• Journal of the Korean Society of Hazard Mitigation
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• v.7 no.5
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• pp.47-60
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• 2007

In this paper, we investigate the natural frequencies and buckling loads of functionally graded material (FGM) plates and shells, using a quasi-conforming shell element that accounts for the transverse shear strains and rotary inertia. The eigenvalue of the FGM plates and shells are calculated by varying the volume fraction of the ceramic and metallic constituents using a sigmoid function, but their Poisson's ratios of the FGM plates and shells are assumed to be constant. The expressions of the membrane, bending and shear stiffness of FGM shell element are more complicated combination of material properties than a homogeneous element. In order to validate the finite element numerical solutions, the Navier's solutions of rectangular plates based on the first-order shear deformation theory are presented. The present numerical solutions of composite and sigmoid FGM (S-FGM) plates are proved by the Navier's solutionsand various examples of composite and FGM structures are presented. The present results are in good agreement with the Navier's theoretical solutions.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.9 no.4
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• pp.1043-1049
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• 2008

In this paper, we investigate the static response. natural frequencies and buckling loads of functionally graded material (FGM) plates, using a Navier method. The eigenvalues of the FGM plates and shells are calculated by varying the volume fraction of the ceramic and metallic constituents using a sigmoid function, but their Poisson's ratios of the FGM plates and shells are assumed to be constant. The expressions of the membrane. bending and shear stiffness of FGM plates art more complicated combination of material properties than a homogeneous element. In order to validate the present solutions, the reference solutions of rectangular plates based on the classical theory are used. The various examples of composite and FGM structures are presented. The present results are in good agreement with the reference solutions.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.28 no.1
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• pp.85-92
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• 2015

This article presents the dynamic instability response of sigmoid functionally graded material plates on elastic foundation using the higher-order shear deformation theory. The higher-order shear deformation theory has ability to capture the quadratic variation of shear strain and consequently shear stress through the plate thickness. The governing equations are then written in the form of Mathieu-Hill equations and then Bolotin's method is employed to determine the instability regions. The boundaries of the instability regions are represented in the dynamic load and excitation frequency plane. The results of dynamic instability analysis of sigmoid functionally graded material plate are presented using the Navier's procedure to illustrate the effect of elastic foundation parameter on dynamic response. The relations between Winkler and Pasternak elastic foundation parameter are discussed by numerical results. Also, the effects of static load factor, power-law index and side-to-thickness ratio on dynamic instability analysis are investigated and discussed. In order to validate the present solutions, the reference solutions are used and discussed. The theoretical development as well as numerical solutions presented herein should serve as reference for the dynamic instability study of S-FGM plates.

• Journal of the Korean Society of Hazard Mitigation
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• v.7 no.5
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• pp.61-71
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• 2007

Navier's and Finite element solutions based on the first-order shear deformation theory are presented for the analysis of through-thickness functionally graded plates and shells. The functionally graded materials are considered: a sigmoid function is utilized for the mechanical properties through the thickness of the isotropic structure which varies smoothly through the plate and shell thickness. The formulation of a nonlinear 9-node Element-based Lagrangian shell element is presented for the geometrically nonlinear analysis. Natural-coordinate-based strains are used in present shell element. Numerical results of the linear and nonlinear analysis are presented to show the effect of the different top/bottom elastic modulus, loading conditions, aspect ratios and side-to-thickness ratios on the mechanical behaviors. Besides, the result according to the variation of the power-law index of isotropic functionally graded structures is investigated.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.14 no.11
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• pp.5930-5938
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• 2013

The sigmoid functionally graded mateiral(S-FGM) theory is reformulated using the nonlocal elatictiry of Erigen. The equation of equilibrium of the nonlocal elasticity are derived. This theory has ability to capture the both small scale effects and sigmoid function in terms of the volume fraction of the constituents for material properties through the plate thickness. Navier's method has been used to solve the governing equations for all edges simply supported boundary conditions. Numerical solutions of biaxial buckling of nano-scale plates are presented using this theory to illustrate the effects of nonlocal theory and power law index of sigmoid function on buckling load. The relations between nonlocal and local theories are discussed by numerical results. Further, effects of (i) power law index, (ii) length, (iii) nonlocal parameter, (iv) aspect ratio and (v) mode number on nondimensional biaxial buckling load are studied. To validate the present solutions, the reference solutions are discussed.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.29 no.6
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• pp.529-538
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• 2016

The simplified plate theory is presented for static and free vibration analysis of power-law(P) and sigmoid(S) Functionally Graded Materials(FGM) plates. This theory considers the parabolic distribution of the transverse shear stress, and satisfies the condition that requires the transverse shear stress to be zero on the upper and lower surfaces of the plate, without the shear correction factor. The simplified plate theory uses only four unknown variables and shares strong similarities with classical plate theory(CPT) in many aspects such as stress-resultant expressions, equation of motion and boundary conditions. The material properties of the plate are assumed to vary according to the power-law and sigmoid distributions of the volume fractions of the constituents. The Hamilton's principle is used to derive the equations of motion and Winkler-Pasternak elastic foundation model is employed. The results of static and dynamic responses for a simply supported FGM plate are calculated and a comparative analysis is carried out. The results of the comparative analysis with the solutions of references show relevant and accurate results for static and free vibration problems of FGM plates. Analytical solutions for the static and free vibration problems are presented so as to reveal the effects of the power law index, elastic foundation parameter, and side-to-thickness ratio.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.15 no.2
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• pp.1109-1117
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• 2014

We study free vibration analysis of sigmoid functionally graded materials(S-FGM) nano-scale plates, using a nonlocal elasticity theory of Eringen in this paper. This theory has ability to capture the both small scale effects and sigmoid function in terms of the volume fraction of the constituents for material properties through the plate thickness. Numerical solutions of S-FGM nano-scale plate are presented using this theory to illustrate the effect of nonlocal theory on natural frequency of the S-FGM nano-scale plates. The relations between nonlocal and local theories are discussed by numerical results. Further, effects of (i) power law index (ii) nonlocal parameters, (iii) elastic modulus ratio and (iv) thickness and aspect ratios on nondimensional frequencies are investigated. In order to validate the present solutions, the reference solutions are compared and discussed. The results of S-FGM nano-scale plates using the nonlocal theory may be the benchmark test for the free vibration analysis.