Closed-form solution for buckling analysis of thick functionally graded plates on elastic foundation

In this article, a closed-form solution for bending/stretching analysis of functionally graded (FG) circular plates under asymmetric loads is presented. It is assumed that the material properties of the FG plate are described by a power function of the thickness variable. The equilibrium equations are derived according to the classical plate theory using the principle of total potential energy. Two new functions are introduced to decouple the governing equilibrium equations. The three highly coupled partial differential equations are then converted into an independent equation in terms of transverse displacement. A closed-form solution for deflection of FG circular plates under arbitrary lateral eccentric concentrated force is obtained by defining a new coordinate system. This solution can be used as a Green function to obtain the closed-form solution of the FG plate under arbitrary loadings. Also, the solution is employed to solve some different asymmetric problems. Finally, the stress and displacement components are obtained exactly for each problem and the effect of volume fraction is also studied.

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Thermal stability analysis of solar functionally graded plates on elastic foundation using an efficient hyperbolic shear deformation theory

Geomechanics and Engineering ◽

10.12989/gae.2016.10.3.357 ◽

2016 ◽

Vol 10 (3) ◽

pp. 357-386 ◽

Cited By ~ 2

Author(s):

Sidi Mohamed El-Hassar ◽

Samir Benyoucef ◽

Houari Heireche ◽

Abdelouahed Tounsi

Keyword(s):

Thermal Stability ◽

Stability Analysis ◽

Shear Deformation ◽

Elastic Foundation ◽

Deformation Theory ◽

Shear Deformation Theory ◽

Functionally Graded ◽

Functionally Graded Plates ◽

Plates On Elastic Foundation

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A Novel Higher-Order Shear and Normal Deformable Plate Theory for the Static, Free Vibration and Buckling Analysis of Functionally Graded Plates

Mathematical Problems in Engineering ◽

10.1155/2017/6879508 ◽

2017 ◽

Vol 2017 ◽

pp. 1-20 ◽

Cited By ~ 1

Author(s):

Shi-Chao Yi ◽

Lin-Quan Yao ◽

Bai-Jian Tang

Keyword(s):

Natural Frequencies ◽

Plate Theory ◽

Closed Form Solution ◽

Higher Order ◽

Form Solution ◽

Functionally Graded ◽

The Novel ◽

Functionally Graded Plates ◽

Graded Materials ◽

Different Shapes

Closed-form solution of a special higher-order shear and normal deformable plate theory is presented for the static situations, natural frequencies, and buckling responses of simple supported functionally graded materials plates (FGMs). Distinguished from the usual theories, the uniqueness is the differentia of the new plate theory. Each individual FGM plate has special characteristics, such as material properties and length-thickness ratio. These distinctive attributes determine a set of orthogonal polynomials, and then the polynomials can form an exclusive plate theory. Thus, the novel plate theory has two merits: one is the orthogonality, where the majority of the coefficients of the equations derived from Hamilton’s principle are zero; the other is the flexibility, where the order of the plate theory can be arbitrarily set. Numerical examples with different shapes of plates are presented and the achieved results are compared with the reference solutions available in the literature. Several aspects of the model involving relevant parameters, length-to-thickness, stiffness ratios, and so forth affected by static and dynamic situations are elaborate analyzed in detail. As a consequence, the applicability and the effectiveness of the present method for accurately computing deflection, stresses, natural frequencies, and buckling response of various FGM plates are demonstrated.

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