• Journal of the Computational Structural Engineering Institute of Korea
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• v.29 no.4
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• pp.293-299
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• 2016

In this paper, a projection method is introduced which is used in topology design optimization. In the projection method, each active design variable is projected onto the design domain depending on the shape and size of the projection functions, and the finite element under this projection receives a solid material. Furthermore, the size of the projection function defines the minimum length scale of the structural members. Therefore, a designer can easily apply design constraints without complicated post-processing procedure. In addition, the projection method can be combined with the homogenization theory, and applied to material design problem for composite materials. Topology design optimization for the unit-cell of the periodic structures can maximize the effective material properties, which yields the optimal material distribution with maximum bulk or shear moduli under a given volume fraction.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.24 no.4
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• pp.413-419
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• 2011

The nano-size hoenycomb structures have the higher ratio of the surface to the volume than macro-size honeycomb structures, and they can maximize the functionality of the electrical and chemical catalyst. The mechanical behaviors of the nano-sized structures are different from ones of the macro-size structure, and it is caused by the surface effect. This surface effect can be investigated by the atomistic simulation; however, the prediction of mechanical behaviors of the nano-sized honeycombs are practically impossible due to excessive computational resources and computation time. In this paper, by combining the bridging method considering the surface stress elasticity model with homogenization method, the mechanical behaviors of the nano-sized honeycombs are predicted efficiently.

• Structural Engineering and Mechanics
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• v.71 no.1
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• pp.99-107
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• 2019

Wave propagation analysis of a porous graphene platelet reinforced (GPLR) nanocomposite shell is investigated for the first time. The homogenization of the utilized material is procured by extending the Halpin-Tsai relations for the porous nanocomposite. Both symmetric and asymmetric porosity distributions are regarded in this analysis. The equations of the shell's motion are derived according to Hamilton's principle coupled with the kinematic relations of the first-order shear deformation theory of the shells. The obtained governing equations are considered to be solved via an analytical solution which includes two longitudinal and circumferential wave numbers. The accuracy of the presented formulations is examined by comparing the results of this method with those reported by former authors. The simulations reveal a stiffness decrease in the cases which porosity influences are regarded. Also, one must pay attention to the effects of longitudinal wave number on the wave dispersion curves of the nanocomposite structure.

• Advances in nano research
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• v.7 no.5
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• pp.325-335
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• 2019

In the present study, nonlocal strain gradient theory (NSGT) is developed for wave propagation of functionally graded (FG) nanoscale plate in the thermal environment by considering the porosity effect. $Si_3N_4$ as ceramic phase and SUS304 as metal phase are regarded to be constitutive material of FG nanoplate. The porosity effect is taken into account on the basis of the newly extended method which considers coupling influence between Young's modulus and mass density. The motion relation is derived by applying Hamilton's principle. NSGT is implemented in order to account for small size effect. Wave frequency and phase velocity are obtained by solving the problem via an analytical method. The effects of different parameters such as porosity coefficient, gradient index, wave number, scale factor and temperature change on phase velocity and wave frequency of FG porous nanoplate have been examined and been presented in a group of illustrations.

• Structural Engineering and Mechanics
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• v.61 no.2
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• pp.209-220
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• 2017

The purpose of this paper is to study the geometrically nonlinear free vibration of functionally graded nano/micro beams (FGNBs) based on the modified couple stress theory. For practical applications, some analytical expressions of nonlinear frequencies for FGNBs on a nonlinear Pasternak foundation are developed. Hamilton's principle is employed to obtain nonlinear governing differential equations in the context of both Euler-Bernoulli and Timoshenko beam theories for a comprehensive investigation. The modified continuum theory contains one material length scale parameter to capture the size effect. The variation of two-constituent material along the thickness is modeled using Reddy's power-law. Also, the Mori-Tanaka method as an accurate homogenization technique is implemented to estimate the effective material properties of the FGNBs. The results are presented for both hinged-hinged and clamped-clamped boundary conditions. The nonlinear partial differential equations are reduced to ordinary differential equations using Galerkin method and then the powerful method of homotopy analysis is utilized to obtain the semi-analytical solutions. Eventually, the presented analytical expressions are used to examine the influences of the length scale parameter, material gradient index, and elastic foundation on the nonlinear free vibration of FGNBs.

• International journal of advanced smart convergence
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• v.13 no.1
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• pp.162-179
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• 2024

With the acceleration of China's urbanization process, the economic development and market potential of small and medium-sized cities have been constantly enhanced, with the urbanization competition having been caught in the vortex of homogenization. However, small and medium-sized cities are exposed to limited resources and funds, and therefore need to be more flexible and innovative in the strategy implementation, while urban brand communication is one of the key factors to promote the competitiveness of cities. Taking the small and medium-sized cities in China as the research objects, this study, based on the domestic and foreign theories about the brand communication of small and medium-sized cities, as well as other city-related theories, analyzes textual materials about the current situation and new changes in brand communication of small and medium-sized cities with grounded theory, reflecting on the problems in brand communication in China's small and medium-sized cities. Combining the basic elements of urban brand communication, a model for constructing brand communication strategies for small and medium-sized cities is further proposed, so as to provide the differentiated and distinctive strategies for the construction and communication of urban brands in small and medium-sized cities in China, as well as provide a new perspective and strategy on how to enhance the competitiveness and contribute to the sustainable economic development of small and medium-sized.

• Steel and Composite Structures
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• v.18 no.4
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• pp.1063-1081
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• 2015

In this paper, a new nonlocal hyperbolic refined plate model is presented for free vibration properties of functionally graded (FG) plates. This nonlocal nano-plate model incorporates the length scale parameter which can capture the small scale effect. The displacement field of the present theory is chosen based on a hyperbolic variation in the in-plane displacements through the thickness of the nano-plate. By dividing the transverse displacement into the bending and shear parts, the number of unknowns and equations of motion of the present theory is reduced, significantly facilitating structural analysis. The material properties are assumed to vary only in the thickness direction and the effective properties for the FG nano-plate are computed using Mori-Tanaka homogenization scheme. The governing equations of motion are derived based on the nonlocal differential constitutive relations of Eringen in conjunction with the refined four variable plate theory via Hamilton's principle. Analytical solution for the simply supported FG nano-plates is obtained to verify the theory by comparing its results with other available solutions in the open literature. The effects of nonlocal parameter, the plate thickness, the plate aspect ratio, and various material compositions on the dynamic response of the FG nano-plate are discussed.

• Steel and Composite Structures
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• v.20 no.2
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• pp.227-249
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• 2016

The objective of this work is to present a zeroth-order shear deformation theory for free vibration analysis of functionally graded (FG) nanoscale plates resting on elastic foundation. The model takes into consideration the influences of small scale and the parabolic variation of the transverse shear strains across the thickness of the nanoscale plate and thus, it avoids the employ use of shear correction factors. Also, in this present theory, the effect of transverse shear deformation is included in the axial displacements by using the shear forces instead of rotational displacements as in available high order plate theories. The material properties are supposed to be graded only in the thickness direction and the effective properties for the FG nanoscale plate are calculated by considering Mori-Tanaka homogenization scheme. The equations of motion are obtained using the nonlocal differential constitutive expressions of Eringen in conjunction with the zeroth-order shear deformation theory via Hamilton's principle. Numerical results for vibration of FG nanoscale plates resting on elastic foundations are presented and compared with the existing solutions. The influences of small scale, shear deformation, gradient index, Winkler modulus parameter and Pasternak shear modulus parameter on the vibration responses of the FG nanoscale plates are investigated.

• Journal of Soil and Groundwater Environment
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• v.9 no.1
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• pp.79-86
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• 2004

Hydraulic conductivity along rock fracture is mainly dependent on fracture geometries such as orientation, aperture, roughness and connectivity. Therefore, it needs to consider fracture geometries sufficiently on a fracture model for a numerical analysis to calculate permeability coefficient in a fracture. This study performed new type of numerical analysis using a homogenization analysis method to calculate permeability coefficient accurately along single fractures with several fracture models that were considered fracture geometries as much as possible. First of all, fracture roughness and aperture variation due to normal stress applied on a fracture were directly measured under a confocal laser scaning microscope (CLSM). The acquired geometric data were used as input data to construct fracture models for the homogenization analysis (HA). Using the constructed fracture models, the homogenization analysis method can compute permeability coefficient with consideration of material properties both in microscale and in macroscale. The HA is a new type of perturbation theory developed to characterize the behavior of a micro inhomogeneous material with a periodic microstructure. It calculates micro scale permeability coefficient at homogeneous microscale, and then, computes a homogenized permeability coefficient (C-permeability coefficient) at macro scale. Therefore, it is possible to analyze accurate characteristics of permeability reflected with local effect of facture geometry. Several computations of the HA were conducted to prove validity of the HA results compared with the empirical equations of permeability in the previous studies using the constructed 2-D fracture models. The model can be classified into a parallel plate model that has fracture roughness and identical aperture along a fracture. According to the computation results, the conventional C-permeability coefficients have values in the range of the same order or difference of one order from the permeability coefficients calculated by an empirical equation. It means that the HA result is valid to calculate permeability coefficient along a fracture. However, it should be noted that C-permeability coefficient is more accurate result than the preexisting equations of permeability calculation, because the HA considers permeability characteristics of locally inhomogeneous fracture geometries and material properties both in microscale and macroscale.

• Steel and Composite Structures
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• v.39 no.1
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• pp.1-20
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• 2021

An exact solution based on refined third-order theory (TOT) has been presented for functionally graded porous curved beams having deep curvature. The displacement field of the refined TOT is derived by imposing the shear free conditions at the outer and inner surfaces of curved beams. The properties of the two phase composite are tailored according the power law rule and the effective properties are computed using Mori-Tanaka homogenization scheme. The equations of motion as well as consistent boundary conditions are derived using the Hamilton's principle. The curved beam stiffness coefficients (A, B, D) are obtained numerically using six-point Gauss integration scheme without compromising the accuracy due to deepness (1 + z/R) terms. The porosity has been modeled assuming symmetric (even) as well as asymmetric (uneven) distributions across the cross section of curved beam. The programming has been performed in MATLAB and is validated with the results available in the literature as well as 2D finite element model developed in ABAQUS. The effect of inclusion of 1 + z/R terms is studied for deflection, stresses and natural frequencies for FG curved beams of different radii of curvature. Results presented in this work will be useful for comparison of future studies.