A refined higher order shear and normal deformation theory for E-, P-, and S-FGM plates on Pasternak elastic foundation

This paper deals with the free vibration and buckling analysis of functionally graded material (FGM) plates, resting on the Winkler–Pasternak elastic foundation. The higher order shear deformation plate theory (HSPT) is adopted for the realistic variation of transverse displacement through the thickness, using the power law distribution to describe the variation of the material properties. Both the effects of shear deformation and rotary inertia are considered. In the present model, the plate is discretised into [Formula: see text] eight noded serendipity quadratic elements with seven nodal degrees of freedom (DOFs). The validation study is carried out by comparing the calculated values with those given in the literature. The effects of various parameters like the Winkler and Pasternak modulus coefficients, volume fraction index, aspect ratio, thickness ratio and different boundary conditions on the behaviour of the FGM plates are studied.

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A NEW SIMPLE HYPERBOLIC SHEAR DEFORMATION THEORY FOR FUNCTIONALLY GRADED PLATES RESTING ON WINKLER–PASTERNAK ELASTIC FOUNDATIONS

International Journal of Computational Methods ◽

10.1142/s0219876213500989 ◽

2014 ◽

Vol 11 (06) ◽

pp. 1350098 ◽

Cited By ~ 5

Author(s):

ABDERRAHMANE SAID ◽

MOHAMMED AMEUR ◽

ABDELMOUMEN ANIS BOUSAHLA ◽

ABDELOUAHED TOUNSI

Keyword(s):

Shear Deformation ◽

Deformation Theory ◽

Virtual Work ◽

Shear Deformation Theory ◽

Higher Order ◽

Functionally Graded ◽

Functionally Graded Plates ◽

Governing Equations ◽

Pasternak Elastic Foundation ◽

Shear Deformation Theories

An improved simple hyperbolic shear deformation theory involving only four unknown functions, as against five functions in case of first or other higher-order shear deformation theories, is introduced for the analysis of functionally graded plates resting on a Winkler–Pasternak elastic foundation. The governing equations are derived by employing the principle of virtual work and the physical neutral surface concept. The accuracy of the present analysis is demonstrated by comparing some of the present results with those of the classical, the first-order and the other higher-order theories.

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Dynamic Response of FG-CNT Composite Plate Resting on an Elastic Foundation Based on Higher-Order Shear Deformation Theory

Journal of Aerospace Engineering ◽

10.1061/(asce)as.1943-5525.0001052 ◽

2019 ◽

Vol 32 (5) ◽

pp. 04019061

Author(s):

Balakrishna Adhikari ◽

B. N. Singh

Keyword(s):

Dynamic Response ◽

Shear Deformation ◽

Elastic Foundation ◽

Composite Plate ◽

Deformation Theory ◽

Shear Deformation Theory ◽

Higher Order

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A new higher-order shear and normal deformation theory for functionally graded sandwich beams

Steel and Composite Structures ◽

10.12989/scs.2015.19.3.521 ◽

2015 ◽

Vol 19 (3) ◽

pp. 521-546 ◽

Cited By ~ 37

Author(s):

Riadh Bennai ◽

Hassen Ait Atmane ◽

Abdelouahed Tounsi

Keyword(s):

Deformation Theory ◽

Higher Order ◽

Functionally Graded ◽

Sandwich Beams ◽

Normal Deformation

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FREE VIBRATION OF FUNCTIONALLY GRADED PLATES WITH A HIGHER-ORDER SHEAR AND NORMAL DEFORMATION THEORY

International Journal of Structural Stability and Dynamics ◽

10.1142/s0219455413500041 ◽

2013 ◽

Vol 13 (01) ◽

pp. 1350004 ◽

Cited By ~ 12

Author(s):

D. K. JHA ◽

TARUN KANT ◽

R. K. SINGH

Keyword(s):

Free Vibration ◽

Material Properties ◽

Deformation Theory ◽

Numerical Solutions ◽

Volume Fraction ◽

Free Vibration Analysis ◽

Higher Order ◽

Functionally Graded ◽

Normal Deformation ◽

Fg Plates

Free vibration analysis of functionally graded elastic, rectangular, and simply supported (diaphragm) plates 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 functionally graded (FG) plates are assumed here to be varying through the thickness of the plate in a continuous manner. The Poisson ratios of the FG plates are assumed to be constant, but their Young's modulii and densities vary continuously in the thickness direction according to the volume fraction of constituents which is mathematically modeled as a power law function. The equations of motion are derived using Hamilton's principle for the FG plates on the basis of a HOSNT assuming varying material properties. Numerical solutions are obtained by the use of Navier solution method. The accuracy of the numerical solutions is first established through comparison with the exact three-dimensional (3D) elasticity solutions and the present solutions are then compared with available solutions of other models.

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