• Structural Engineering and Mechanics
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• v.28 no.2
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• pp.129-152
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• 2008

This paper considers the solution of the stochastic differential equations (SDEs) with random operator and/or random excitation using the spectral SFEM. The random system parameters (involved in the operator) and the random excitations are modeled as second order stochastic processes defined only by their means and covariance functions. All random fields dealt with in this paper are continuous and do not have known explicit forms dependent on the spatial dimension. This fact makes the usage of the finite element (FE) analysis be difficult. Relying on the spectral properties of the covariance function, the Karhunen-Loeve expansion is used to represent these processes to overcome this difficulty. Then, a spectral approximation for the stochastic response (solution) of the SDE is obtained based on the implementation of the concept of generalized inverse defined by the Neumann expansion. This leads to an explicit expression for the solution process as a multivariate polynomial functional of a set of uncorrelated random variables that enables us to compute the statistical moments of the solution vector. To check the validity of this method, two applications are introduced which are, randomly loaded simply supported reinforced concrete beam and reinforced concrete cantilever beam with random bending rigidity. Finally, a more general application, randomly loaded simply supported reinforced concrete beam with random bending rigidity, is presented to illustrate the method.

• Polymer(Korea)
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• v.25 no.6
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• pp.866-875
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• 2001

In this work, thermal decomposition mechanism based on kinetic parameters and thermal stability of carbon fiber-reinforced carbon matrix composites (C/C composites), have been studied under high temperature oxidative conditions with addition of tetra-ethylorthosilicate (TEOS) as an oxidation inhibitor. Thermogravimetric analysis (TGA) was executed to evaluate the thermal decomposition mechanism and thermal stability of C/C composites in the temperature range of 30 ～ $850^{\circ}C$. As a result, the kinetic parameters of the composites impregnated with TEOS, i.e., activation energy for thermal decomposition ($E_d$), order of reaction (n) , and pre-exponential factor (A) were evaluated as 136 kJ/mol, 0, and 2.3$\times$$10^9s^{-1}$, respectively. Especially, the IPDT and $E_d$ of C/C composites impregnated with TEOS were improved largely compared with the composites impregnated without TEOS, due to the formation of $SiO_2$ on composite surfaces, resulting in interrupting the oxygen attack to carbon active site in the composites.

• Korea-Australia Rheology Journal
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• v.16 no.4
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• pp.183-191
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• 2004

High Deborah or Weissenberg number problems in viscoelastic flow modeling have been known formidably difficult even in the inertialess limit. There exists almost no result that shows satisfactory accuracy and proper mesh convergence at the same time. However recently, quite a breakthrough seems to have been made in this field of computational rheology. So called matrix-logarithm (here we name it tensor-logarithm) formulation of the viscoelastic constitutive equations originally written in terms of the conformation tensor has been suggested by Fattal and Kupferman (2004) and its finite element implementation has been first presented by Hulsen (2004). Both the works have reported almost unbounded convergence limit in solving two benchmark problems. This new formulation incorporates proper polynomial interpolations of the log­arithm for the variables that exhibit steep exponential dependence near stagnation points, and it also strictly preserves the positive definiteness of the conformation tensor. In this study, we present an alternative pro­cedure for deriving the tensor-logarithmic representation of the differential constitutive equations and pro­vide a numerical example with the Leonov model in 4:1 planar contraction flows. Dramatic improvement of the computational algorithm with stable convergence has been demonstrated and it seems that there exists appropriate mesh convergence even though this conclusion requires further study. It is thought that this new formalism will work only for a few differential constitutive equations proven globally stable. Thus the math­ematical stability criteria perhaps play an important role on the choice and development of the suitable con­stitutive equations. In this respect, the Leonov viscoelastic model is quite feasible and becomes more essential since it has been proven globally stable and it offers the simplest form in the tensor-logarithmic formulation.

• The Transactions of the Korea Information Processing Society
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• v.3 no.3
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• pp.640-654
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• 1996

This paper presents a synthesis method for multi-level Reed-Muller circuits using BDDs(Binary Decision Diagrams). The existing synthesis tool for Reed circuits, FACTOR, is not appropriate to the synthesis of large circuits because it uses matrix (map-type) to represent given logic functions, resulting in the exponential time and space in number of imput to the circuits. For solving this problems, a syntheisis method based on BDD is presented. Using BDDs, logic functions are represented compactly. Therefor storage spaces and computing time for synthesizing logic functions were greatly decreased, and this technique can be easily applied to large circuits. Using BDD representations, the proposed method extract best patterns to minimize multi-level Reed Muller circuits with good performance in area optimization and testability. Experimental results using the proposed method show better performance than those using previous methods〔2〕. For large circuits of considering the best input partition, synthesis results have been improved.

• Journal of Korea Water Resources Association
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• v.35 no.3
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• pp.295-306
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• 2002

The modified TOPMODEL of two storage systems has been integrated to the generalized assumptions of decreasing hydraulic conductivity to vertical direction. Three different recharge functions were introduced to explore the impact of the macropore flow to vortical direction, the storage at the surface zone and the relative storage deficit of the soil matrix. Combinations of these approaches provide 30 type of the model structure for the hillslope hydrology. Developed models have been applied to several hydrologic events at the Sulmachun watershed. The performance evaluation with the Monte carlo simulation suggests that the exponential function of transmissivity reduction should be appropriate form for the physically -based hydrologic simulation on the Sulmachun watershed. It has been shown that the recharge function of macropore flow contributes to improve the predictability of the generalized version of modified TOPMODEL.

• Nuclear Engineering and Technology
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• v.55 no.5
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• pp.1763-1774
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• 2023

In this study, a series of flexible neutron/gamma shielding composites are fabricated through the doping of Gd₂O₃ into the matrix of SEBS with (M_Gd2O3: M_SEBS) % from 5% to 100%. Neutron transmittance test shows an exponential attenuation with the increase of areal density of Gd, in which the transmittance T ranges from 59.1440% to 35.3026%, with standard deviation less than 2.2743%, mass attenuation coefficient 𝜇_m from 0.3194 cm²/g to 0.4999 cm²/g, and half value layer-HVL value from 2.4530 mm to 1.1313 mm. Shielding efficiency of the Gd₂O₃/SEBS composites is basically improved in comparison with that of B₄C/SEBS. The transmittance T, mass/linear attenuation coefficient 𝜇_m and 𝜇, HVL and effective atomic number Z_eff for the shielding of γ rays (39 keV, 59 keV and 122 keV) are measured and calculated with XCOM as well as MCX programs. Finally, plots of the three dimensional relationships between transmittance, doping amount and thickness are provided to the guidance for engineering shielding design. In summary, the Gd₂O₃/SEBS composite is proved to be an effective flexible neutron/low energy γ rays shielding material, which could be of potential applications in the field of nuclear technology and nuclear engineering.

• Advances in nano research
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• v.16 no.5
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• pp.509-519
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• 2024

In this study, the static analysis of carbon nanotube-reinforced composites (CNTRC) beams resting on a Winkler-Pasternak elastic foundation is presented. The developed theories account for higher-order variation of transverse shear strain through the depth of the beam and satisfy the stress-free boundary conditions on the top and bottom surfaces of the beam. To study the effect of carbon nanotubes distribution in functionally graded (FG-CNT), we introduce in the equation of CNT volume fraction a new exponent equation. The SWCNTs are assumed to be aligned and distributed in the polymeric matrix with different patterns of reinforcement. The rule of mixture is used to describe the material properties of the CNTRC beams. The governing equations were derived by employing Hamilton's principle. The models presented in this work are numerically provided to verify the accuracy of the present theory. The analytical solutions are presented, and the obtained results are compared with the existing solutions to verify the validity of the developed theories. Many parameters are investigated, such as the Pasternak shear modulus parameter, the Winkler modulus parameter, the volume fraction, and the order of the exponent in the volume fraction equation. New results obtained from bending and stresses are presented and discussed in detail. From the obtained results, it became clear the influence of the exponential CNTs distribution and Winkler-Pasternak model improved the mechanical properties of the CNTRC beams.

• The Journal of the Petrological Society of Korea
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• v.10 no.3
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• pp.157-171
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• 2001

This study investigated the effects of Pb/Tl ratio, Pb concentration and concomitant matrix elements on the measurement of Pb isotope ratios using multi-collector ICP/MS (AXIOM MC model). Accuracy and reproducibility of Pb isotope ratios in NBS 981 solution were estimated for 42 data measured from March to August 2001. Pb isotopes measured in rocks, bronzes and sediments were compared to data measured by TIMS. Reproducibilities for $^{206}Pb/^{204}Pb,\; ^{207}Pb/^{204}Pb,\;and\;^{208}Pb/^{204}Pb$ ratio were about 500 ppm (2sd) and for $^{207}Pb/^{206}Pb$\;and\;^{208}Pb/^{206}Pb$ were 100~200 ppm for 200 ng of Pb in NBS 981 solution. The optimum conditions for the analysis of Pb isotope ratios with AXIOM MC for best accuracy and reproducibility were defined as follows; 1) Pb/Tl ratio is about 10 2) Pb concentration is about 100 ng/ml 3) correction for mass discrimination is performed by exponential law using 2.3887 of $^{205}Tl/^{203}Tl$ and Pb mass fractionation factor empirically obtained from $ln(^{208}Pb/^{206}Pb)-ln(^{205}Tl/^{203}Tl)$ relationship. The sample data measured with MC/ICP/MS for acid-digested and chemically separated rock samples, and acid-digested bronze samples and sediment samples coincide with those of TIMS within analytical errors. Therefore, MC/ICP/MS is a rapid analytical technique for Pb isotope ratios with the similar precision compared with TIMS.

• Restorative Dentistry and Endodontics
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• v.31 no.4
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• pp.290-299
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• 2006

Objectives: The purpose of this study is to evaluate the effect of ethylene glycol analogs on modulus of elasticity and ultimate tensile strength of moist, demineralized dentin matrix. Methods: Dentin disks 0.5 mrn thick were prepared from mid-coronal dentin of extracted. unerupted, human third molars. 'I' beam and hour-glass shaped specimens were prepared from the disks, the ends protected with nail varnish and the central regions completely demineralized in 0.5M EDTA for 5 days. Ultimate tensile stress (UTS) and low strain modulus of elasticity (E) were determined with specimens immersed for 60 min in distilled water $(H_{2}O)$, ethylene glycol $(HO-CH_{2}-CH_{2}-OH)$, 2-methoxyethanol $(H_{3}CO-CH_{2}-CH_{2}-OH)$, and 1,2-dimethoxyethane $(H_{3}CO-CH_{2}-CH_{3}-OCH_{3})$ prior to testing in those same media. Modulus of elasticity was measured on the same specimens in a repeated measures experimental design. The results were analyzed with a one-way ANOVA on ranks, followed by Dunn's test at ${\alpha}\;=\;0.05$. Regression analysis examined the relationship between UTS or E and hoy's solubility parameter for hydrogen bonding $({\delta}_{h})$ of each solvent. Results: The UTS of demineralized dentin in water, ethylene glycol, 2-methoxyethanol, and 1,2-dimethoxyethane was 24 (3), 30 (5), 37 (6), and 45 (6) MPa, ${\times}$ (SD) N = 10. Low strain E for the same media were 16 (13), 23 (14), 52 (24), and 62 (22) MPa. Regression analysis of UTS vs ${\delta}_{h}$ revealed a significant $(p\;<\;0.0001,\;r\;=\;-0.99,\;R^{2}\;=\;0.98)$ inverse, exponential relationship. A similar inverse relationship was obtained between low strain E vs ${\delta}_{h}\;(p\;<\;0.0005,\;r\;=\;-0.93,\;R^{2}\;=\;0.86)$. Significance: The tensile properties of demineralized dentin are dependent upon the hydrogen bonding ability of polar solvents $({\delta}_{h})$. Solvents with low ${\delta}_{h}$ values may permit new interpeptide H-bonding in collagen that increases its tensile properties. Solvents with high ${\delta}_{h}$ values prevent the development of these new interpeptide H-bonds.

• Composites Research
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• v.30 no.5
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• pp.323-330
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• 2017

In this study, multiscale analysis in which the information obtained from molecular dynamics simulation is applied to the continuum mechanics level is conducted to investigate the effects of clustering of silicon carbide nanoparticles reinforced into polypropylene matrix on mechanical behavior of nanocomposites. The elastic behavior of polymer nanocomposites is observed for various states of nanoparticulate agglomeration according to the model reflecting the degradation of interphase properties. In addition, factors which mainly affect the mechanical behavior of the nanocomposites are identified, and new index 'clustering density' is defined. The correlation between the clustering density and the elastic modulus of nanocomposites is understood. As the clustering density increases, the interfacial effect decreased and finally the improvement of mechanical properties is suppressed. By considering the random distribution of the nanoparticles, the range of elastic modulus of nanocomposites for same value of clustering density can be investigated. The correlation can be expressed in the form of exponential function, and the mechanical behavior of the polymer nanocomposites can be effectively predicted by using the nanoparticulate clustering density.