• Advances in nano research
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• v.12 no.3
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• pp.231-251
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• 2022

Dynamic behavior of temperature-dependent Reddy functionally graded (RFG) nanobeam subjected to thermomagnetic effects under the action of moving point load is carried out in the present work. Both symmetric and sigmoid functionally graded material distributions throughout the beam thickness are considered. To consider the significance of strain-stress gradient field, a material length scale parameter (LSP) is introduced while the significance of nonlocal elastic stress field is considered by introducing a nonlocal parameter (NP). In the framework of the nonlocal strain gradient theory (NSGT), the dynamic equations of motion are derived through Hamilton's principle. Navier approach is employed to solve the resulting equations of motion of the functionally graded (FG) nanoscale beam. The developed model is verified and compared with the available previous results and good agreement is observed. Effects of through-thickness variation of FG material distribution, beam aspect ratio, temperature variation, and magnetic field as well as the size-dependent parameters on the dynamic behavior are investigated. Introduction of the magnetic effect creates a hardening effect; therefore, higher values of natural frequencies are obtained while smaller values of the transverse deflections are produced. The obtained results can be useful as reference solutions for future dynamic and control analysis of FG nanobeams reinforced nanocomposites under thermomagnetic effects.

• Advances in nano research
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• v.17 no.1
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• pp.19-32
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• 2024

Functionally graded-carbon nanotube (FG-CNT) is expected to be a new generation of materials with a wide range of potential applications in technological fields such as aerospace, defense, energy, and structural industries. In this paper, an exact finite strip method for functionally graded-carbon nanotube sandwich plates is developed using first-order shear deformation theory to get the exact natural frequencies of the plates. The face sheets of the plates are made of FG-CNT with continuous and smooth grading based on the power law index. The equations of motion have been generated based on the Hamilton principle. By extracting the exact stiffness matrix for any strip of the sandwich plate as a non-algebraic function of natural frequencies, it is possible to calculate the exact free vibration frequencies. The accuracy and efficiency of the current method is established by comparing its findings to the results of the literature works. Examples are presented to prove the efficiency of the generated method to deal with various problems, such as the influence of the length-to-height ratio, the power law index, and a core-to-face sheet thickness of the single and multi-span sandwich plates with various boundary conditions on the natural frequencies. The exact results obtained from this analysis can check the validity and accuracy of other numerical methods.

• Computers and Concrete
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• v.33 no.1
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• pp.27-39
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• 2024

In this study, the authors investigate the free vibration behavior of three-phases functionally graded sandwich plates using a novel nth-order shear deformation theory. These plates are composed of a homogeneous core and two face-sheet layers made of different functionally graded materials. This is the novel type of the sandwich structures that can be applied in many fields of mechanical engineering and industrial. The proposed theory only requires four unknown displacement functions, and the transverse displacement does not need to be separated into bending and shear parts, simplifying the theory. One noteworthy feature of the proposed theory is its ability to capture the parabolic distribution of transverse shear strains and stresses throughout the plate's thickness while ensuring zero values on the two free surfaces. By eliminating the need for shear correction factors, the theory further enhances computational efficiency. Equations of motion are established using Hamilton's principle and solved via Navier's solution. The accuracy and efficiency of the proposed theory are verified by comparing results with available solutions. The authors then use the proposed theory to investigate the free vibration characteristics of three-phases functionally graded sandwich plates, considering the effects of parameters such as aspect ratio, side-to-thickness ratio, skin-core-skin thicknesses, and power-law indexes. Through careful analysis of the free vibration behavior of three-phases functionally graded sandwich plates, the work highlighted the significant roles played by individual material ingredients in influencing their frequencies.

• Advances in nano research
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• v.9 no.3
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• pp.193-210
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• 2020

In this research, beside presenting real images of produced Functionally Graded Carbon Nanotube-Reinforced Composites (FG-CNTRCs) and a brief review of the synthesis method of FG-CNTRCs, static and buckling analysis of FG-CNTRC with piezoelectric layers are investigated. It is assumed that the material properties of FG-CNTRC are varied through the thickness direction using four different distributions of Carbon Nanotubes (CNTs). To capture the size effects, nonlocal elasticity theory proposed by A.C. Eringen is also adopted in our model. One of the topics in our paper is using a higher order theory with eight different displacement fields and comparing their results with each other. To solve the governing equations, an analytical method is used to find the deflections and critical buckling loads of FG-CNTRCs. To show the accuracy of present methodology, our results are compared with the results of simply supported rectangular nano plates available in the literature. In this research, the effects of aspect ratio, piezoelectric layer and nonlocal parameter are also studied. It is hoped that this work leads to more accurate models on FG-CNTRC.

• Advances in nano research
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• v.14 no.5
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• pp.475-493
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• 2023

In the context of nonclassical nonlocal strain gradient elasticity, this article studies the free and forced responses of functionally graded material (FGM) porous nanoplates exposed to thermal and magnetic fields under a moving load. The developed mathematical model includes shear deformation, size-scale, miscorstructure influences in the framework of higher order shear deformation theory (HSDT) and nonlocal strain gradient theory (NSGT), respectively. To explore the porosity effect, the study considers four different porosity models across the thickness: uniform, symmetrical, asymmetric bottom, and asymmetric top distributions. The system of quations of motion of the FGM porous nanoplate, including the effects of thermal load, Lorentz force, due to the magnetic field and moving load, are derived using the Hamilton's principle, and then solved analytically by employing the Navier method. For the free and forced responses of the nanoplate, the effects of nonlocal elasticity, strain gradient elasticity, temperature rise, magnetic field intensity, porosity volume fraction, and porosity distribution are analyzed. It is found that the forced vibrations of FGM porous nanoplates under thermal and live loads can be damped by applying a directed magnetic field.

• Steel and Composite Structures
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• v.20 no.4
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• pp.889-911
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• 2016

Using the hyperbolic shear deformation plate model and including plate-foundation interaction (Winkler and Pasternak model), an analytical method in order to determine the deflection and stress distributions in simply supported rectangular functionally graded plates (FGP) subjected to a sinusoidal load, a temperature and moisture fields. The present theory exactly satisfies stress boundary conditions on the top and the bottom of the plate. No transversal shear correction factors are needed because a correct representation of the transversal shearing strain is given. Materials properties of the plate (elastic, thermal and moisture expansion coefficients) are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. Numerical examples are presented and discussed for verifying the accuracy of the present theory in predicting the bending response of FGM plates under sinusoidal load and a temperature field as well as moisture concentration. The effects of material properties, temperature, moisture, plate aspect ratio, side-to-thickness ratio, ratio of elastic coefficients (ceramic-metal) and three distributions for both temperature and moisture on deflections and stresses are investigated.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.4
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• pp.1275-1289
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• 1996

The plane elasticity problem of collinear cracks in a layered medium is investigated. The medium is modeled as bonded structure constituted from a surface layer and a semi-infinite substrate. Along the bond line between the two dissimilar homegeneous constituents, it is assumed that as interfacial zone having the functionally graded, nonhomogeneous elastic modulus exists. The layered medium contains three collinear cracks, one in each constituent material oriented perpendicular to the nominal interfaces. The stiffness matrix formulation is utilized and a set of homogeneous conditions relevant to the given problem is readily satisfied. The proposed mixed boundary value problem is then represented in the form of a system of integral equations with Cauchy-type singular kernels. The stress intensity factors are defined from the crack-tip stress fields possessing the standard square-root singular behavior. The resulting values of stress intensity factors mainly address the interactions among the cracks for various crack sizes and material combinations.

• Structural Engineering and Mechanics
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• v.73 no.4
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• pp.407-426
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• 2020

In this present paper, a semi-analytical mesh-free method is employed for the three-dimensional free vibration analysis of a bi-directional functionally graded piezoelectric circular structure. The dependent variables have been expanded by Fourier series with respect to the circumferential direction and have been discretized through radial and axial directions based on the mesh-free shape function. The current approach has a distinct advantage. The nonlinear Green-Lagrange strain is employed as the relationship between strain and displacement fields to observe thermal impacts in stiffness matrices. Nevertheless, high order terms have been neglected at the final steps of equations driving. The material properties are assumed to vary continuously in both radial and axial directions simultaneously in accordance with a power law distribution. The convergence and validation studies are conducted by comparing our proposed solution with available published results to investigate the accuracy and efficiency of our approach. After the validation study, a parametric study is undertaken to investigate the temperature effects, different types of polarization, mechanical and electric boundary conditions and geometry parameters of structures on the natural frequencies of functionally graded piezoelectric circular structures.

• Steel and Composite Structures
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• v.25 no.2
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• pp.127-139
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• 2017

In this paper, an exact analytical solution for simply supported sandwich plate which considers the permeation effect of adhesives is presented. The permeation layer is described as functionally graded material (FGM), the elastic modulus of which is assumed to be graded along the thickness following the exponential law. Based on the exact three-dimensional (3-D) elasticity theory, the solution of stresses and displacements for each layer is derived. By means of the recursive matrix method, the solution can be efficiently obtained for plates with many layers. The present solution obtained can be used as a benchmark to access other simplified solutions. The comparison study indicates that the finite element (FE) solution is close to the present one when the FGM layer in the FE model is divided into a series of homogeneous layers. However, the present method is more efficient than the FE method, with which the mesh division and computation are time-consuming. Moreover, the solution based on Kirchhoff-Love plate theory is greatly different from the present solution for thick plates. The influence of the thickness of the permeation layer on the stress and displacement fields of the sandwich plate is discussed in detail. It is indicated that the permeation layer can effectively relieve the discontinuity stress at the interface.

• Steel and Composite Structures
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• v.45 no.3
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• pp.305-330
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• 2022

This article aims to investigate the static deflection and stress analysis of bi-directional functionally graded porous plate (BDFGPP) modeled by unified higher order kinematic theories to include the shear stress effects, which not be considered before. Different shear functions are described according to higher order models that satisfy the zero-shear influence at the top and bottom surfaces, and hence refrain from the need of shear correction factor. The material properties are graded through two spatial directions (i.e., thickness and length directions) according to the power law distribution. The porosities and voids inside the material constituent are described by different cosine functions. Hamilton's principle is implemented to derive the governing equilibrium equation of bi-directional FG porous plate structures. An efficient numerical differential integral quadrature method (DIQM) is exploited to solve the coupled variable coefficients partial differential equations of equilibrium. Problem validation and verification have been proven with previous prestigious work. Numerical results are illustrated to present the significant impacts of kinematic shear relations, gradation indices through thickness and length, porosity type, and boundary conditions on the static deflection and stress distribution of BDFGP plate. The proposed model is efficient in design and analysis of many applications used in nuclear, mechanical, aerospace, naval, dental, and medical fields.