• Title/Summary/Keyword: functional equations

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Computational Materials Engineering: Recent Applications of VASP in the MedeA® Software Environment

  • Wimmer, Erich;Christensen, Mikael;Eyert, Volker;Wolf, Walter;Reith, David;Rozanska, Xavier;Freeman, Clive;Saxe, Paul
    • Journal of the Korean Ceramic Society
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    • v.53 no.3
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    • pp.263-272
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    • 2016
  • Electronic structure calculations have become a powerful foundation for computational materials engineering. Four major factors have enabled this unprecedented evolution, namely (i) the development of density functional theory (DFT), (ii) the creation of highly efficient computer programs to solve the Kohn-Sham equations, (iii) the integration of these programs into productivity-oriented computational environments, and (iv) the phenomenal increase of computing power. In this context, we describe recent applications of the Vienna Ab-initio Simulation Package (VASP) within the MedeA$^{(R)}$ computational environment, which provides interoperability with a comprehensive range of modeling and simulation tools. The focus is on technological applications including microelectronic materials, Li-ion batteries, high-performance ceramics, silicon carbide, and Zr alloys for nuclear power generation. A discussion of current trends including high-throughput calculations concludes this article.

Prediction of Optimal Microwave Extraction Conditions for Functional Compounds from Agrimonia pilosa Ledeb Using Response Surface Methodology (반응표면분석법을 이용한 용아초 기능성 성분의 마이크로웨이브 최적 추출조건 예측)

  • Park, Jong Jin;Lee, Won Young
    • Korean Journal of Medicinal Crop Science
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    • v.24 no.4
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    • pp.263-270
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    • 2016
  • Background: In this study, microwave extraction was used, which is an effective method to extract useful bioactive substances as it requires low quantities of solvent and short time periods. The aim of this study was to determine the optimal extraction conditions for Agrimonia pilosa Ledeb. Methods and Results: The independent variables were ethanol concentration, microwave power, and extraction time, each of which had five levels. The dependent variables were total polyphenol and total flavonoid content, and DPPH radical scavenging activity. To determine the optimal extraction conditions for bioactive compounds, a response surface methodology was employed. Contour maps were generated from polynomial equations. The optimal conditions were then assumed by superimposing these contour maps. Based on the resulting graph, the optimal microwave extraction conditions for Agrimonia pilosa Ledeb were determined as 42 - 48% ethanol concentration, 240 - 280W microwave power, and 13 - 20 min of extraction time. Conclusions: Ethanol concentration had a significant effect on microwave extraction, in terms of total polyphenol and total flavonoid content, as well as DPPH radical scavenging activity. Microwave power and extraction time influenced the total polyphenol content, but not the total flavonoid content or the DPPH radical scavenging activity.

Investigation of microstructure and surface effects on vibrational characteristics of nanobeams based on nonlocal couple stress theory

  • Shariati, Ali;Barati, Mohammad Reza;Ebrahimi, Farzad;Toghroli, Ali
    • Advances in nano research
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    • v.8 no.3
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    • pp.191-202
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    • 2020
  • The article brings the study of nonlocal, surface and the couple stress together to apparent the frequency retaliation of FG nanobeams (Functionally graded). For the examination of frequency retaliation, the article considers the accurate spot of neutral axis. This article aims to enhance the coherence of proposed model to accurately encapsulate the significant effects of the nonlocal stress field, size effects together with material length scale parameters. These considered parameters are assimilated through what are referred to as modified couple stress as well as nonlocal elasticity theories, which encompasses the stiffness-hardening and softening influence on the nanobeams frequency characteristics. Power-law distribution is followed by the functional gradation of the material across the beam width in the considered structure of the article. Following the well-known Hamilton's principle, fundamental basic equations alongside their correlated boundary conditions are solved analytically. Validation of the study is also done with published result. Distinct parameters (such as surface energy, slenderness ratio, as nonlocal material length scale and power-law exponent) influence is depicted graphically following the boundary conditions on non-dimensional FG nanobeams frequency.

Utilization of Cotton Stalks-Biomass Waste in the Production of Carbon Adsorbents by KOH Activation for Removal of Dye-Contaminated Water

  • Fathy, Nady A.;Girgis, Badie S.;Khalil, Lila B.;Farah, Joseph Y.
    • Carbon letters
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    • v.11 no.3
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    • pp.224-234
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    • 2010
  • Four activated carbons were produced by two-stage process as followings; semi-carbonization of indigenous biomass waste, i.e. cotton stalks, followed by chemical activation with KOH under various activation temperatures and chemical ratios of KOH to semi-carbonized cotton stalks (CCS). The surface area, total pore volume and average pore diameter were evaluated by $N_2$-adsorption at 77 K. The surface morphology and oxygen functional groups were determined by SEM and FTIR, respectively. Batch equilibrium and kinetic studies were carried out by using a basic dye, methylene blue as a probe molecule to evaluate the adsorption capacity and mechanism over the produced carbons. The obtained activated carbon (CCS-1K800) exhibited highly microporous structure with high surface area of 950 $m^2/g$, total pore volume of 0.423 $cm^3/g$ and average pore diameter of 17.8 ${\AA}$. The isotherm data fitted well to the Langmuir isotherm with monolayer adsorption capacity of 222 mg/g for CCS-1K800. The kinetic data obtained at different concentrations were analyzed using a pseudo-first-order, pseudo-second-order and intraparticle diffusion equations. The pseudo-second-order model fitted better for kinetic removal of MB dye. The results indicate that such laboratory carbons could be employed as low cost alternative to commercial carbons in wastewater treatment.

Empirical Initial Scantling Equations on Optimal Structural Design of Submarine Pressure Hull

  • Oh, Dohan;Koo, Bonguk
    • Journal of Advanced Research in Ocean Engineering
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    • v.4 no.1
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    • pp.7-15
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    • 2018
  • The submarine is an underwater weapon system which covertly attacks the enemy. Pressure hull of a submarine is a main system which has to have a capacity which can improve the survivability (e.g., protection of crews) from the high pressure and air pollution by a leakage of water, a fire caused by outside shock, explosion, and/or operational errors. In addition, pressure hull should keep the functional performance under the harsh environment. In this study, optimal design of submarine pressure hull is dealt with 7 case studies done by analytic method and then each result's adequacy is verified by numerical method such as Finite Element Analysis (FEA). For the structural analysis by FEM, material non-linearity and geometric non-linearity are considered. After FEA, the results by analytic method and numerical method are compared. Weight optimized pressure hull initial scantling methods are suggested such as a ratio with shell thickness, flange width, web height and/or relations with radius, yield strength and design pressure (DP). The suggested initial scantling formulae can reduce the pressure hull weight from 6% and 19%.

Optimal Control and Robust Control of Rotating Shaft Using Magnetic Bearings (자기베어링을 이용한 회전축의 최적제어 및 강건제어)

  • Kang, Ho-Shik;Jeong, Namheul;Yoon, Il-Soung;Song, Ohseop
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.14 no.12
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    • pp.1330-1337
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    • 2004
  • In this study, the equations of motion of a rigid rotor supported by magnetic bearings are derived via Hamilton's principle, and transformed to a state-space form for control purpose. The optimal motion control of rotor magnetic bearing system based on the LQR(linear quadratic regulator) theory is addressed. New schemes related to the selection of the state weighting matrix Q and the control weighting matrix R involved in the quadratic functional to be minimized are proposed. And the robust control of the system with an LMI(linear matrix inequality) based H$_{\infty}$ theory is dealt with in this paper. Loop shapings of TFM (transfer function matrix) are used to increase the performance of control capability of the system. The control abilities of LQR and H$_{\infty}$ controller are compared by simulation and experimental tests and show that the capability of H$_{\infty}$ controller is superior to that of LQR.

Large deflection analysis of orthotropic, elliptic membranes

  • Chucheepsakul, Somchai;Kaewunruen, Sakdirat;Suwanarat, Apiwat
    • Structural Engineering and Mechanics
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    • v.31 no.6
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    • pp.625-638
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    • 2009
  • Applications of membrane mechanisms are widely found in nano-devices and nano-sensor technologies nowadays. An alternative approach for large deflection analysis of the orthotropic, elliptic membranes - subject to gravitational, uniform pressures often found in nano-sensors - is described in this paper. The material properties of membranes are assumed to be orthogonally isotropic and linearly elastic, while the principal directions of elasticity are parallel to the coordinate axes. Formulating the potential energy functional of the orthotropic, elliptic membranes involves the strain energy that is attributed to inplane stress resultant and the potential energy due to applied pressures. In the solution method, Rayleigh-Ritz method can be used successfully to minimize the resulting total potential energy generated. The set of equilibrium equations was solved subsequently by Newton-Raphson. The unparalleled model formulation capable of analyzing the large deflections of both circular and elliptic membranes is verified by making numerical comparisons with existing results of circular membranes as well as finite element solutions. The results are found in excellent agreements at all cases. Then, the parametric investigations are given to delineate the impacts of the aspect ratios and orthotropic elasticity on large static tensions and deformations of the orthotropic, elliptic membranes.

Development of a Quadrilateral Enhanced Assumed Strain Element for Efficient and Accurate Thermal Stress Analysis (효과적인 열응력 해석을 위한 사각형 추가 변형률 요소의 개발)

  • Ko, Jin-Hwan;Lee, Byung-Chai
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.23 no.7 s.166
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    • pp.1205-1214
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    • 1999
  • A new quadrilateral plane stress element is developed for efficient and accurate analysis of thermal stress problems. It is convenient to use the same mesh and the same shape functions for thermal analysis and stress analysis. But, because of the inconsistency between deformation related strain field and thermal strain field, oscillatory responses and considerable errors in stresses are resulted in. To avoid undesired oscillations, strain approximation is enhanced by supplementing several assumed strain terms based on the variational principle. Thermal deformation is incorporated into the generalized mixed variational principle for displacement, strain and stress fields, and basic equations for the modified enhanced assumed strain method are derived. For the stress approximation of bilinear elements, the $5{\beta}$ version of Pian and Sumihara is adopted. The numerical results for several problems show that the present element behaves well and reduces oscillatory responses. it also results in almost the same magnitude of error as compared with the quadratic element.

Free vibration analysis of bidirectional functionally graded annular plates resting on elastic foundations using differential quadrature method

  • Tahouneh, Vahid
    • Structural Engineering and Mechanics
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    • v.52 no.4
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    • pp.663-686
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    • 2014
  • This paper deals with free vibration analysis of bidirectional functionally graded annular plates resting on a two-parameter elastic foundation. The formulations are based on the three-dimensional elasticity theory. This study presents a novel 2-D six-parameter power-law distribution for ceramic volume fraction of 2-D functionally graded materials that gives designers a powerful tool for flexible designing of structures under multi-functional requirements. Various material profiles along the thickness and in the in-plane directions are illustrated by using the 2-D power-law distribution. The effective material properties at a point are determined in terms of the local volume fractions and the material properties by the Mori-Tanaka scheme. The 2-D differential quadrature method as an efficient and accurate numerical tool is used to discretize the governing equations and to implement the boundary conditions. The fast rate of convergence of the method is shown and the results are compared against existing results in literature. Some new results for natural frequencies of the plates are prepared, which include the effects of elastic coefficients of foundation, boundary conditions, material and geometrical parameters. The interesting results indicate that a graded ceramic volume fraction in two directions has a higher capability to reduce the natural frequency than conventional 1-D functionally graded materials.

Effect of Random Geometry Perturbation on Acoustic Scattering (기하형상의 임의교란이 음향산란에 미치는 영향)

  • 주관정
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 1992.10a
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    • pp.117-123
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    • 1992
  • In recent years, the finite element method has become one of the most popular numerical technique for obtaining solutions of engineering science problems. However, there exist various uncertainties in modeling the problems, such as the dimensions(geometry shape), the material properties, boundary conditions, etc. The consideration for the uncertainties inherent in the problems can be made by understanding the influences of uncertain parameters[1]. Determining the influences of uncertainties as statistical quantities using the standard finite element method requires enormous computing time, while the probabilistic finite element method is realized as an efficient scheme[2,3] yielding statistical solution with just a few direct computations. In this paper, a formulation of the probabilistic fluid-structure interaction problem accounting for the first order perturbation of geometric shape is derived, and especially probabilistical acoustic pressure scattering from the structure with surrounding fluid is focused on. In Section 2, governing equations for the fluid-structure problems are given. In Section 3, a finite element formulation, based on the functional, is presented. First order perturbation of geometric shape with randomness is incorporated into the finite element formulation in conjunction with discretization of the random fields in Section 4 and 5. Finally, the proposed formulation is applied to a acoustic pressure scattering problem from an infinitely long cylindrical shell structure with randomness of radial perturbation.

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