• Structural Engineering and Mechanics
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• 제72권1호
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• pp.61-70
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• 2019

The functionally graded materials (FGM) used in plates contain probably a porosity volume fraction which needs taking into account this aspect of imperfection in the mechanical bahavior of such structures. The present work aims to study the effect of the distribution forms of porosity on the bending of simply supported FG plate reposed on the Winkler-Pasternak foundation. A refined theory of shear deformation is developed to study the effect of the distribution shape of porosity on static behavior of FG plates. It was found that the distribution form of porosity significantly influence the mechanical behavior of FG plates, in terms of deflection, normal and shear stress. It can be concluded that the proposed theory is simple and precise for the resolution of the behavior of flexural FGM plates resting on elastic foundations while taking into account the shape of distribution of the porosity.

• Advances in nano research
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• 제6권4호
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• pp.339-356
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• 2018

In this article, the critical buckling of a single-walled carbon nanotube (SWCNT) embedded in Kerr's medium is studied. Based on the nonlocal continuum theory and the Euler-Bernoulli beam model. The governing equilibrium equations are acquired and solved for CNTs subjected to mechanical loads and embedded in Kerr's medium. Kerr-type model is employed to simulate the interaction of the (SWNT) with a surrounding elastic medium. A first time, a comparison with the available results is made, and another comparison between various models Winkler-type, Pasternak-type and Kerr-type is studied. Effects of nonlocal parameter and aspect ratio of length to diameter of nanobeam, as well as the foundation parameters on buckling of CNT are investigated. These results are important in the mechanical design considerations of nanocomposites based on carbon nanotubes.

• Advances in materials Research
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• 제7권3호
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• pp.163-174
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• 2018

This article studies the free and forced vibrations of the carbon nanotubes CNTs embedded in an elastic medium including thermal and dynamic load effects based on nonlocal Euler-Bernoulli beam. A Winkler type elastic foundation is employed to model the interaction of carbon nanotube and the surrounding elastic medium. Influence of all parameters such as nonlocal small-scale effects, high temperature change, Winkler modulus parameter, vibration mode and aspect ratio of short carbon nanotubes on the vibration frequency are analyzed and discussed. The non-local Euler-Bernoulli beam model predicts lower resonance frequencies. The research work reveals the significance of the small-scale coefficient, the vibrational mode number, the elastic medium and the temperature change on the non-dimensional natural frequency.

• Earthquakes and Structures
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• 제16권5호
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• pp.601-609
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• 2019

The effect of the porosity and its distribution shape on the normal and shear interfacial stresses of the FGM beam strengthened with FRP plate subjected to a uniformly distributed load are investigated analytically in the present paper. Basically, the governing equations of FGM beams with porosity strengthened with composite plates are identical to the ones without porosity. Nonetheless, when the effect of the porosity and its distribution shape are taken into account, the rule of mixture was reformulated to assess the material characteristics with the porosity phases and its distribution shape. This work discusses the influence of the gradient index, the porosity and its distribution shape on the interfacial stresses.

• 대한수학회논문집
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• 제39권3호
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• pp.785-802
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• 2024

Given M a monoid with a neutral element e. We show that the solutions of d'Alembert's functional equation for n × n matrices Φ(pr, qs) + Φ(sp, rq) = 2Φ(r, s)Φ(p, q), p, q, r, s ∈ M are abelian. Furthermore, we prove under additional assumption that the solutions of the n-dimensional mixed vector-matrix Wilson's functional equation $$\begin{cases}f(pr, qs) + f(sp, rq) = 2\phi(r, s)f(p, q),\\Φ(p, q) = \phi(q, p),{\quad}p, q, r, s {\in} M\end{cases}$$ are abelian. As an application we solve the first functional equation on groups for the particular case of n = 3.

• Advances in materials Research
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• 제5권1호
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• pp.1-9
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• 2016

The bending problem of a functionally graded cantilever beam subjected to uniformly distributed load is investigated. The material properties of the functionally graded beam are assumed to vary continuously through the thickness, according to a power-law distribution of the volume fraction of the constituents. First, the partial differential equation, which is satisfied by the stress functions for the axisymmetric deformation problem is derived. Then, stress functions are obtained by proper manipulation. A practical example is presented to show the application of the method.

• 대한수학회논문집
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• 제35권3호
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• pp.711-722
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• 2020

Given a semigroup S generated by its squares equipped with an involutive automorphism 𝝈 and a multiplicative function 𝜇 : S → ℂ such that 𝜇(x𝜎(x)) = 1 for all x ∈ S, we determine the complex-valued solutions of the following functional equations f(xy) + 𝜇(y)f(𝜎(y)x) = 2f(x)g(y), x, y ∈ S and f(xy) + 𝜇(y)f(𝜎(y)x) = 2f(y)g(x), x, y ∈ S.

• 대한수학회논문집
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• 제34권2호
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• pp.671-684
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• 2019

In this paper, we propose a new interior point method for solving nonlinear complementarity problems. In this method, we use a new profitable searching direction and instead of using the logarithmic quadratic term, we use a square root quadratic term. We prove the global convergence of the proposed method under the assumption that F is monotone. Some preliminary computational results are given to illustrate the efficiency of the proposed method.

• 대한수학회지
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• 제59권6호
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• pp.1139-1151
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• 2022

This paper studies the eigenvalues of the G(·)-Laplacian Dirichlet problem $$\{-div\;\(\frac{g(x,\;{\mid}{\nabla}u{\mid})}{{\mid}{\nabla}u{\mid}}{\nabla}u\)={\lambda}\;\(\frac{g(x,{\mid}u{\mid})}{{\mid}u{\mid}}u\)\;in\;{\Omega}, \\u\;=\;0\;on\;{\partial}{\Omega},$$ where Ω is a bounded domain in ℝ^N and g is the density of a generalized Φ-function G(·). Using the Lusternik-Schnirelmann principle, we show the existence of a nondecreasing sequence of nonnegative eigenvalues.

• 한국재료학회지
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• 제33권9호
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• pp.367-371
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• 2023

In this study we examine variations in the structure of perovskite compounds of LaBa₂Cu₂O₉, LaBa2₂CaCu₃O₁₂ and LaBa₂Ca₂Cu₅O₁₅ synthesized using the solid state reaction method. The samples' compositions were assessed using X-ray fluorescence (XRF) analysis. The La: Ba: Ca: Cu ratios for samples LaBa₂Cu₂O₉, LaBa2₂CaCu₃O₁₂ and LaBa₂Ca₂Cu₅O₁₅ were found by XRF analysis to be around 1:2:0:2, 1:2:1:3, and 1:2:2:5, respectively. The samples' well-known structures were then analyzed using X-ray diffraction. The three samples largely consist of phases 1202, 1213, and 1225, with a trace quantity of an unknown secondary phase, based on the intensities and locations of the diffraction peaks. According to the measured parameters a, b, and c, every sample has a tetragonal symmetry structure. Each sample's mass density was observed to alter as the lead oxide content rose. Scanning electron microscope (SEM) images of the three phases revealed that different Ca-O and Cu-O layers can cause different grain sizes, characterized by elongated thin grains, without a preferred orientation.