plate model is presented based on the modified strain gradient elasticity theory to capture size effects, in contrast with the classical plate theory. The analysis is general and can be reduced to the modified couple stress plate model or classical plate model once two or all material length scale parameters in the theory are set zero respectively. Governing equation and boundary conditions of an isotropic rectangular micro-plate are derived using minimum potential energy principle. Various boundary conditions including simply supported and clamped edges are covered by the analysis. The extended Kantorovich method (EKM) which is an accurate approximate closed-form solution is applied to solve the resulting sixth order boundary value problem. Application of EKM to the partial differential equation (PDE) yields two ordinary differential equations (ODEs) in the independent x and y coordinates. The resulted ODEs are solved in an iterative manner. Exact closed-form solutions are presented for both ODEs in all of the iteration. It is shown that the method provides accurate predictions with very fast convergence. Numerical results reveal that the differences between the deflection predicted by the modified strain gradient model, the couple stress model and the classical model are large when the plate thickness is small and comparable to the material length scale parameters. However, the differences decrease with increasing the plate thickness. Validation of the presented EKM solution shows good agreement with available literature.

Modeling and analysis of micro-sized plates resting on elastic medium using the modified couple stress theory

Abstract: Analytical solutions for bending, buckling, and vibration of micro-sized plates on elastic medium using the modified couple stress theory are presented. The governing equations for bending, buckling and vibration are obtained via Hamilton’s principles in conjunctions with the modified couple stress and Kirchhoff plate theories. The surrounding elastic medium is modeled as the Winkler elastic foundation. Navier’s method is being employed and analytical solutions for the bending, buckling and free vibration problems are obtained. Influences of the elastic medium and the length scale parameter on the bending, buckling, and vibration properties are discussed.

A non-classical third-order shear deformation plate model based on a modified couple stress theory

Abstract: A non-classical third-order shear deformation plate model is developed using a modified couple stress theory and Hamilton’s principle. The equations of motion and boundary conditions are simultaneously obtained through a variational formulation. This newly developed plate model contains one material length scale parameter and can capture both the size effect and the quadratic variation of shear strains and shear stresses along the plate thickness direction. It is shown that the new third-order shear deformation plate model recovers the non-classical Reddy-Levinson beam model and Mindlin plate model based on the modified couple stress theory as special cases. Also, the current non-classical plate model reduces to the classical elasticity-based third-order shear deformation plate model when the material length scale parameter is taken to be zero. To illustrate the new model, analytical solutions for the static bending and free vibration problems of a simply supported plate are obtained by directly applying the general forms of the governing equations and boundary conditions of the model. The numerical results show that the deflection and rotations predicted by the new plate model are smaller than those predicted by its classical elasticity-based counterpart, while the natural frequency of the plate predicted by the former is higher than that by the latter. It is further seen that the differences between the two sets of predicted values are significant when the plate thickness is small, but they are diminishing with increasing plate thickness.