Buckling analysis of FGM plates under uniform, linear and non-linear in-plane loading

Singh, S. J.; Harsha, S. P.

doi:10.1007/s12206-019-0328-8

Cited by 48 publications

(19 citation statements)

References 17 publications

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“…In a similar way, numerous studies have been reported on rectangular FGM plates of constant thickness based on power-law FGM (P-FGM), [17][18][19] exponential FGM (E-FGM), 20,21 and sigmoid FGM (S-FGM). [22][23][24] This section reviews the literature related to the varying thickness of plate for bending, buckling, and free vibration response.…”

Section: Introductionmentioning

confidence: 90%

“…Thus, implementing Galerkin-Vlasov's method discussed so far, the governing equation of tapered FG material plate is obtained by substituting equation (18) into governing differential equations (17) where each equation is multiplied by the corresponding eigenfunction. The simultaneous coupled equations are then obtained via the integration over a whole domain a Â b ð Þ .…”

Section: Assumed Solutionsmentioning

confidence: 99%

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Exact solution for free vibration analysis of linearly varying thickness FGM plate using Galerkin-Vlasov’s method

Kumar

Singh

Saran

et al. 2020

Proceedings of the Institution of Mechanical Engineers, Part L:

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The present paper investigates the free vibration analysis for functionally graded material plates of linearly varying thickness. A non-polynomial higher order shear deformation theory is used, which is based on inverse hyperbolic shape function for the tapered FGM plate. Three different types of material gradation laws, specifically: a power (P-FGM), exponential (E-FGM), and sigmoid law (S-FGM) are used to calculate the property variation in the thickness direction of FGM plate. The variational principle has been applied to derive the governing differential equation for the plates. Non-dimensional frequencies have been evaluated by considering the semi-analytical approach viz. Galerkin-Vlasov’s method. The accuracy of the preceding formulation has been validated through numerical examples consisting of constant thickness and tapered (variable thickness) plates. The findings obtained by this method are found to be in close agreement with the published results. Parametric studies are then explored for different geometric parameters like taper ratio and boundary conditions. It is deduced that the frequency parameter is maximum for S-FGM tapered plate as compared to E- and P-FGM tapered plate. Consequently, it is concluded that the S-FGM tapered plate is suitable for those engineering structures that are subjected to huge excitations to avoid resonance conditions. In addition, it is found that the taper ratio is significantly affected by the type of constraints on the edges of the tapered FGM plate. Some novel results for FGM plate with variable thickness are also computed that can be used as benchmark results for future reference.

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Section: Introductionmentioning

confidence: 90%

Section: Assumed Solutionsmentioning

confidence: 99%

Exact solution for free vibration analysis of linearly varying thickness FGM plate using Galerkin-Vlasov’s method

Kumar

Singh

Saran

et al. 2020

Proceedings of the Institution of Mechanical Engineers, Part L:

View full text Add to dashboard Cite

show abstract

“…Semi‐inverse methods based on Fourier series are still the most commonly adopted for solving plate problems. Navier solution was only suitable for plates under fully simply‐supported boundaries [32]. Shahraki et al.…”

Section: Introductionmentioning

confidence: 99%

Buckling analysis of rectangular thin plates with two opposite edges free and others rotationally restrained by finite Fourier integral transform method

Zhang

Ullah

et al. 2020

Z Angew Math Mech

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This paper investigates the classical buckling problem of rectangular thin plates with two opposite edges free and others rotationally restrained by the finite Fourier integral transform method. The rotationally restrained edges are typically practical boundary conditions in many engineering structures, such as bridge decks. However, these non‐classic edges bring mathematical difficulties in solving boundary value problems of governing partial differential equations of plate. Based on the integral transform theory, the title problem is transformed into solving regular linear algebraic simultaneous equations, which provides a more rational and theoretical solution process than traditional inverse/semi‐inverse approaches. The acquired comprehensive results of critical buckling load factors and mode shapes are in excellent agreement with the ones obtained by finite element method, which verifies the validity and accuracy of the present approach. In addition, classical boundary conditions, such as simply supported and clamped edges, can be investigated by choosing different rotational fixity factors. Furthermore, the features of the employed method that no preselection of trial function and the generality for various boundary conditions enable one to analytically solve static problems for moderately thick plates and thick plates.

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“…Gilhooley et al 18 used HSDT with the meshless Petrov Galerkin method with radial basis functions to present the thick FGM plate. Few researchers [19][20][21][22][23][24][25][26][27] studied static, free vibration, and dynamic behavior of the FGM structure and FGM bonded with piezoelectric material under thermal, electrical, and mechanical loading.…”

Section: Introductionmentioning

confidence: 99%

Response analysis of hybrid functionally graded material plate subjected to thermo-electro-mechanical loading

Kumar

Harsha

2020

Proceedings of the Institution of Mechanical Engineers, Part L:

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Static and free vibration response analysis of a functionally graded piezoelectric material plate under thermal, electric, and mechanical loads is done in this study. The displacement field is acquired using the first-order shear deformation theory, and the Hamilton principle is applied to deduce the motion equations. Temperature-dependent material properties of the functionally graded material plate are used, and these properties follow the power-law distributions along the thickness direction. However, the properties of piezoelectric material layers are assumed to be independent of the electric field and temperature. Finite element formulation for the functionally graded piezoelectric material plate is done using the combined effect of mechanical and electrical loads. The effects of parameters like electrical loading, volume fraction exponent N, and temperature distribution on the static and free vibration characteristics of the functionally graded piezoelectric material square plate are analyzed and presented. Responses are obtained in terms of the centerline deflection, axial stress and the nondimensional natural frequency with various boundary conditions. It is observed that the centerline deflection and nondimensional natural frequency increases as exponent N increases. At the same time, the axial stress decreases with an increase in exponent N. The findings of the static and the free vibration analysis suggest the potential application of the functionally graded piezoelectric material plate in the piezoelectric actuator as well as for sensing deflection in bimorph.

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Buckling analysis of FGM plates under uniform, linear and non-linear in-plane loading

Cited by 48 publications

References 17 publications

Exact solution for free vibration analysis of linearly varying thickness FGM plate using Galerkin-Vlasov’s method

Exact solution for free vibration analysis of linearly varying thickness FGM plate using Galerkin-Vlasov’s method

Buckling analysis of rectangular thin plates with two opposite edges free and others rotationally restrained by finite Fourier integral transform method

Response analysis of hybrid functionally graded material plate subjected to thermo-electro-mechanical loading

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