• Coupled systems mechanics
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• v.11 no.5
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• pp.389-409
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• 2022

During the manufacture of FGM plates, defects such as porosities can appear. Those can change the entire behavior of these plates. This paper aims to investigate the free vibration characteristics of porous functionally graded (FG) plates resting on elastic foundations. The Young's modulus of the plate is assumed to vary continuously through the thickness according to a power-law formulation, and the Poisson ratio is held constant. Different types of porosity distribution rates are considered. To examine the accuracy of the present formulation, several comparison studies are investigated. Effects of variation of porosity distribution rate, foundation parameter, power-law index and thickness ratio on the fundamental frequency of plates have been investigated.

• Structural Engineering and Mechanics
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• v.24 no.4
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• pp.447-461
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• 2006

Here, the axisymmetric free flexural vibrations and thermal stability behaviors of functionally graded spherical caps are investigated employing a three-noded axisymmetric curved shell element based on field consistency approach. The formulation is based on first-order shear deformation theory and it includes the in-plane and rotary inertia effects. The material properties are graded in the thickness direction according to the power-law distribution in terms of volume fractions of the constituents of the material. The effective material properties are evaluated using homogenization method. A detailed numerical study is carried out to bring out the effects of shell geometries, power law index of functionally graded material and base radius-to-thickness on the vibrations and buckling characteristics of spherical shells.

• Structural Engineering and Mechanics
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• v.55 no.3
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• pp.473-494
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• 2015

A graded harmonic finite element formulation based on three-dimensional elasticity theory is developed for the structural analysis of 2D functionally graded axisymmetric structures. The mechanical properties of the axisymmetric solid structures composed of two different metals and ceramics are assumed to vary in radial and axial directions according to power law variations as a function of the volume fractions of the constituents. The material properties of the graded element are calculated at the integration points. Effects of material distribution profile on the static deformation, natural frequency and dynamic response analyses of particular axisymmetric solid structures are investigated by changing the power law exponents. It is observed that the displacements, stresses and natural frequencies are severely affected by the variation of axial and radial power law exponents. Good accuracy is obtained with fewer elements in the present study since Fourier series expansion eliminates the need of finite element mesh in circumferential direction and continuous material property distribution within the elements improves accuracy without refining the mesh size in axial and radial directions.

• Steel and Composite Structures
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• v.50 no.3
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• pp.299-318
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• 2024

The main objective of this paper is to compute the far-field acoustic radiation (sound radiation) of functionally graded plates (FGM) loaded by sinusoidally varying point load subjected to the arbitrary boundary condition is carried out. The governing differential equations for thin functionally graded plates (FGM) are derived using classical plate theory (CPT) and Rayleigh integral using the elemental radiator approach. Four cases, segregated on power-law index k=0,1,5,10, are studied. A novel approach is illustrated to compute sound fields of vibrating FGM plates using the physical neutral surface with an elemental radiator approach. The material properties of the FGM plate for all cases are calculated considering the power law indexes. An in-house MATLAB code is written to compute the natural frequencies, normal surface velocities, and sound radiation fields are analytically calculated using semi-analytical formulation. Ansys is used to validate the computed sound power level. The parametric effects of the power law index, modulus ratios, different constituent of FGM plates, boundary conditions, damping loss factor on the sound power level, and radiation efficiency is illustrated. This work is the benchmark approach that clearly explains how to calculate acoustic fields using a solid layered FGM model in ANSYS ACT. It shows that it is possible to asymptotically stabilize the structure by controlling the intermittent layers' stiffness. It is found that sound fields radiated by the elemental radiators approach in MATLAB, ANSYS and literatures are in good agreement. The main novelty of this research is that the FGM plate is analyzed in the low-frequency range, where the stiffness-controlled region governs the whole analysis. It is concluded that a clamped mono-ceramic FGM plate radiates a lesser sound power level and higher radiation efficiency than a mono-metallic or metal-rich FGM plate due to higher stiffness. It is found that change in damping loss factor does not affect the same constituents of FGM plates but has significant effects on the different constituents of FGM plates.

• Advances in materials Research
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• v.5 no.2
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• pp.107-120
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• 2016

The static analysis of the simply supported functionally graded plate under transverse load by using a new sinusoidal shear deformation theory based on the neutral surface concept is investigated analytically in the present paper. No transversal shear correction factors are needed because a correct representation of the transversal shearing strain is given. The mechanical properties of the FGM plate are assumed to vary continuously through the thickness according to a power law formulation except Poisson's ratio, which is kept constant. The equilibrium and stability equations are derived by employing the principle of virtual work. Results are provided for thick to thin plates and for different values of the gradient index k, which subjected to sinusoidal or uniformly distributed lateral loads. The accuracy of the present results is verified by comparing it with finite element solution. From the obtained results, it can be concluded that the proposed theory is accurate and efficient in predicting the displacements and stresses of functionally graded plates.

• Smart Structures and Systems
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• v.26 no.1
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• pp.77-87
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• 2020

By employing a quasi-3D plate formulation, the present research studies static stability of magneto-electro-thermo-elastic functional grading (METE-FG) nano-sized plates. Accordingly, influences of shear deformations as well as thickness stretching have been incorporated. The gradation of piezo-magnetic and elastic properties of the nano-sized plate have been described based on power-law functions. The size-dependent formulation for the nano-sized plate is provided in the context of nonlocal elasticity theory. The governing equations are established with the usage of Hamilton's rule and then analytically solved for diverse magnetic-electric intensities. Obtained findings demonstrate that buckling behavior of considered nanoplate relies on the variation of material exponent, electro-magnetic field, nonlocal coefficient and boundary conditions.

• Steel and Composite Structures
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• v.49 no.5
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• pp.547-570
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• 2023

In the present work, a comparative study has been carried out between power, exponential, and sigmoidal sandwich FGM plates for free vibration conditions under hygro-thermal conditions. Rules of mixture is used to determine effective material properties across the thickness for power-law and sigmoid sandwich FGM plates. Exponential law is used to plot effective material properties for exponentially graded sandwich FGM plates. Temperature and moisture dependent material properties were used during the analysis. Free vibration analysis is carried out using recently proposed finite element based HOZT. Present formulation satisfies interlayer transverse stress continuity conditions at interfaces and transverse shear stress-free conditions at the plate's top and bottom surfaces. The present model is free from any penalty or post-processing requirements. Several new results are reported in the present work, especially for unsymmetric sandwich FGM plates and exponential and sigmoidal sandwich FGM plates.

• Steel and Composite Structures
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• v.52 no.3
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• pp.273-291
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• 2024

This paper presents a three-dimensional displacement-based formulation to investigate the free vibration of functionally graded nanoplates resting on a Winkler-Pasternak foundation based on the nonlocal elasticity theory. The material properties of the FG nanoplate are considered to vary continuously through the thickness of the nanoplate according to the power-law distribution model. A general three-dimensional displacement field is considered for the plate, which takes into account the out-of-plane strains of the plate as well as the in-plane strains. Unlike the shear deformation theories, in the present formulation, no predetermined form for the distribution of displacements and transverse strains is considered. The equations of motion for functionally graded nanoplate are derived based on Hamilton's principle. The solution is obtained for simply-supported nanoplate, and the predicted results for natural frequencies are compared with the predictions of shear deformation theories which are available in the literature. The predictions of the present theory are discussed in detail to investigate the effects of power-law index, length-to-thickness ratio, mode numbers and the elastic foundation on the dynamic behavior of the functionally graded nanoplate. The present study presents a three-dimensional solution that is able to determine more accurate results in predicting of the natural frequencies of flexural and thickness modes of nanoplates. The effects of parameters that play a key role in the analysis and mechanical design of functionally graded nanoplates are investigated.

• Advances in aircraft and spacecraft science
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• v.9 no.3
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• pp.243-261
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• 2022

Broad writing on the examination of sandwich structures mirrors the significance of incorporating thermal loadings during their investigation stage. In the current work, an endeavor has been made to concentrate on sandwich FGM beams' bending behaving under thermal loadings utilizing shear deformation theory. Temperature-dependent material properties are used during the analysis. The formulation includes the transverse displacement field, which helps better predict the behavior of thick FGM beams. Three-different thermal profiles across the thickness of the beam are assumed during the analysis. The study has been carried out on both symmetric and unsymmetric sandwich FGM beams. It has been observed that the bending behavior of sandwich FGM beams is impacted by the temperature profile to which it is subjected. Power-law exponent and thickness of core also affect the behavior of the beam.

• Wind and Structures
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• v.23 no.6
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• pp.543-558
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• 2016

The response of functionally graded ceramic-metal plates is investigated using theoretical formulation, Navier's solutions, and a new displacement based on the high-order shear deformation theory are presented for static analysis of functionally graded plates. The theory accounts for a quadratic variation of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. The plates are assumed to have isotropic, two-constituent material distribution through the thickness, and the modulus of elasticity of the plate is assumed to vary according to a power-law distribution in terms of the volume fractions of the constituents. Numerical results of the new refined plate theory are presented to show the effect of the material distribution on the deflections, stresses and fundamental frequencies. It can be concluded that the proposed theory is accurate and simple in solving the static and free vibration behavior of functionally graded plates.