• Structural Engineering and Mechanics
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• v.53 no.3
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• pp.411-427
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• 2015

Based on linear elastic theory of quasicrystals, various equations and solutions for quasicrystal beams are deduced systematically and directly from plane problem of two-dimensional quasicrystals. Without employing ad hoc stress or deformation assumptions, the refined theory of beams is explicitly established from the general solution of quasicrystals and the Lur'e symbolic method. In the case of homogeneous boundary conditions, the exact equations and exact solutions for beams are derived, which consist of the fourth-order part and transcendental part. In the case of non-homogeneous boundary conditions, the exact governing differential equations and solutions under normal loadings only and shear loadings only are derived directly from the refined beam theory, respectively. In two illustrative examples of quasicrystal beams, it is shown that the exact or accurate analytical solutions can be obtained in use of the refined theory.

• Steel and Composite Structures
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• v.49 no.3
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• pp.293-306
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• 2023

This article focuses on the study of the buckling behavior of two-dimensional functionally graded (2D-FG) nanosize tubes, including porosity, based on the first shear deformation and higher-order theory of the tube. The nano-scale tube is simulated using the nonlocal gradient strain theory, and the general equations and boundary conditions are derived using Hamilton's principle for the Zhang-Fu's tube model (as a higher-order theory) and Timoshenko beam theory. Finally, the derived equations are solved using a numerical method for both simply-supported and clamped boundary conditions. A parametric study is performed to investigate the effects of different parameters, such as axial and radial FG power indices, porosity parameter, and nonlocal gradient strain parameters, on the buckling behavior of the bi-dimensional functionally graded porous tube. Keywords: Nonlocal strain gradient theory; buckling; Zhang-Fu's tube model; Timoshenko theory; Two-dimensional functionally graded materials; Nanotubes; Higher-order theory.

• Journal of Nuclear Fuel Cycle and Waste Technology(JNFCWT)
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• v.16 no.2
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• pp.203-209
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• 2018

To correctly predict the neutron behavior based on diffusion calculations, it is necessary to adopt well-specified boundary conditions using suitable diffusion approximations to transport boundary conditions. Boundary conditions such as the zero net-current, the Marshak, the Mark, the zero scalar flux, and the Albedo condition have been used extensively in diffusion theory to approximate the reflective and vacuum conditions in transport theory. In this paper, we derive and analyze these conditions to prove their mathematical validity and to understand their physical implications, as well as their relationships with one another. To show the validity of these diffusion boundary conditions, we solve a sample problem. The results show that solutions of the diffusion equation with these well-formulated boundary conditions are very close to the solution of the transport equation with transport boundary conditions.

• Structural Engineering and Mechanics
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• v.75 no.6
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• pp.737-746
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• 2020

This paper attempts to investigate the free vibration of functionally graded material beams with nonuniform width based on the nonlocal elasticity theory. The theoretical formulations are established following the Euler-Bernoulli beam theory, and the governing equations of motion of the system are derived from the minimum total potential energy principle using the nonlocal elasticity theory. In addition, the Differential Quadrature Method (DQM) is applied, along with the Chebyshev-Gauss-Lobatto polynomials, in order to determine the weighting coefficient matrices. Furthermore, the effects of the nonlocal parameter, cross-section area of the functionally graded material (FGM) beam and various boundary conditions on the natural frequencies are examined. It is observed that the nonlocal parameter and boundary conditions significantly influence the natural frequencies of the functionally graded material beam cross-section. The results obtained, using the Differential Quadrature Method (DQM) under various boundary conditions, are found in good agreement with analytical and numerical results available in the literature.

• Advances in nano research
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• v.6 no.4
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• pp.299-321
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• 2018

A layerwise shear deformation theory is applied in this paper for buckling analysis of piezoelectric truncated conical shell. The core is a multiphase nanocomposite reinforced by carbon nanotubes (CNTs) and carbon fibers. The top and bottom face sheets are piezoelectric subjected to 3D electric field and external voltage. The Halpin-Tsai model is used for obtaining the effective moisture and temperature dependent material properties of the core. The proposed layerwise theory is based on Mindlin's first-order shear deformation theory in each layer and results for a laminated truncated conical shell with three layers considering the continuity boundary condition. Applying energy method, the coupled motion equations are derived and analyzed using differential quadrature method (DQM) for different boundary conditions. The influences of some parameters such as boundary conditions, CNTs weight percent, cone semi vertex angle, geometrical parameters, moisture and temperature changes and external voltage are investigated on the buckling load of the smart structure. The results show that enhancing the CNTs weight percent, the buckling load increases. Furthermore, increasing the moisture and temperature changes decreases the buckling load.

• Geomechanics and Engineering
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• v.22 no.2
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• pp.119-132
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• 2020

In this study a new innovative three unknowns trigonometric shear deformation theory is proposed for the buckling and vibration responses of exponentially graded sandwich plates resting on elastic mediums under various boundary conditions. The key feature of this theoretical formulation is that, in addition to considering shear deformation effect, it has only three unknowns in the displacement field as in the case of the classical plate theory (CPT), contrary to five as in the first shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). Material characteristics of the sandwich plate faces are considered to vary within the thickness direction via an exponential law distribution as a function of the volume fractions of the constituents. Equations of motion are obtained by employing Hamilton's principle. Numerical results for buckling and free vibration analysis of exponentially graded sandwich plates under various boundary conditions are obtained and discussed. Verification studies confirmed that the present three -unknown shear deformation theory is comparable with higher-order shear deformation theories which contain a greater number of unknowns.

• Journal of KSNVE
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• v.9 no.3
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• pp.485-492
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• 1999

The effects of boundary conditions on vibration characteristics for the ring stiffered composite cylindrical shells are investigated by theoretical and experimental method. In the theoretical procedure, the Love's thin shell theory combined with the discrete stiffener theory to consider the ring stiffening effect are adopted to derive the frequency equation. In experiment, the impact exciting method is used to obtain the vibraton results. Five different boundary conditions: clamped-clamped, simply supported-simply supported, free-free, clamped-free, clamped-simply supported are considered in this study.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.831-836
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• 2000

In this study, the Rayleigh inextensional theory and extensional theory for thin shells was employed to predict the natural frequencies of the hemi-spherical shell with free and simply. supported boundary condition. The frequencies and mode shapes from theoretical calculation were compared with those of commercial finite element code, ANSYS. In order to validate the theory, modal test was also performed by impact test and FFT analysis. Modal test and FEM analysis of the free, simply supported and clamped boundary condition was also carried out.

• Journal of Energy Engineering
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• v.6 no.1
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• pp.19-25
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• 1997

This paper presents the short-term operation scheduling on cogeneration system connected with auxiliary equipment by using the possibility fuzzy theory. The possibility fuzzy theory is a method to obtain the possibility boundary of the solution from the fuzzification of coefficients. Simulation is carried out to obtain the boundary of heat production in each time interval. Simulation results show the flexible operation boundary to establish effectively operation scheduling.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.5 no.3
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• pp.17-22
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• 2006

Sunroof is getting widely used in automobiles since it maintains, compare to window, better air circulation as well as less noise while driving in high speed. In this study, we consider an electronic control type spoiler sunroof which slides backward after tilting a rear part of a glass. Installing a wind deflector on the sunroof reduces noise much more effectively. The height of the wind deflector is designed using a boundary theory related to incompressible air layer. The developed wind deflector is investigated experimentally by measuring a wind noise. When the height of the wind deflector is designed by a fixed type, the sunroof maintains a very quiet interior noise over a certain driving speed, nevertheless it produces relatively loud noise in low driving speed.