• Structural Engineering and Mechanics
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• v.82 no.4
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• pp.477-490
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• 2022

This article investigates the nonlinear behavior of two-directional functionally graded materials (TDFGM) doubly curved panels with porosities for the first time. An improved and effectual approach is established based on the improved first-order shear deformation shell theory (IFSDST) and von Karman's type nonlinearity. The IFSDST considers the effects of shear deformation without the need for a shear correction factor. The composition of TDFGM constitutes four different materials, and the modified power-law function is employed to vary the material properties continuously in both thickness and longitudinal directions. A nonlinear finite element method in conjunction with Hamilton's principle is used to obtain the governing equations. Then, the direct iterative method is incorporated to accomplish the numerical results using the frequency-amplitude, nonlinear central deflection relations. Finally, the influence of volume fraction grading indices, porosity distributions, porosity volume, curvature ratio, thickness ratio, and aspect ratio provides a thorough insight into the linear and nonlinear responses of the porous curved panels. Meanwhile, this study emphasizes the influence of the volume fraction gradation profiles in conjunction with the various material and geometrical parameters on the linear frequency, nonlinear frequency, and deflection of the TDFGM porous shells. The numerical analysis reveals that the frequencies and nonlinear deformations can be significantly regulated by changing the volume fraction gradation profiles in a specified direction with an appropriate combination of materials. Hence, TDFGM panels can overcome the drawbacks of the functionally graded materials with a gradation of properties in a single direction.

• Coupled systems mechanics
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• v.13 no.1
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• pp.43-60
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• 2024

This work presents an analytical approach to investigate wave propagation in bi-directional functionally graded cantilever porous beam. The formulations are based on Touratier's higher-order shear deformation beam theory. The physical properties of the porous functionally graded material beam are graded through the width and thickness using a power law distribution. Two porosities models approximating the even and uneven porosity distributions are considered. The governing equations of the wave propagation in the porous functionally graded beam are derived by employing the Hamilton's principle. Closed-form solutions for various parameters and porosity types are obtained, and the numerical results are compared with those available in the literature.The numerical results show the power law index, number of wave, geometrical parameters and porosity distribution models affect the dynamic of the FG beam significantly.

• Nuclear Engineering and Technology
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• v.54 no.6
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• pp.2067-2076
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• 2022

The importance of safety culture has been emphasized to achieve a high level of safety. In this light, a systematic method to more properly deal with safety culture is necessary. Here, a decision-making tool that can apply a graded approach to the analysis of safety culture is proposed, called the F-D matrix, which determines the frequency and the difficulty of safety culture attributes recently defined by the IAEA. A hierarchical model of difficulty contributors was developed as a scoring standard, and its elements were weighted via expert evaluation using the analytic hierarchy process. The frequency of the attributes was derived by analyzing reported events from nuclear power plants in the Republic of Korea. Period-by-period comparisons with the F-D matrix can show trends in the change of the maturity level of an organization's safety culture and help to evaluate the effectiveness of previously implemented measures. In the evaluating the difficulty of the attributes in the recently developed harmonized safety culture model, the difficulties of Trending, Benchmarking, Resilience, and Documentation and Procedures were found to be relatively high, while the difficulties of Conflicts are Resolved, Ownership, Collaboration, and Respect is Evident were found to be relatively low. A case study was conducted with an analysis period of 10 years to attempt to reflect the many changes in safety culture that have been made following the Fukushima accident in March 2011. As a result of comparing two periods following the Fukushima accident, the overall frequency decreased by about 40%, providing evidence for the effects of the various improvements and measures taken following the increased emphasis on safety culture. The proposed F-D matrix provides a new analytical perspective and enables an in-depth analysis of safety culture.

• Geomechanics and Engineering
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• v.32 no.2
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• pp.159-177
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• 2023

In the present work, a simple and refined shear deformation theory is used to analyze the effect of visco-elastic foundation on the buckling response of exponentially-gradient sandwich plates under various boundary conditions. The proposed theory includes indeterminate integral variables kinematic with only four generalized parameters, in which no shear correction factor is used. The visco-Pasternak's foundation is taken into account by adding the influence of damping to the usual foundation model which characterized by the linear Winkler's modulus and Pasternak's foundation modulus. The four governing equations for FGM sandwich plates are derived by employing principle of virtual work. To solve the buckling problem, Galerkin's approach is utilized for FGM sandwich plates for various boundary conditions. The analytical solutions for critical buckling loads of several types of powerly graded sandwich plates resting on visco-Pasternak foundations under various boundary conditions are presented. Some numerical results are presented to indicate the effects of inhomogeneity parameter, elastic foundation type, and damping coefficient of the foundation, on the critical buckling loads.

• Structural Engineering and Mechanics
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• v.65 no.5
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• pp.523-533
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• 2018

In this study, the dynamic response of a functionally graded material (FGM) circular plate in contact with incompressible fluid under the harmonic load is investigated. Analysis of the plate is based on First-order Shear Deformation Plate Theory (FSDT). The governing equation of the oscillatory behavior of the fluid is obtained by solving Laplace equation and satisfying its boundary conditions. A new set of admissible functions, which satisfy both geometrical and natural boundary conditions, are developed for the free vibration analysis of moderately thick circular plate. The Chebyshev-Ritz Method is employed together with this set of admissible functions to determine the vibrational behaviors. The modal superposition approach is used to determine the dynamic response of the plate exposed to harmonic loading. Numerical results of the force vibrations and the effects of the different geometrical parameters on the dynamic response of the plate are investigated. Finally, the results of this research in the limit case are compared and validated with the results of other researches and finite element model (FEM).

• Smart Structures and Systems
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• v.21 no.4
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• pp.493-519
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• 2018

This article presents a finite element (FE) model to assess the free vibration and static response of a functionally graded skew magneto-electro-elastic (FGSMEE) plate. Through the thickness material grading of FGSMEE plate is achieved using power law distribution. The coupled constitutive equations along with the total potential energy approach are used to develop the FE model of FGSMEE plate. The transformation matrix is utilized in bringing out the element matrix corresponding to the global axis to a local axis along the skew edges to specify proper boundary conditions. The effect of skew angle on the natural frequency of an FGSMEE plate is analysed. Further, the study includes the evaluation of the static behavior of FGSMEE plate for various skew angles. The influence of skew angle on the primary quantities such as displacements, electric potential, and magnetic potential, and secondary quantities such as stresses, electric displacement and magnetic induction is studied in detail. In addition, the effect of power-law gradient, thickness ratio, boundary conditions and aspect ratio on the free vibration and static response characteristics of FGSMEE plate has been investigated.

• Advances in nano research
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• v.9 no.1
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• pp.33-45
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• 2020

Geometrically nonlinear buckling of functionally graded magneto-electro-elastic (FG-MEE) nanoshells with the use of classical shell theory and nonlocal strain gradient theory (NSGT) has been analyzed in present research. Mathematical formulation based on NSGT gives two scale coefficients for simultaneous description of structural stiffness reduction and increment. Functional gradation of material properties is described based on power-law formulation. The nanoshell is under a multi-physical field related to applied voltage, magnetic potential, and mechanical load. Exerting a strong electric voltage, magnetic potential or mechanical load may lead to buckling of nanoshell. Taking into account geometric nonlinearity effects after buckling, the behavior of nanoshell in post-buckling regime can be analyzed. Nonlinear governing equations are reduced to ordinary equations utilizing Galerkin's approach and post-buckling curves are obtained based on an analytical procedure. It will be shown that post-buckling curves are dependent on nonlocal/strain gradient parameters, electric voltage magnitude and sign, magnetic potential magnitude and sign and material gradation exponent.

• Steel and Composite Structures
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• v.28 no.5
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• pp.541-557
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• 2018

This paper presents the influence of carbon nanotubes (CNTs) waviness and aspect ratio on the vibrational behavior of functionally graded nanocomposite sandwich annular sector plates resting on two-parameter elastic foundations. The carbon nanotube-reinforced (CNTR) sandwich plate has smooth variation of CNT fraction along the thickness direction. The distributions of CNTs are considered functionally graded (FG) or uniform along the thickness and their mechanical properties are estimated by an extended rule of mixture. In this study, the classical theory concerning the mechanical efficiency of a matrix embedding finite length fibers has been modified by introducing the tube-to-tube random contact, which explicitly accounts for the progressive reduction of the tubes' effective aspect ratio as the filler content increases. Effects of CNT distribution, volume fraction, aspect ratio and waviness, and also effects of Pasternak's elastic foundation coefficients, sandwich plate thickness, face sheets thickness and plate aspect ratio are investigated on the free vibration of the sandwich plates with wavy CNT-reinforced face sheets. The study is carried out based on three-dimensional theory of elasticity and in contrary to two-dimensional theories, such as classical, the first- and the higher-order shear deformation plate theories, this approach does not neglect transverse normal deformations. The sandwich 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.

• Smart Structures and Systems
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• v.19 no.3
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• pp.243-257
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• 2017

In this paper, free vibration of functionally graded (FG) size-dependent nanobeams is studied within the framework of nonlocal Timoshenko beam model. It is assumed that material properties of the FG nanobeam, vary continuously through the thickness according to a power-law form. The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. The non-classical governing differential equations of motion are derived through Hamilton's principle and they are solved utilizing both Navier-based analytical method and an efficient and semi-analytical technique called differential transformation method (DTM). Various types of boundary conditions such as simply-supported, clamped-clamped, clamped-simply and clamped-free are assumed for edge supports. The good agreement between the presented DTM and analytical results of this article and those available in the literature validated the presented approach. It is demonstrated that the DTM has high precision and computational efficiency in the vibration analysis of FG nanobeams. The obtained results show the significance of the material graduation, nonlocal effect, slenderness ratio and boundary conditions on the vibration characteristics of FG nanobeams.

• Advances in concrete construction
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• v.9 no.6
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• pp.569-576
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• 2020

Employment of the wave propagation approach with the combination of Pasternak foundation equation gives birth to the shell frequency equation. Mathematically, the integral form of the Lagrange energy functional is converted into a set of three partial differential equations. A cylindrical shell is placed on the elastic foundation of Pasternak. For isotropic materials, the physical properties are same everywhere, whereas the laminated and functionally graded materials, they vary from point to point. Here the shell material has been taken as functionally graded material. The influence of the elastic foundation, wave number, length and height-to-radius ratios is investigated with different boundary conditions. The frequencies of length-to-radius and height-to-radius ratio are counter part of each other. The frequency first increases and gain maximum value in the midway of the shell length and then lowers down for the variations of wave number. It is found that due to inducting the elastic foundation of Pasternak, the frequencies increases. It is also exhibited that the effect of frequencies is investigated by varying the surfaces with stainless steel and nickel as a constituent material. MATLAB software is utilized for the vibration of functionally graded cylindrical shell with elastic foundation of Pasternak and the results are verified with the open literature.