• Advances in aircraft and spacecraft science
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• v.9 no.1
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• pp.69-93
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• 2022

Reduced graphene oxide (rGO) is one of the derivatives of graphene, which has drawn some experimental research interests in recent years however, numerical research studying the mechanical behaviors of composites made of rGO has not been taken into consideration yet. The objective of this research is to investigate the buckling, and free vibration of functionally graded reduced graphene oxide reinforced nanocomposite (FG rGORC) plates employing isogeometric analysis (IGA). The effective Young's modulus of rGORC is determined based onthe Halpin-Tsai model. Four different FG distribution types of rGO are considered varying across plate thickness. Besides, the refined plate theory is used based on Reddy's third-order function. To capture the size effect, modified couple stress theory (MCST) is employed. A comprehensive study is provided examining the effect of various parameters including rGO weight fraction, FG distribution types, boundary conditions, material length scale parameter, etc. Our obtained results show that the addition of only 1% of uniformly distributed rGO into epoxy plates leads to the fundamental frequency and critical buckling load 18% and 39% higher than those of pure epoxy plates, respectively.

• Structural Engineering and Mechanics
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• v.86 no.4
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• pp.535-546
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• 2023

In the present paper, multiple interface cracks between a functionally graded orthotropic coating and an orthotropic half-plane substrate under concentrated loading are considered by means of the distribution dislocation technique (DDT). With the use of integration of Fourier transform the problem is reduced to a system of Cauchy-type singular integral equations which are solved numerically to compute the dislocation density on the surfaces of the cracks. The distribution dislocation is a powerful method to calculate accurate solutions to plane crack problems, especially this method is very good to find SIFs for multiple unequal cracks located at the interface. Hence this technique allows considering any number of interface cracks. The primary objective of this paper is to investigate the effects of the interaction of multiple interface cracks, load location, material orthotropy, nonhomogeneity parameters and geometry parameters on the modes I and II SIFs. Numerical results show that modes I/II SIFs decrease with increasing the nonhomogeneity parameter and the highest magnitude of SIF occurs where distances between the load location and crack tips are minimal.

• Computers and Concrete
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• v.32 no.5
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• pp.439-454
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• 2023

In this article, the surface stress effects on the buckling analysis of the annular sandwich plate is developed. The proposed plate is composed of two face layers made of carbon nanotubes (CNT) reinforced composite with assuming of fully bonded to functionally graded porous core. The generalized rule of the mixture is employed to predict the mechanical properties of the microcomposite sandwich plate. The derived potentials energy based on higher order shear deformation theory (HSDT) and modified couple stress theory (MCST) is solved by employing the Ritz method. An exact analytical solution is presented to calculate the critical buckling loads of the annular sandwich plate. The predicted results are validated by carrying out the comparison studies for the buckling analysis of annular plates with those obtained by other analytical and finite element methods. The effects of various parameters such as material length scale parameter, core thickness to total thickness ratio (hc/h), surface elastic constants based on surface stress effect, various boundary condition and porosity distributions, size of the internal pores (e0), Skempton coefficient and elastic foundation on the critical buckling load have been studied. The results can be served as benchmark data for future works and also in the design of materials science, injunction high-pressure micropipe connections, nanotechnology, and smart systems.

• Steel and Composite Structures
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• v.49 no.6
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• pp.603-614
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• 2023

In this paper, frequency analysis of curved functionally graded (FG) nanobeam by consideration of deepness effect has been studied. Differential transform method (DTM) has been used to obtain frequency responses. The nonlocal theory of Eringen has been applied to consider nanoscales. Material properties are supposed to vary in radial direction according to power-law distribution. Differential equations and related boundary conditions have been derived using Hamilton's principle. Finally, by consideration of nonlocal theory, the governing equations have been derived. Natural frequencies have been obtained using semi analytical method (DTM) for different boundary conditions. In order to study the effect of deepness, the deepness term is considered in strain field. The effects of the gradient index, radius of curvature, the aspect ratio, the nonlocal parameter and interaction of aforementioned parameters on frequency value for different boundary conditions such as clamped-clamped (C-C), clamped-hinged (C-H), and clamped-free (C-F) have been investigated. In addition, the obtained results are compared with the results in previous literature in order to validate present study, a good agreement was observed in the present results.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.31 no.3
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• pp.127-132
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• 2018

In this paper, a scheme for the evaluation of variability in the eigen-modes of functionally graded material(FGM) beams is proposed within the framework of perturbation-based stochastic analysis. As a random parameter, the spatially varying elastic modulus of FGM along the axial direction at the mid-surface of the beam is chosen, and the thru-thickness variation of the elastic modulus is assumed to follow the original form of exponential variation. In deriving the formulation, the first order Taylor expansion on the eigen-modes is employed. As an example, a simply supported FGM beam having symmetric elastic modulus with respect to the mid-surface is chosen. Monte Carlo analysis is also performed to check if the proposed scheme gives reasonable outcomes. From the analyses it is found that the two schemes give almost identical results of the mean and standard deviation of eigen-modes. With the propose scheme, the standard deviation shape of respective eigen-modes can be evaluated easily. The deviated mode shape is found to have one more zero-slope points than the mother modes shapes, irrespective of order of modes. The amount of deviation from the mean is found to have larger values for the higher modes than the lower modes.

• 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.

• Steel and Composite Structures
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• v.25 no.3
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• pp.361-374
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• 2017

In this study, the influences of triaxial magnetic field on the wave propagation behavior of anisotropic nanoplates are studied. In order to include small scale effects, nonlocal strain gradient theory has been implemented. To study the nanoplate as a continuum model, the three-dimensional elasticity theory is adopted in Cartesian coordinate. In our study, all the elastic constants are considered and assumed to be the functions of (x, y, z), so all kind of anisotropic structures such as hexagonal and trigonal materials can be modeled, too. Moreover, all types of functionally graded structures can be investigated. eigenvalue method is employed and analytical solutions for the wave propagation are obtained. To justify our methodology, our results for the wave propagation of isotropic nanoplates are compared with the results available in the literature and great agreement is achieved. Five different types of anisotropic structures are investigated in present paper and then the influences of wave number, material properties, nonlocal and gradient parameter and uniaxial, biaxial and triaxial magnetic field on the wave propagation analysis of anisotropic nanoplates are presented. From the best knowledge of authors, it is the first time that three-dimensional elasticity theory and nonlocal strain gradient theory are used together with no approximation to derive the governing equations. Moreover, up to now, the effects of triaxial magnetic field have not been studied with considering size effects in nanoplates. According to the lack of any common approximations in the displacement field or in elastic constant, present theory has the potential to be used as a bench mark for future works.

• Steel and Composite Structures
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• v.35 no.1
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• pp.111-127
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• 2020

The goal of this study is to fill this apparent gap in the area about investigating the effect of porosity distributions on vibrational behavior of FG sectorial plates resting on a two-parameter elastic foundation. The response of the elastic medium is formulated by the Winkler/Pasternak model. The internal pores and graphene platelets (GPLs) are distributed in the matrix either uniformly or non-uniformly according to three different patterns. The model is proposed with material parameters varying in the thickness of plate to achieve graded distributions in both porosity and nanofillers. The elastic modulus of the nanocomposite is obtained by using Halpin-Tsai micromechanics model. The annular sector plate is assumed to be simply supported in the radial edges while any arbitrary boundary conditions are applied to the other two circular edges including simply supported, clamped and free. The 2-D differential quadrature method as an efficient and accurate numerical approach is used to discretize the governing equations and to implement the boundary conditions. The convergence of the method is demonstrated and to validate the results, comparisons are made between the present results and those reported by well-known references for special cases treated before, have confirmed accuracy and efficiency of the present approach. It is observed that the maximum vibration frequency obtained in the case of symmetric porosity and GPL distribution, while the minimum vibration frequency is obtained using uniform porosity distribution. Results show that for better understanding of mechanical behavior of nanocomposite plates, it is crucial to consider porosities inside the material structure.

• Structural Engineering and Mechanics
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• v.64 no.4
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• pp.391-402
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• 2017

In this paper, a new nonlocal trigonometric shear deformation theory is proposed for thermal buckling response of nanosize functionally graded (FG) nano-plates resting on two-parameter elastic foundation under various types of thermal environments. This theory uses for the first time, undetermined integral variables and it contains only four unknowns, that is even less than the first shear deformation theory (FSDT). It is considered that the FG nano-plate is exposed to uniform, linear and sinusoidal temperature rises. Mori-Tanaka model is utilized to define the gradually variation of material properties along the plate thickness. Nonlocal elasticity theory of Eringen is employed to capture the size influences. Through the stationary potential energy the governing equations are derived for a refined nonlocal four-variable shear deformation plate theory and then solved analytically. A variety of examples is proposed to demonstrate the importance of elastic foundation parameters, various temperature fields, nonlocality, material composition, aspect and side-to-thickness ratios on critical stability temperatures of FG nano-plate.

• Advances in nano research
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• v.7 no.4
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• pp.249-263
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• 2019

In the current paper, an exact solution method is carried out for analyzing the thermo-mechanical vibration of curved FG nano-beams subjected to uniform thermal environmental conditions, by considering porosity distribution via nonlocal strain gradient beam theory for the first time. Nonlocal strain gradient elasticity theory is adopted to consider the size effects in which the stress for not only the nonlocal stress field but also the strain gradients stress field is considered. It is perceived that during manufacturing of functionally graded materials (FGMs) porosities and micro-voids can be occurred inside the material. Material properties of curved porous FG nanobeam are assumed to be temperature-dependent and are supposed to vary through the thickness direction of beam which modeled via modified power-law rule. Since variation of pores along the thickness direction influences the mechanical and physical properties, porosity play a key role in the mechanical response of curved FG nano-structures. The governing equations and related boundary condition of curved porous FG nanobeam under temperature field are derived via the energy method based on Timoshenko beam theory. An analytical Navier solution procedure is utilized to achieve the natural frequencies of porous FG curved nanobeam supposed to thermal loading. The results for simpler states are confirmed with known data in the literature. The effects of various parameters such as nonlocality parameter, porosity volume fractions, thermal effect, gradient index, opening angle and aspect ratio on the natural frequency of curved FG porous nanobeam are successfully discussed. It is concluded that these parameters play key roles on the dynamic behavior of porous FG curved nanobeam. Presented numerical results can serve as benchmarks for future analyses of curve FG nanobeam with porosity phases.