Static Response of Functionally Graded Plates using Higher Order Theories (original) (raw)
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Bending response of functionally graded plates by using a new higher order shear deformation theory
Composite Structures
This paper presents an analytical solution to the static analysis of functionally graded plates, using a recently developed higher order shear deformation theory (HSDT) and provides detailed comparisons with other HSDT's available in the literature. These theories account for adequate distribution of the transverse shear strains through the plate thickness and tangential stress-free boundary conditions on the plate boundary surfaces, thus a shear correction factor is not required. The mechanical properties of the plates are assumed to vary in the thickness direction according to a power-law distribution in terms of the volume fractions of the constituents. The governing equations of a functionally graded (FG) plate and boundary conditions are derived by employing the principle of virtual work. Navier-type analytical solution is obtained for FG plates subjected to transverse bi-sinusoidal and distributed loads for simply supported boundary conditions. Results are provided for thick to thin FG plates and for different volume fraction distributions. The accuracy of the present code is verified by comparing it with known results in the literature.
A Theoretical Analysis for Static and Dynamic Behavior of Functionally Graded Plates
2012
Theoretical formulation, Navier’s solutions of rectangular plates based on a new higher order shear deformation model are presented for the static and dynamic analysis of functionally graded plates (FGPs). This theory enforces traction free boundary conditions at plate surfaces. Shear correction factors are not required because a correct representation of transverse shearing strain is given. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The mechanical properties of the plate are assumed to vary continuously in the thickness direction by a simple power-law distribution in terms of the volume fractions of the constituents. Numerical illustrations concern flexural behavior of FG plates with Metal–Ceramic composition. Parametric studies are performed for varying ceramic volume fraction, volume fraction profiles, aspect ratios and length to thickness ratios. Results are verified with available ...
Analysis of functionally graded plates using higher order shear deformation theory
This work addresses a static analysis of functionally graded material (FGM) plates using higher order shear deformation theory. In the theory the transverse shear stresses are represented as quadratic through the thickness and hence it requires no shear correction factor. The material property gradient is assumed to vary in the thickness direction. Mori and Tanaka theory (1973) [1] is used to represent the material property of FGM plate at any point. The thermal gradient across the plate thickness is represented accurately by utilizing the thermal properties of the constituent materials. Results have been obtained by employing a C° continuous isoparametric Lagrangian finite element with seven degrees of freedom for each node. The convergence and comparison studies are presented and effects of the different material composition and the plate geometry (side-thickness, side–side) on deflection and temperature are investigated. Effect of skew angle on deflection and axial stress of the plate is also studied. Effects of material constant n on deflection and the temperature distribution are also discussed in detail.
A higher-order shear and normal deformation functionally graded plate model: some recent results
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A two variable refined plate theory for the bending analysis of functionally graded plates
Acta Mechanica Sinica, 2010
Bending analysis of functionally graded plates using the two variable refined plate theory is presented in this paper. The number of unknown functions involved is reduced to merely four, as against five in other shear deformation theories. The variationally consistent theory presented here has, in many respects, strong similarity to the classical plate theory. It does not require shear correction factors, and gives rise to such transverse shear stress variation that the transverse shear stresses vary parabolically across the thickness and satisfy shear stress free surface conditions. Material properties of the plate are assumed to be graded in the thickness direction with their distributions following a simple power-law in terms of the volume fractions of the constituents. Governing equations are derived from the principle of virtual displacements, and a closed-form solution is found for a simply supported rectangular plate subjected to sinusoidal loading by using the Navier method. Numerical results obtained by the present theory are compared with available solutions, from which it can be concluded that the proposed theory is accurate and simple in analyzing the static bending behavior of functionally graded plates.
A flexural response of functionally graded material (FGM) plates is carried out using multi quadric radial based functional based meshless method. The governing equations are based on the higher order shear deformation theory are obtained using energy principle. A RBF based meshless code in MATLAB 2013 is developed to find out the results. In present paper, the effects of significant parameters, such as gradation index, span to thickness ratio is obtained at transverse point load. The present paper mainly focuses on the analysis of FGM plates under point load.
An efficient and simple refined theory for bending and vibration of functionally graded plates
Composite Structures, 2009
A two-dimensional theory of functionally graded plates is presented using a mixed variational approach. The theory accounts for a displacements field in which the inplane displacements vary linearly through the plate thickness, while the out-of-plane displacement is a second-degree function of thickness coordinate. The advantages of the present theory are that it contains both the transverse normal strain and stress in complete consistence with the boundary conditions at the top and bottom surfaces of the plates without loss of its simplicity. Therefore, the rationale for the shear correction factor used in such theories is obviated. The bending and free vibration problems of isotropic plates with material properties varying in the thickness direction are solved. Numerical results for frequencies are presented for two-phase graded material with a power-law through the plate thickness variation of the volume fractions of the constituents based on Mori-Tanaka scheme. In addition, numerical results of transverse deflections are obtained for FG simply supported isotropic plates with Young's modulus varying exponentially through the thickness and constant Poisson's ratio. The validity of the present theory is investigated by comparing some of the present results with their counterparts obtained due to three-dimensional approaches by Qian et al. and by Kashtalyan. The influence of the transverse normal strain on the bending and vibration of the FG plates is illustrated.
Static analysis of orthotropic functionally graded (FG) elastic, rectangular, and simply supported (diaphragm) plates under transverse loads is presented based on a higher order shear and normal deformation theory (HOSNT). Although functionally graded materials (FGMs) are highly heterogeneous in nature, they are generally idealized as continua with mechanical properties changing smoothly with respect to the spatial coordinates. The material properties of FG plates are assumed here to be varying through the thickness of the plate in a continuous manner. The Poisson's ratios of the FG plates are assumed to be constant, but their Young's moduli vary continuously in the thickness direction according to the volume fraction of constituents, which are mathematically modeled as an exponential function. The governing equations of equilibrium for the FG plates are derived on the basis of a HOSNT assuming varying material properties. Numerical solutions are obtained by the use of the Navier solution method. Several examples of isotropic, orthotropic, and FG plates are presented. The accuracy of the numerical solutions has been compared with the solutions obtained by other models and the exact three-dimensional (3D) elasticity solutions.
Mechanical behaviour of functionally graded plates under static and dynamic loading
Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2010
This article presents an analytical solution for the mechanical behaviour of rectangular plates made of functionally graded materials (FGMs) based on the first-order shear deformation theory (FSDT) and the third-order shear deformation theory (TSDT). The FGM plate is assumed to be graded across the thickness. The material properties of the FGM plate are assumed to vary continuously through the thickness of the plate according to a power law distribution of the volume fraction of the constituent materials, except Poisson's ratio, which is assumed to be constant. The plate is subjected to a lateral mechanical load on its upper surface. The equations of motion are written based on displacement fields. The partial differential equations have been solved by the Fourier series expansion. Using the Laplace transform, unknown variables are obtained in the Laplace domain. The resulting formulations enable one to perform the static, dynamic, and free vibration analysis for both FSDT and T...
Electronic Journal of Vocational Colleges, 2018
In this research, an efficient shear deformation plate theory for a functionally graded plate has been investigated by the use of the new four variable refined plate theory. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory account for higher-order variation of transverse shear strain through the depth of the plate and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factors. Based on the present higher-order shear deformation plate theory, the equations of the motion are derived from Hamilton's principal. The plate faces are assumed to have isotropic, two-constituent material distribution through the thickness, and the modulus of elasticity, Poisson's ratio of the faces, and thermal expansion coefficients are assumed to vary according to a power law distribution in terms of the volume fractions of the constituents. The validity of the present theory is investigated by comparing some of the present results with those of the classical, the first-order and the other higher-order theories. The influences played by the transverse shear deformation, aspect ratio, side-to-thickness ratio, and volume fraction distribution are studied. Numerical results for deflections and stresses of functionally graded plate are investigated.