• Communications of the Korean Mathematical Society
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• v.29 no.1
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• pp.23-26
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• 2014

Let E be a graded central division algebra (GCDA) over a grade field R. Let S be an unramified graded field extension of R. We describe the grading on the underlying GCDA E' of $E{\otimes}_RS$ which is analogous to the valuation on a tame division algebra over Henselian valued field.

• Composites Research
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• v.26 no.6
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• pp.392-397
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• 2013

Functionally graded materials graded continuously and discretely, and are modeled using modified Mori- Tanaka and self-consistent methods. The proposed micromechanics model accounts for multi-phase heterogeneity and arbitrary number of layers. The influence of geometries and distinct elastic material properties of each constituent and voids on the effective elastic properties of FGM is investigated. Numerical examples of different functionally graded materials are presented. The predicted elastic properties obtained from the current model agree well with experimental results from the literature.

• Wind and Structures
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• v.32 no.1
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• pp.19-30
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• 2021

This study presents buckling analysis of a simply supported sandwich plate with functionally graded porous layers. In the kinematic relation of the plate, a hyperbolic shear displacement model is used. The governing equations of the problem are derived by using the principle of virtual work. In the solution of the governing equations, the Navier procedure is implemented. In the porosity effect, four different porosity types are used for functionally graded sandwich layers. In the numerical examples, the effects of the porosity parameters, porosity types and geometry parameters on the critical buckling of the functionally graded sandwich plates are investigated.

• International Journal of Highway Engineering
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• v.16 no.5
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• pp.29-38
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• 2014

PURPOSES : The purpose of this study is to evaluate moisture susceptibility of a dense graded and an open graded asphalt mixtures by the method of AASHTO T-283. METHODS : To simulate moisture damage of asphalt pavements with continuously rainfall during summer rainy season, the dense graded and the open graded asphalt mixtures were immersed in water for 15 days and were measured the weight and the change of strength. Also, the mixtures were performed five freeze-thaw cycles to simulate moisture damage of the mixtures by freeze-thaw during winter and were measured the change of strength. The degradation characteristics model was used to analyze the relationship between strength and moisture damage. RESULTS : According to the results, the dense graded and the open graded asphalt mixtures were shown in the similar trends of the strength changes by immersion time and freeze-thaw cycle. However, the moisture damage reduction of open graded asphalt mixture was more sensitive in early phase than that of dense graded asphalt mixture.

• Structural Engineering and Mechanics
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• v.53 no.6
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• pp.1143-1165
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• 2015

In this work, various higher-order shear deformation plate theories for wave propagation in functionally graded plates are developed. Due to porosities, possibly occurring inside functionally graded materials (FGMs) during fabrication, it is therefore necessary to consider the wave propagation in plates having porosities in this study. The developed refined plate theories have fewer number of unknowns and equations of motion than the first-order shear deformation theory, but accounts for the transverse shear deformation effects without requiring shear correction factors. The rule of mixture is modified to describe and approximate material properties of the functionally graded plates with porosity phases. The governing equations of the wave propagation in the functionally graded plate are derived by employing the Hamilton's principle. The analytic dispersion relation of the functionally graded plate is obtained by solving an eigenvalue problem. The effects of the volume fraction distributions and porosity volume fraction on wave propagation of functionally graded plate are discussed in detail. The results carried out can be used in the ultrasonic inspection techniques and structural health monitoring.

• Bulletin of the Korean Mathematical Society
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• v.56 no.4
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• pp.1041-1057
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• 2019

Let ${\Gamma}$ be a nonzero commutative cancellative monoid (written additively), $R={\bigoplus}_{{\alpha}{\in}{\Gamma}}$ $R_{\alpha}$ be a ${\Gamma}$-graded integral domain with $R_{\alpha}{\neq}\{0\}$ for all ${\alpha}{\in}{\Gamma}$, and $S(H)=\{f{\in}R{\mid}C(f)=R\}$. In this paper, we study homogeneously divisorial domains which are graded integral domains whose nonzero homogeneous ideals are divisorial. Among other things, we show that if R is integrally closed, then R is a homogeneously divisorial domain if and only if $R_{S(H)}$ is an h-local $Pr{\ddot{u}}fer$ domain whose maximal ideals are invertible, if and only if R satisfies the following four conditions: (i) R is a graded-$Pr{\ddot{u}}fer$ domain, (ii) every homogeneous maximal ideal of R is invertible, (iii) each nonzero homogeneous prime ideal of R is contained in a unique homogeneous maximal ideal, and (iv) each homogeneous ideal of R has only finitely many minimal prime ideals. We also show that if R is a graded-Noetherian domain, then R is a homogeneously divisorial domain if and only if $R_{S(H)}$ is a divisorial domain of (Krull) dimension one.

• Steel and Composite Structures
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• v.49 no.6
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• pp.667-684
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• 2023

In the context of finite element method, a computational simulation is presented to study and analyze the dynamic behavior of regularly perforated functionally graded rotating beam for the first time. To investigate the effect of perforation configurations, both regular circular and squared perforation patterns are studied. To explore impacts of graded material distributions, both axial and transverse gradation profiles are considered. The material characteristics of graded materials are assumed to be smoothly and continuously varied through the axial or the thickness direction according the nonlinear power gradation law. A computational finite elements procedure is presented. The accuracy of the numerical procedure is verified and compared. Resonant frequencies, axial displacements as well as internal stress distributions throughout the perforated graded rotating cantilever beam are studied. Effects of material distributions, perforation patterns, as well as the rotating beam speed are investigated. Obtained results proved that the graded material distribution has remarkable effects on the dynamic performance. Additionally, circular perforation pattern produces more softening effect compared with squared perforation configuration thus larger values of axial displacements and maximum principal stresses are detected. Moreover, squared perforation provides smaller values of nondimensional frequency parameters at most of vibration modes compared with circular pattern.

• Earthquakes and Structures
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• v.13 no.3
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• pp.255-265
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• 2017

In this paper, an efficient shear deformation theory is developed for wave propagation analysis in a functionally graded beam. More particularly, porosities that may occur in Functionally Graded Materials (FGMs) during their manufacture are considered. The proposed shear deformation theory is efficient method because it permits us to show the effect of both bending and shear components and this is carried out by dividing the transverse displacement into the bending and shear parts. Material properties are assumed graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents; but the rule of mixture is modified to describe and approximate material properties of the functionally graded beams with porosity phases. The governing equations of the wave propagation in the functionally graded beam are derived by employing the Hamilton's principle. The analytical dispersion relation of the functionally graded beam is obtained by solving an eigenvalue problem. The effects of the volume fraction distributions, the depth of beam, the number of wave and the porosity on wave propagation in functionally graded beam are discussed in details. It can be concluded that the present theory is not only accurate but also simple in predicting the wave propagation characteristics in the functionally graded beam.

• Bulletin of the Korean Mathematical Society
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• v.53 no.1
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• pp.163-180
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• 2016

We study the structure of an arbitrary graded Lie triple system $\mathfrak{T}$ with restrictions neither on the dimension nor the base field. We show that $\mathfrak{T}$ is of the form $\mathfrak{T}=U+\sum_{j}I_j$ with U a linear subspace of the 1-homogeneous component $\mathfrak{T}_1$ and any $I_j$ a well described graded ideal of $\mathfrak{T}$, satisfying $[I_j,\mathfrak{T},I_k]=0$ if $j{\neq}k$. Under mild conditions, the simplicity of $\mathfrak{T}$ is characterized and it is shown that an arbitrary graded Lie triple system $\mathfrak{T}$ is the direct sum of the family of its minimal graded ideals, each one being a simple graded Lie triple system.

• Steel and Composite Structures
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• v.23 no.3
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• pp.263-271
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• 2017

A theoretical study was carried-out of mode II delamination fracture behavior of the End Loaded Split (ELS) functionally graded beam configuration with considering the material non-linearity. The mechanical response of ELS was modeled analytically by using a power-law stress-strain relation. It was assumed that the material is functionally graded transversally to the beam. The non-linear fracture was investigated by using the J-integral approach. Equations were derived for the crack arm curvature and zero axes coordinate that are needed for the J-integral solution. The analysis developed is valid for a delamination crack located arbitrary along the beam height. The J-integral solution was verified by analyzing the strain energy release rate with considering material non-linearity. The effects of material gradient, non-linear material behavior and crack location on the fracture were evaluated. The solution derived is suitable for parametric analyses of non-linear fracture. The results obtained can be used for optimization of functionally graded beams with respect to their mode II fracture performance. Also, such simplified analytical models contribute for the understanding of delamination fracture in functionally graded beams exhibiting material non-linearity.