• 제목/요약/키워드: Fourth-order differential equations

검색결과 40건 처리시간 0.025초

Stability study on tenon-connected SHS and CFST columns in modular construction

  • Chen, Yisu;Hou, Chao;Peng, Jiahao
    • Steel and Composite Structures
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    • 제30권2호
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    • pp.185-199
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    • 2019
  • Modular construction is an emerging technology to accommodate the increasing restrictions in terms of construction period, energy efficiency and environmental impacts, since each structural module is prefabricated offsite beforehand and assembled onsite using industrialized techniques. However, some innate structural drawbacks of this innovative method are also distinct, such as connection tying inaccessibility, column instability and system robustness. This study aims to explore the theoretical and numerical stability analysis of a tenon-connected square hollow section (SHS) steel column to address the tying and stability issue in modular construction. Due to the excellent performance of composite structures in fire resistance and buckling prevention, concrete-filled steel tube (CFST) columns are also taken into account in the analysis to evaluate the feasibility of adopting composite sections in modular buildings. Characteristic equations with three variables, i.e., the length ratio, the bending stiffness ratio and the rotational stiffness ratio, are generated from the fourth-order governing differential equations. The rotational stiffness ratio is recognized as the most significant factor, with interval analysis conducted for its mechanical significance and domain. Numerical analysis using ABAQUS is conducted for validation of characteristic equations. Recommendations and instructions in predicting the buckling performance of both SHS and CFST columns are then proposed.

Computer simulation for stability analysis of the viscoelastic annular plate with reinforced concrete face sheets

  • Zhang, Yonggang;Wang, Yonghong;Zhao, Yuanyuan
    • Computers and Concrete
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    • 제27권4호
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    • pp.369-383
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    • 2021
  • This article deals with the frequency analysis of viscoelastic sandwich disk with graphene nano-platelets (GPLs) reinforced viscoelastic concrete (GPLRVC) face sheets and honeycomb core. The honeycomb core is made of aluminum due to its low weight and high stiffness. The rule of the mixture and modified Halpin-Tsai model are engaged to provide the effective material constant of the concrete. By employing Hamilton's principle, the governing equations of the structure are derived and solved with the aid of the Generalize Differential Quadrature Method (GDQM). In this paper, viscoelastic properties are modeled according to Kelvin-Voigt viscoelasticity. The deflection as the function of time can be solved by the fourth-order Runge-Kutta numerical method. Afterward, a parametric study is carried out to investigate the effects of the outer to inner radius ratio, hexagonal core angle, thickness to length ratio of the concrete, the weight fraction of GPLs into concrete, and the thickness of honeycomb core to inner radius ratio on the frequency of the viscoelastic sandwich disk with honeycomb core and FG-GPLRVC face sheet.

Entropy Generation Minimization in MHD Boundary Layer Flow over a Slendering Stretching Sheet in the Presence of Frictional and Joule Heating

  • Afridi, Muhammad Idrees;Qasim, Muhammad;Khan, Ilyas
    • Journal of the Korean Physical Society
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    • 제73권9호
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    • pp.1303-1309
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    • 2018
  • In the present paper, we study the entropy analysis of boundary layer flow over a slender stretching sheet under the action of a non uniform magnetic field that is acting perpendicular to the flow direction. The effects of viscous dissipation and Joule heating are included in the energy equation. Using similarity transformation technique the momentum and thermal boundary layer equations to a system of nonlinear differential equations. Numerical solutions are obtained using the shooting and fourth-order Runge-Kutta method. The expressions for the entropy generation number and Bejan number are also obtained using a suggested similarity transformation. The main objective of this article is to investigate the effects of different governing parameters such as the magnetic parameter ($M^2$), Prandtl number (Pr), Eckert number (Ec), velocity index parameter (m), wall thickness parameter (${\alpha}$), temperature difference parameter (${\Omega}$), entropy generation number (Ns) and Bejan number (Be). All these effects are portrayed graphically and discussed in detail. The analysis reveals that entropy generation reduces with decreasing wall thickness parameter and increasing temperature difference between the stretching sheet and the fluid outside the boundary layer. The viscous and magnetic irreversibilities are dominant in the vicinity of the stretching surface.

4계 타원형 미분 방정식을 위한 웨이블릿 급수해석 (The Wavelet Series Analysis for the Fourth-order Elliptic Differential Equation)

  • 조준형;우광성;신영식
    • 한국전산구조공학회논문집
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    • 제24권4호
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    • pp.355-364
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    • 2011
  • 본 논문은 이미지 처리나 신호처리 및 정보압축 등에 사용되는 웨이블릿 급수를 이용하여 4계 타원형 미분방정식을 풀때 그 방법에 대하여 논의하고자 한다. 본 논문에서 사용한 Hat 웨이블릿 함수는 $H^1$-공간에 속한 급수로서 일반적으로 2계 타원형 미분방정식에 적용하기에는 무리가 없으나 4계 타원형 미분방정식에 적용하기에는 불충분한 미분가능회수를 가지고 있다. 따라서 이 문제를 극복하기 위해 모멘트와 처짐을 미지수로 하는 선형방정식을 순차적으로 구성하고 풀어내는 방법을 사용하였다. 모멘트와 처짐을 미지수로 하는 순차적 해석법은 탄성하중법(모멘트면적법)의 응용으로 생각할 수 있다. 또한 그 정식화과정에서 무요소법과 동일한 점과 차이점을 언급하였다. 예측한 바와 같이 Hat 웨이블릿 함수의 항을 많이 고려할수록 수치해석의 해가 향상되는 것을 확인할 수 있었다. 또한 응력특이를 갖는 오일러보 문제의 경우 제안된 해석법은 종래의 유한요소 해석값과도 비교되었다.

급성 동정맥루를 포함하는 인체 심혈관계의 혈류역학적 거동에 관한 수치 해석적 연구 (Computational Study on the Hemodynamic Behaviors of the Human Cardiovascular System with an Acute Arteriovenous Fistula)

  • 변수영;손정락;심은보;노승탁
    • 대한의용생체공학회:의공학회지
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    • 제24권4호
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    • pp.329-337
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    • 2003
  • 선천적 혹은 후천적인 이유로 인하여 인체 특정 부위의 정맥과 동맥이 서로 관통하여 동맥계의 혈류가 말초 혈관계를 우회하여 정맥계로 흐르게 되는 동정맥루는 인체 심혈관계의 혈류 역학적 거동에 큰 영향을 미치게 된다. 본 연구에서는 lumped parameter 모델을 기반으로 하는 수치 해석 방법을 사용하여 우측 하지에 위치한 급성 동정맥루가 전체 심혈관계에 미치는 영향을 해석적으로 고찰하였다. 이를 위하여 동정맥루가 포함된 인체 심혈관계를 전기 회로 상사계로 구성하였으며. 부위별 혈압과 관련된 상미분 연립 방정식을 4차의 Runge-Kutta방법으로 풀어서 시간에 따른 혈류 역학적 변수들을 구하였다 이때 급성 동정맥루의 생성에 따른 혈류 역학적 보상작용을 분석하기 위하여 arterial baroreflex 제어계를 모델에 포함하였다.

연안지역의 정체수역에서 방류되는 하$\cdot$폐수의 근역거동 수치모의 (Numerical Simulation for Near Field-Behavior of Wastewater Discharged into Stagnant Ambient in Coastal Region)

  • 권석재;서일원
    • 한국해안해양공학회지
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    • 제17권3호
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    • pp.166-177
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    • 2005
  • 본 연구에서는 정체수역에서 유입이론과 일부 형상계수의 조정을 통해 근역에서의 하$\cdot$폐수 혼합거동을 해석할 수 있는 근역제트적분모형을 개발하기위해 총 6개의 상미분 보존방정식에 6개의 미지수를 가지는 문제를 수치적으로 풀기 위한 4차의 Runge-Kutta기법을 사용하였다. 또한, LIF 시스템을 이용하여 검정과정을 통해서 단일수평부력제트의 수리실험을 수행하였다. 그리고 기존의 모형 CORMIX 1, WSJET,그리고 본 모형의 계산결과를 수리실험결과와 서로 비교하였다. VISJET모형에 의해 예측된 중심선 제적이 운동량과 부력이 지배적인 구간에서는 실험결과와 근접한 반면에 본 제트적분모형에 의해 예측된 결과는 천이영역에서 측정된 궤적과 잘 일치하였다. 중심선희석률에 있어서 운동량과 부력이 지배적인 구간에서 CORMIX1 모형의 결과와 잘 일치하는 반면에 초기영역과 천이 영역에서 본 모형의 결과와 대체로 잘 일치하는 경향을 보였다.

평판형 전개판의 3차원 운동 모델링 (Modeling of flat otter boards motion in three dimensional space)

  • 최무열;이춘우;이건호
    • 수산해양기술연구
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    • 제43권1호
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    • pp.49-61
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    • 2007
  • Otter boards in the trawl are the one of essential equipments for the net mouth to be spread to the horizontal direction. Its performance should be considered in the light of the spreading force to the drag and the stability of towing in the water. Up to the present, studies of the otter boards have focused mainly on the drag and lift force, but not on the stability of otter boards movement in 3 dimensional space. In this study, the otter board is regarded as a rigid body, which has six degrees of freedom motion in three dimensional coordinate system. The forces acting on the otter boards are the underwater weight, the resistance of drag and spread forces and the tension on the warps and otter pendants. The equations of forces were derived and substituted into the governing equations of 6 degrees of freedom motion, then the second order of differential equations to the otter boards were established. For the stable numerical integration of this system, Backward Euler one of implicit methods was used. From the results of the numerical calculation, graphic simulation was carried out. The simulations were conducted for 3 types of otter boards having same area with different aspect ratio(${\lambda}=0.5,\;1.0,\;1.5$). The tested gear was mid-water trawl and the towing speed was 4k't. The length of warp was 350m and all conditions were same to each otter board. The results of this study are like this; First, the otter boards of ${\lambda}=1.0$ showed the longest spread distance, and the ${\lambda}=0.5$ showed the shorted spread distance. Second, the otter boards of ${\lambda}=1.0$ and 1.5 showed the upright at the towing speed of 4k't, but the one of ${\lambda}=0.5$ heeled outside. Third, the yawing angles of three otter boards were similar after 100 seconds with the small oscillation. Fourth, it was revealed that the net height and width are affected by the characteristics of otter boards such as the lift coefficient.

Biokinetics of Protein Degrading Clostridium cadaveris and Clostridium sporogenes in Batch and Continuous Mode of Operations

  • Koo, Taewoan;Jannat, Md Abu Hanifa;Hwang, Seokhwan
    • Journal of Microbiology and Biotechnology
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    • 제30권4호
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    • pp.533-539
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    • 2020
  • A quantitative real-time polymerase chain reaction (QPCR) was applied to estimate biokinetic coefficients of Clostridium cadaveris and Clostridium sporogenes, which utilize protein as carbon source. Experimental data on changes in peptone concentration and 16S rRNA gene copy numbers of C. cadaveris and C. sporogenes were fitted to model. The fourth-order Runge-Kutta approximation with non-linear least squares analysis was employed to solve the ordinary differential equations to estimate biokinetic coefficients. The maximum specific growth rate (μmax), half-saturation concentration (Ks), growth yield (Y), and decay coefficient (Kd) of C. cadaveris and C.sporogenes were 0.73 ± 0.05 and 1.35 ± 0.32 h-1, 6.07 ± 1.52 and 5.67 ± 1.53 g/l, 2.25 ± 0.75 × 1010 and 7.92 ± 3.71 × 109 copies/g, 0.002 ± 0.003 and 0.002 ± 0.001 h-1, respectively. The theoretical specific growth rate of C. sporogenes always exceeded that of C. cadaveris at peptone concentration higher than 3.62 g/l. When the influent peptone concentration was 5.0 g/l, the concentration of C.cadaveris gradually decreased to the steady value of 2.9 × 1010 copies/ml at 4 h Hydraulic retention time (HRT), which indicates a 67.1% reduction of the initial population, but the wash out occurred at HRTs of 1.9 and 3.2 h. The 16S rRNA gene copy numbers of C. sporogenes gradually decreased to steady values ranging from 1.1 × 1010 to 2.9 × 1010 copies/ml. C. sporogenes species was predicted to wash out at an HRT of 1.6 h.

정식화를 이용한 3차원 구조물의 형상 최적설계 (Variational Formulation for Shape Optimization of Spatial Beam Structures)

  • 최주호;김종수
    • 한국전산구조공학회:학술대회논문집
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    • 한국전산구조공학회 2002년도 봄 학술발표회 논문집
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    • pp.123-130
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    • 2002
  • A general formulation for shape design sensitivity analysis over three dimensional beam structure is developed based on a variational formulation of the beam in linear elasticity. Sensitivity formula is derived based on variational equations in cartesian coordinates using the material derivative concept and adjoint variable method for the displacement and Von-Mises stress functionals. Shape variation is considered for the beam shape in general 3-dimensional direction as well as for the orientation angle of the beam cross section. In the sensitivity expression, the end points evaluation at each beam segment is added to the integral formula, which are summed over the entire structure. The sensitivity formula can be evaluated with generality and ease even by employing piecewise linear design velocity field despite the bending model is fourth order differential equation. For the numerical implementation, commercial software ANSYS is used as analysis tool for the primal and adjoint analysis. Once the design variable set is defined using ANSYS language, shape and orientation variation vector at each node is generated by making finite difference to the shape with respect to each design parameter, and is used for the computation of sensitivity formula. Several numerical examples are taken to show the advantage of the method, in which the accuracy of the sensitivity is evaluated. The results are found excellent even by employing a simple linear function for the design velocity evaluation. Shape optimization is carried out for the geometric design of an archgrid and tilted bridge, which is to minimize maximum stress over the structure while maintaining constant weight. In conclusion, the proposed formulation is a useful and easy tool in finding optimum shape in a variety of the spatial frame structures.

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후향적인 인과성은 가능한가? (Is Backwards Causation Possible?)

  • 안건훈
    • 철학연구
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    • 제105권
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    • pp.269-290
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    • 2008
  • 이 논문에서는 '후향적인 인과관계'를 주장하는 견해들을 크게, 자의적인 행위에 근거한 접근방법, 분석수준별 차이에 근거한 접근방법, 물리방정식에 의한 접근방법, 물리현상에 근거한 접근방법으로 나누어 고찰하고, 그 각각의 특징과 문제점들을 지적했다. 이어서 후향적인 인과성을 펼치는 어떠한 견해도 아직은 설득력 있게 받아들여지지 않고 있음을 밝혔다. 후향적인 인과관계를 펼치는 견해들이 인과성분석에서 주류는 아닐지라도, 상호조건적 동시발생적인 측면에 근거해 대칭적인 관계 속에서 인과관계를 파악하거나, 전체상적인 접근에 의거해 서로가 직접 간접으로 인과관계를 유지하는 것으로 파악할 경우는 어느 정도 논거가 선다. 특히 인과그물이나 전체상적인 측면에서 접근할 경우는 더욱 그렇다. 그러나 유용성이라는 측면에서 본다면, 후향적인 인과성고찰은 원인선행설에 비해 그 설득력이 약하다. 이런 점에서 현재로서는 결과가 원인에 앞서지 못한다는 견해가 주류를 이룰 수밖에 없다.