• Advances in materials Research
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• v.4 no.1
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• pp.31-44
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• 2015

This paper presents a simple n-order four variable refined theory for buckling analysis of functionally graded plates. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations of the present theory is reduced, and hence, makes it simple to use. The present theory is variationally consistent, uses the n-order polynomial term to represent the displacement field, does not require shear correction factor, and eliminates the shear stresses at the top and bottom surfaces. A power law distribution is used to describe the variation of volume fraction of material compositions. Equilibrium and stability equations are derived based on the present n-order refined theory. The non-linear governing equations are solved for plates subjected to simply supported boundary conditions. The thermal loads are assumed to be uniform, linear and non-linear distribution through-the-thickness. The effects of aspect and thickness ratios, gradient index, on the critical buckling are all discussed.

• Geomechanics and Engineering
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• v.13 no.3
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• pp.385-410
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• 2017

This work presents a simple and refined nth-order shear deformation theory for mechanical and thermal buckling behaviors of functionally graded (FG) plates resting on elastic foundation. The proposed refined nth-order shear deformation theory has a new displacement field which includes undetermined integral terms and contains only four unknowns. Governing equations are obtained from the principle of minimum total potential energy. A Navier type analytical solution methodology is also presented for simply supported FG plates resting on elastic foundation which predicts accurate solution. The accuracy of the present model is checked by comparing the computed results with those obtained by classical plate theory (CPT), first-order shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). Moreover, results demonstrate that the proposed theory can achieve the same accuracy of the existing HSDTs which have more number of variables.

• Earthquakes and Structures
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• v.17 no.3
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• pp.257-270
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• 2019

The purpose of this work is to analyze the bending behavior of laminated composite plates using the refined fourvariable theory and the finite element method approach using an ANSYS 12 computational code. The analytical model is based on the multilayer plate theory of shear deformation of the nth-order proposed by Xiang et al 2011 using the theory principle developed by Shimpi and Patel 2006. Unlike other theories, the number of unknown functions in the present theory is only four, while five or more in the case of other theories of shear deformation. The formulation of the present theory is based on the principle of virtual works, it has a strong similarity with the classical theory of plates in many aspects, it does not require shear correction factor and gives a parabolic description of the shear stress across the thickness while filling the condition of zero shear stress on the free edges. The analysis is validated by comparing results with those in the literature.

• Steel and Composite Structures
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• v.17 no.1
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• pp.21-46
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• 2014

This paper presents a simple n-order four variable refined theory for the bending and vibration analyses of functionally graded plates. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations of the present theory is reduced, and hence, makes it simple to use. The present theory is variationally consistent, uses the n-order polynomial term to represent the displacement field, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. The governing equations are derived by employing the Hamilton's principle and the physical neutral surface concept. The accuracy of the present solutions is verified by comparing the obtained results with available published ones.