• Title/Summary/Keyword: analytical solutions

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A displacement solution for circular openings in an elastic-brittle-plastic rock

  • Huang, Houxu;Li, Jie;Rong, Xiaoli;Hao, Yiqing;Dong, Xin
    • Geomechanics and Engineering
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    • v.13 no.3
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    • pp.489-504
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    • 2017
  • The localized shear and the slip lines are easily observed in elastic-brittle-plastic rock. After yielding, the strength of the brittle rock suddenly drops from the peak value to the residual value, and there are slip lines which divide the macro rock into numbers of elements. There are slippages of elements along the slip lines and the displacement field in the plastic region is discontinuous. With some restraints, the discontinuities can be described by the combination of two smooth functions, one is for the meaning of averaging the original function, and the other is for characterizing the breaks of the original function. The slip lines around the circular opening in the plastic region of an isotropic H-B rock which subjected to a hydrostatic in situ stress can be described by the logarithmic spirals. After failure, the deformation mechanism of the plastic region is mainly attributed to the slippage, and a slippage parameter is introduced. A new analytical solution is presented for the plane strain analysis of displacements around circular openings. The displacements obtained by using the new solution are found to be well coincide with the exact solutions from the published sources.

Numerical Simulation of Subaerial and Submarine Landslides Using the Finite Volume Method in the Shallow Water Equations with (b, s) Coordinate ((b, s) 좌표로 표현된 천수방정식에 유한체적법을 사용하여 해상 및 해저 산사태 수치모의)

  • Pham, Van Khoi;Lee, Changhoon;Vu, Van Nghi
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.31 no.4
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    • pp.229-239
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    • 2019
  • A model of landslides is developed using the shallow water equations to simulate time-dependent performance of landslides. The shallow water equations are derived using the (b, s) coordinate system which can be applied in both river and ocean. The finite volume scheme employing the HLL approximate Riemann solver and the total variation diminishing (TVD) limiter is applied to deal with the numerical discontinuities occurring in landslides. For dam-break water flow and debris flow, numerical results are compared with analytical solutions and experimental data and good agreements are observed. The developed landslide model is successfully applied to predict subaerial and submarine landslides. It is found that the subaerial landslide propagates faster than the submarine landslide and the speed of propagation becomes faster with steeper bottom slope and less bottom roughness.

Design formulas for vibration control of sagged cables using passive MR dampers

  • Duan, Yuanfeng;Ni, Yi-Qing;Zhang, Hongmei;Spencer, Billie F. Jr.;Ko, Jan-Ming;Dong, Shenghao
    • Smart Structures and Systems
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    • v.23 no.6
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    • pp.537-551
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    • 2019
  • In this paper, a method for analyzing the damping performance of stay cables incorporating magnetorheological (MR) dampers in the passive control mode is developed taking into account the cable sag and inclination, the damper coefficient, stiffness and mass, and the stiffness of damper support. Both numerical and asymptotic solutions are obtained from complex modal analysis. With the asymptotic solution, analytical formulas that evaluate the equivalent damping ratio of the sagged cable-damper system in consideration of all the above parameters are derived. The main thrust of the present study is to develop an general design formula and a universal curve for the optimal design of MR dampers for adjustable passive control of sagged cables. Two sag-affecting coefficients are derived to reflect the effects of cable sag on the maximum attainable damping ratio and the optimal damper coefficient. For the cable configurations commonly used in cable-stayed bridges, the sag-affecting coefficients are directly expressed in terms of the sag-extensibility parameter to facilitate the control design. A case study on adjustable passive vibration control of the longest cable (536 m) on Stonecutters Bridge is carried out to demonstrate the influence of the sag for the damper design, and to figure out the necessity of adjustability of damper coefficients for achieving maximum damping ratio for different vibration modes.

Optimization of 1D 1H Quantitative NMR (Nuclear Magnetic Resonance) Conditions for Polar Metabolites in Meat

  • Kim, Hyun Cheol;Ko, Yoon-Joo;Kim, Minsu;Choe, Juhui;Yong, Hae In;Jo, Cheorun
    • Food Science of Animal Resources
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    • v.39 no.1
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    • pp.1-12
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    • 2019
  • The objective of this study was to establish an optimized 1D $^1H$ quantitative nuclear magnetic resonance (qNMR) analytical method for analyzing polar metabolites in meat. Three extraction solutions [0.6 M perchloric acid, 10 mM phosphate buffer, water/methanol (1:1)], three reconstitution buffers [20 mM 3-morpholinopropane-1-sulfonic acid, 2-[4-(2-hydroxyethyl)piperazin-1-yl]ethanesulfonic acid, phosphate buffer], and two pulse programs (zg30, noesypr1d) were evaluated. Extraction with 0.6 M perchloric acid and 20 mM phosphate resulted in a stable baseline and no additional overlap for quantifying polar metabolites in chicken breast. In qNMR analysis, zg30 pulse program (without water-suppression) showed smaller relative standard deviation (RSD) and faster running time than noesypr1d (water-suppression). High-performance liquid chromatography was compared with qNMR analyses to validate accuracy. The zg30 pulse program showed good accuracy and lower RSD. The optimized qNMR method was able to apply for beef and pork samples. Thus, an optimized 1D $^1H$ qNMR method for meat metabolomics was established.

Fluid-structure interaction system predicting both internal pore pressure and outside hydrodynamic pressure

  • Hadzalic, Emina;Ibrahimbegovic, Adnan;Dolarevic, Samir
    • Coupled systems mechanics
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    • v.7 no.6
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    • pp.649-668
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    • 2018
  • In this paper, we present a numerical model for fluid-structure interaction between structure built of porous media and acoustic fluid, which provides both pore pressure inside porous media and hydrodynamic pressures and hydrodynamic forces exerted on the upstream face of the structure in an unified manner and simplifies fluid-structure interaction problems. The first original feature of the proposed model concerns the structure built of saturated porous medium whose response is obtained with coupled discrete beam lattice model, which is based on Voronoi cell representation with cohesive links as linear elastic Timoshenko beam finite elements. The motion of the pore fluid is governed by Darcy's law, and the coupling between the solid phase and the pore fluid is introduced in the model through Biot's porous media theory. The pore pressure field is discretized with CST (Constant Strain Triangle) finite elements, which coincide with Delaunay triangles. By exploiting Hammer quadrature rule for numerical integration on CST elements, and duality property between Voronoi diagram and Delaunay triangulation, the numerical implementation of the coupling results with an additional pore pressure degree of freedom placed at each node of a Timoshenko beam finite element. The second original point of the model concerns the motion of the outside fluid which is modeled with mixed displacement/pressure based formulation. The chosen finite element representations of the structure response and the outside fluid motion ensures for the structure and fluid finite elements to be connected directly at the common nodes at the fluid-structure interface, because they share both the displacement and the pressure degrees of freedom. Numerical simulations presented in this paper show an excellent agreement between the numerically obtained results and the analytical solutions.

Bending analysis of functionally graded plates with arbitrary shapes and boundary conditions

  • Panyatong, Monchai;Chinnaboon, Boonme;Chucheepsakul, Somchai
    • Structural Engineering and Mechanics
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    • v.71 no.6
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    • pp.627-641
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    • 2019
  • The paper focuses on bending analysis of the functionally graded (FG) plates with arbitrary shapes and boundary conditions. The material property of FG plates is modelled by using the power law distribution. Based on the first order shear deformation plate theory (FSDT), the governing equations as well as boundary conditions are formulated and obtained by using the principle of virtual work. The coupled Boundary Element-Radial Basis Function (BE-RBF) method is established to solve the complex FG plates. The proposed methodology is developed by applying the concept of the analog equation method (AEM). According to the AEM, the original governing differential equations are replaced by three Poisson equations with fictitious sources under the same boundary conditions. Then, the fictitious sources are established by the application of a technique based on the boundary element method and approximated by using the radial basis functions. The solution of the actual problem is attained from the known integral representations of the potential problem. Therefore, the kernels of the boundary integral equations are conveniently evaluated and readily determined, so that the complex FG plates can be easily computed. The reliability of the proposed method is evaluated by comparing the present results with those from analytical solutions. The effects of the power index, the length to thickness ratio and the modulus ratio on the bending responses are investigated. Finally, many interesting features and results obtained from the analysis of the FG plates with arbitrary shapes and boundary conditions are demonstrated.

Implementation of Markov chain: Review and new application (관리도에서 Markov연쇄의 적용: 복습 및 새로운 응용)

  • Park, Changsoon
    • The Korean Journal of Applied Statistics
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    • v.34 no.4
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    • pp.537-556
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    • 2021
  • Properties of statistical process control procedures may not be derived analytically in many cases; however, the application of a Markov chain can solve such problems. This article shows how to derive the properties of the process control procedures using the generated Markov chains when the control statistic satisfies the Markov property. Markov chain approaches that appear in the literature (such as the statistical design and economic design of the control chart as well as the variable sampling rate design) are reviewed along with the introduction of research results for application to a new control procedure and reset chart. The joint application of a Markov chain approach and analytical solutions (when available) can guarantee the correct derivation of the properties. A Markov chain approach is recommended over simulation studies due to its precise derivation of properties and short calculation times.

Information Technologies of Accounting and Analysis in Modern Companies

  • Yaremenko, Liudmyla;Hevchuk, Anna;Vuzh, Tetiana;Vashchilina, Elena;Yermolaieva, Maryna
    • International Journal of Computer Science & Network Security
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    • v.21 no.5
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    • pp.151-159
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    • 2021
  • This article addresses the issue of finding optimal solutions using the information technologies of accounting and analysis in modern companies. The aim of the study is to reveal available information technologies for the needs of small, medium and large businesses operating in modern conditions. This goal is achieved by using systematization, comparison, and analysis of information, obtained under the survey and open management statistics. For the first time, the paper systematizes up-to-date information of 2021 about the most popular programs, online services, platforms and cloud services that are used to improve accounting and analytical processes in enterprises of various sizes. The main global trends in software development in terms of COVID-19 pandemic have been identified. In particular, the study defines the countries that occupy the leading positions in the informatization of business processes. An attempt was made to classify information technologies by their use by various volume of businesses. The analysis of research results of the Internet search query frequency regarding the use of information technologies enabled to determine the most popular software products worldwide. The peculiarities of information technologies, their advantages and disadvantages were examined and the common and distinctive features were compared. It was determined that for the new enterprises to implement information technologies, it is necessary to conduct a step-by-step study of all available software products. The software evaluation algorithm was described to help select the optimal software for the specific business processes. The paper also describes the way to solve the problem of using accounting and analysis software for the businesses of a specific kind of activity.

Natural Frequency Characteristics of Vertically Loaded Barrettes (수직하중을 받는 Barrette 말뚝의 고유진동수 특성)

  • Lee, Joon Kyu;Ko, Jun Young;Choi, Yong Hyuk;Park, Ku Byoung;Kim, Jae Young
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.41 no.1
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    • pp.39-48
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    • 2021
  • In this paper, an analytical model is proposed for assessing the natural frequency of barrettes subjected to vertical loading. The differential equation governing the free vibration of rectangular friction piles embedded in inhomogeneous soil is derived. The governing equation is numerically integrated by Runge-Kutta technique and the eigenvalue of natural frequency is computed by Regula-Falsi method. The numerical solutions for the natural frequency of barrettes compare well with those obtained from finite element analysis. Illustrated examples show that the natural frequencies increase with an increase of the cross-sectional aspect ratio, the friction resistance ratio and the soil stiffness ratio, and decrease with an increase of the friction aspect ratio, the slenderness ratio and the load factor, respectively.

Investigation on the dynamic response of porous FGM beams resting on variable foundation using a new higher order shear deformation theory

  • Atmane, Redhwane Ait;Mahmoudi, Noureddine;Bennai, Riadh;Atmane, Hassen Ait;Tounsi, Abdelouahed
    • Steel and Composite Structures
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    • v.39 no.1
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    • pp.95-107
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    • 2021
  • In this work, the dynamic response of functionally graded beams on variable elastic foundations is studied using a novel higher-order shear deformation theory (HSDT). Unlike the conventional HSDT, the present one has a new displacement field which introduces undetermined integral variables. The FG beams were assumed to be supported on Winkler-Pasternak type foundations in which the Winkler modulus is supposed to be variable in the length of the beam. The variable rigidity of the elastic foundation is assumed to be linear, parabolic and sinusoidal along the length of the beam. The material properties of the FG porous beam vary according to a power law distribution in terms of the volume fraction of the constituents. The equations of motion are determined using the virtual working principle. For the analytical solution, Navier method is used to solve the governing equations for simply supported porous FG beams. Numerical results of the present theory for the free vibration of FG beams resting on elastic foundations are presented and compared to existing solutions in the literature. A parametric study will be detailed to investigate the effects of several parameters such as gradient index, thickness ratio, porosity factor and foundation parameters on the frequency response of porous FG beams.