Investigation of the Static Bending Response of FGM Sandwich Plates

In the present work, a displacement-based high-order shear deformation theory is introduced for the static response of functionally graded plates. The present theory is variationally consistent and strongly similar to the classical plate theory in many aspects. It does not require the shear correction factor, and gives rise to the transverse shear stress variation so that the transverse shear stresses vary parabolically across the thickness to satisfy free surface conditions for the shear stress. By dividing the transverse displacement into the bending and shear parts and making further assumptions, the number of unknowns and equations of motion of the present theory is reduced a and hence makes them simple to use. The material properties of the plate are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of volume fractions of material constituents. The equilibrium equations of a functionally graded plate are given based on the higher order shear deformation theory. The numerical results presented in the paper are demonstrated by comparing the results with solutions derived from other higher-order models found in the literature and the present numerical results of Finite Element Analysis (FEA). In the numerical results, the effects of the grading materials, lay-up scheme and aspect ratio on the normal stress, shear stress and static deflections of the functionally graded sandwich plates are presented and discussed. It can be concluded that the proposed theory is accurate, elegant and simple in solving the problem of the bending behavior of functionally graded plates

A Static and Free Vibration Analysis of Porous Functionally Graded Beams

In this work, the static and free vibration analysis of functionally graded (FG) porous beams is investigated using a new higher-order shear deformation model (HSD). The porosity that develops naturally during the fabrication of a material is arbitrary in nature. Therefore, in the present study, a variation is considered taking into account three distribution patterns, namely (i) even distribution, (ii) uneven distribution, and (iii) the logarithmic-uneven pattern. Furthermore, the impact of several micromechanical models on the bending and free vibration behavior of the beams was investigated. Different micromechanical models were used to examine the mechanical properties of functionally graded beams, the properties of which change continuously throughout the thickness following a power law. Using the HSD model, the equations of motion are obtained using Hamilton's principle. To obtain displacements, stresses, and frequencies, the Navier type solution method was employed, and the numerical results were compared to those published in the literature. The impact of porosity and volume fraction index, different micromechanical models, mode numbers, and geometry on the bending and natural frequencies of imperfect FG beams were investigated

Bending and free vibration analysis of functionally graded beams on elastic foundations with analytical validation

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Thermal buckling in multi-directional porous plates: The effects of material grading and aspect ratio

International audienceIn the present study, a trigonometric shear deformation plate theory was employed to perform a thermal buckling analysis of multi-directional functionally graded (FG) plates. During the manufacturing of the multi-directional graded plate, the formation of pores is abounded. Hence, the effect of porosity on the buckling performance was investigated by considering the variation of porosity in the plate for power law gradation variation of material properties. The adverse effect of porosity on the material properties was taken into account by employing the rule of mixture relation. Finite element results show that the thermal expansion coefficient is unaffected by the presence of porosity. For simply supported boundary conditions, the non-linear governing equations are solved for different thermal loads such as uniform, linear, and non-linear. A parametric study was performed in which the effect of grading parameters, aspect ratio, and side-to-thickness ratio under variable temperature change was studies. Critical material grading indices for multi-directional plates have been identified that help researchers and industry personnel in fabrication planning

An analytical solution for bending and free vibration responses of functionally graded beams with porosities Effect of the micromechanical models

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On the mechanics of FG nanobeams: A review with numerical analysis

Since the classical continuum theories are insufficient to account the small size effects of nanobeams, the nonlocal continuum theories such as Eringen's nonlocal elasticity theory, couple stress theory, strain gradient theory and surface elasticity theory have been proposed by researchers to predict the accurate structural response of isotropic and functionally graded composite nanobeams. This review focuses on research work concerned with analysis of size dependent nanoscale isotropic and functionally graded beams using classical and refined beam theories based on Eringen's nonlocal elasticity theory. The present review article also highlight the possible scope for the future research on nanobeams. In the present study, the authors have developed a new hyperbolic shear deformation theory for the analysis of isotropic and functionally graded nanobeams. The theory satisfy the traction free boundary conditions at the top and the bottom surfaces of the nanobeams. Analytical solutions for the bending, buckling and free vibration analysis of simply-supported nanobeams are obtained using the Navier method. To ensure that the present theory is accurate and valid, the results are compared to previous research

Influence of the distribution pattern of porosity on the free vibration of functionally graded plates

In this study, the effect of porosity distribution pattern on the free vibration analysis of porous FG plates with various boundary conditions is studied. The material properties of the plate and the porosities within the plate are considered to vary continuously through the thickness direction according to the volume fraction of constituents defined by the modified rule of the mixture, this includes porosity volume fraction with four different types of porosity distribution over the cross-section. The governing partial differential equation of motion for the free vibration analysis is obtained using hyperbolic shear deformation theory. An analytical solution is presented for the governing PDEs for various boundary conditions. Results of the presented solution are compared and validated by the available results in the literature. Moreover, the effects of material and porosity distribution and geometrical parameters on vibrational properties are investigated