• Title/Summary/Keyword: Approximate Equation

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Inelastic Transient Dynamic Analysis of Two- and Three-dimensional Stress Problems by Particular Integral Boundary Element Method (특수 적분해 경계요소법에 의한 2차원 및 3차원 동적 탄소성 응력 해석)

  • Kim, Jae-Suk;Owatsiriwong, Adisorn;Park, Kyung-Ho
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.21 no.4
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    • pp.375-382
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    • 2008
  • The particular integral formulation for two(2D) and three(3D) dimensional inelastic transient dynamic stress analysis is presented. The elastostatic equation is used for the complementary solution. Using the concept of global shape function, the particular integrals for displacement and traction rates are obtained to approximate acceleration of the inhomogeneous equation. The Houbolt time integration scheme is used for the time-marching process. The Newton-Raphson algorithm for plastic multiplier is used to solve the system equation. Numerical results of four example problems are given to demonstrate the validity and accuracy of the present formulation.

Effects of dead loads on the static analysis of plates

  • Takabatake, Hideo
    • Structural Engineering and Mechanics
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    • v.42 no.6
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    • pp.761-781
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    • 2012
  • The collapse of structures due to snow loads on roofs occurs frequently for steel structures and rarely for reinforced concrete structures. Since the most significant difference between these structures is related to their ability to handle dead loads, dead loads are believed to play an important part in the collapse of structures by snow loads. As such, the effect of dead loads on displacements and stress couples produced by live loads is presented for plates with different edge conditions. The governing equation of plates that takes into account the effect of dead loads is formulated by means of Hamilton's principle. The existence and effect of dead loads are proven by numerical calculations based on the Galerkin method. In addition, a closed-form solution for simply supported plates is proposed by solving, in approximate terms, the governing equation that includes the effect of dead loads, and this solution is then examined. The effect of dead loads on static live loads can be explained explicitly by means of this closed-form solution. A method that reflects the effects of dead loads on live loads is presented as an example. The present study investigates an additional factor in lightweight roof structural elements, which should be considered due to their recent development.

Numerical Analysis for Two-Dimensional Compressible and Two-Phase Flow Fields of Air-Water in Eulerian Grid Framework (2차원 압축공기-물의 압축성 이상 유동 수치 해석)

  • Park, Chan-Wook;Lee, Sung-Su
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.32 no.6
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    • pp.429-445
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    • 2008
  • Two-phase compressible flow fields of air-water are investigated numerically in the fixed Eulerian grid framework. The phase interface is captured via volume fractions of each phase. A way to model two phase compressible flows as a single phase one is found based on an equivalent equation of states of Tait's type for a multiphase cell. The equivalent single phase field is discretized using the Roe‘s approximate Riemann solver. Two approaches are tried to suppress the pressure oscillation phenomena at the phase interface, a passive advection of volume fraction and a direct pressure relaxation with the compressible form of volume fraction equation. The direct pressure equalizing method suppresses pressure oscillation successfully and generates sharp discontinuities, transmitting and reflecting acoustic waves naturally at the phase interface. In discretizing the compressible form of volume fraction equation, phase interfaces are geometrically reconstructed to minimize the numerical diffusion of volume fraction and relevant variables. The motion of a projectile in a water-filled tube which is fired by the release of highly pressurized air is simulated presuming the flow field as a two dimensional one, and several design factors affecting the projectile movement are investigated.

Development of a model for an equation for estimating construction costs based on the resource-based cost estimating system for TBM (TBM 공법의 자원기반 적산 방식에 의한 개산 공사비 예측 식 모델 개발)

  • Han, Seung-Hee;Park, Hong-Tae
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.14 no.3
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    • pp.1474-1480
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    • 2013
  • This study attempted to estimate construction costs in accordance with the resource-based cost estimation (unit cost price) system by diameter for TBM method, and analyzed the direct cost and the total cost. Based on such figures, this study performed a regression analysis and proposed a model for an equation for estimating construction costs. model for the resource-based cost estimation (unit cost price) system classified by diameter for TBM method proposed by this study can be effectively applied to business planning, preliminary investigation, feasibility study, construction cost estimations in the early design stages.

A FINITE DIFFERENCE/FINITE VOLUME METHOD FOR SOLVING THE FRACTIONAL DIFFUSION WAVE EQUATION

  • Sun, Yinan;Zhang, Tie
    • Journal of the Korean Mathematical Society
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    • v.58 no.3
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    • pp.553-569
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    • 2021
  • In this paper, we present and analyze a fully discrete numerical method for solving the time-fractional diffusion wave equation: ∂βtu - div(a∇u) = f, 1 < β < 2. We first construct a difference formula to approximate ∂βtu by using an interpolation of derivative type. The truncation error of this formula is of O(△t2+δ-β)-order if function u(t) ∈ C2,δ[0, T] where 0 ≤ δ ≤ 1 is the Hölder continuity index. This error order can come up to O(△t3-β) if u(t) ∈ C3 [0, T]. Then, in combinination with the linear finite volume discretization on spatial domain, we give a fully discrete scheme for the fractional wave equation. We prove that the fully discrete scheme is unconditionally stable and the discrete solution admits the optimal error estimates in the H1-norm and L2-norm, respectively. Numerical examples are provided to verify the effectiveness of the proposed numerical method.

Numerical Analysis on the Blade Tip Clearance Flow in the Axial Rotor (III) - Evaluation of Tip Leakage Loss and Reduction of Efficiency near Blade Tip Clearance Region of a Rotor - (축류 회전차 익말단 틈새유동에 대한 수치해석 (III) - 회전차 익말단의 누설손실과 효율저하에 대한 평가 -)

  • Ro, Soo-Hyuk;Cho, Kang-Rae
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.23 no.9
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    • pp.1113-1120
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    • 1999
  • Leakage vortices fonned near the blade tip cause an increase of total pressure loss near the casing endwall region and as a result, the efficiency of rotor decreases. The reduction of rotor efficiency is related to the size of tip clearance. In this study, the three-dimensional flow fields in an axial flow rotor were calculated with varying tip clearance under various flow rates, and the numerical results were compared with experimental ones. The effects of tip clearance and the of attack on the leakage vortex and overall performance, and the los9 distributions were investigated through numerical calculations. In this study, tip leakage flow rate and total pressure loss due to the tip clearance were evaluated using numerical results and approximate equations were presented to evaluate the reduction of rotor efficiency due to the tip leakage flow.

Design Study of a Small Scale Soft Recovery System

  • Yoo, Il-Yong;Lee, Seung-Soo;Cho, Chong-Du
    • Journal of Mechanical Science and Technology
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    • v.20 no.11
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    • pp.1961-1971
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    • 2006
  • A soft recovery system (SRS) is a device that stops a high speed projectile without damaging the projectile. The SRS is necessary to verify the shock resistant requirements of microelectronics and electro-optic sensors in smart munitions, where the projectiles experience over 20,000 g acceleration inside the barrel. In this study, a computer code for the performance evaluation of a SRS based on ballistic compression decelerator concept has been developed. It consists of a time accurate compressible one-dimensional Euler code with use of deforming grid and a projectile motion analysis code. The Euler code employs Roe's approximate Riemann solver with a total variation diminishing (TVD) method. A fully implicit dual time stepping method is used to advance the solution in time. In addition, the geometric conservation law (GCL) is applied to predict the solutions accurately on the deforming mesh. The equation of motion for the projectile is solved with the four-stage Runge-Kutta time integration method. A small scale SRS to catch a 20 mm bullet fired at 500 m/s within 1,600 g-limit has been designed with the proposed method.

A New Method of Estimating the Buried Location and Extracting Approximate image of Underground Structures using Ground Penetrating Radar (지하 탐사용 레이다를 이용한 지하 구조물의 위치 파악법 및 근사 이미지 추출법)

  • 김동호;이승학;김채영
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • v.11 no.4
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    • pp.565-574
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    • 2000
  • A new ground penetrating radar imaging method for the estimation of buried artificial structures location and their approximate shapes in dispersive lossy ground is investigated. Fundamental idea is based on estimating delayed time and amplitude retrieval coefficients from scattered signals by buried scatterers. Using absolute value integration of each scanning site not only improve the accuracy of measured scattered signal, but also offers convenient ways to extract the image of buried structures. Multi-term Debye model was employed to describe a dispersive and lossy ground medium. We used the finite difference time domain method to discretize the wave equation in continuous form into the machine suitable form. This imaging method uses a new wave path tracing technique in time domain, which is helpful to identify the exact position of buried structures against the ground surface fluctuations.

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Analytical approaches to the charging process of stratified thermal storage tanks with variable inlet temperature (변온유입 성층축열조의 충전과정에 대한 해석적 접근)

  • Yoo, Hoseon
    • Korean Journal of Air-Conditioning and Refrigeration Engineering
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    • v.9 no.1
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    • pp.43-54
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    • 1997
  • This paper presents an approximate analytical solution to a two-region one-dimensional model for the charging process of stratified thermal storage tanks with variable inlet temperature in the presence of momentum-induced mixing. Based on the superposition principle, an arbitrary-varying inlet temperature is decomposed into inherent discontinuous steps and continuous intervals approximated as a finite number of piecewise linear functions. This approximation allows the temperature of the upper perfectly-mixed layer to be expressed in terms of constant, linear and exponential functions with respect to time. Applying the Laplace transform technique to the model equation for the lower thermocline layer subject to each of three representative interfacial conditions yields compact-form solutions, a linear combination of which constitutes the final temperature profile. A systematic method for deriving solutions to the plug-flow problem having polynomial-type boundary conditions is also established. The effect of adiabatic exit boundary on solution behaviors proves to be negligible under the actual working conditions, which justifies the assumption of semi-infinite domain introduced in the solution procedure. Finally, the approximate solution is validated by comparing it with an exact solution obtained for a specific variation of inlet temperature. Excellent agreements between them suffice to show the necessity and utility of this work.

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An Approximate Solution for the Local Buckling Coefficient of Pultruded I-Shape Compression Members (펄트루젼 I형 단면 압축재의 국부좌굴계수 계산을 위한 근사식의 개발)

  • Joo H. J.;Jung J. H.;Lee S.;Yoon S. J.
    • Proceedings of the Korean Society For Composite Materials Conference
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    • 2004.04a
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    • pp.223-227
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    • 2004
  • The pultruded structural shapes are usually composed of thin-walled plate elements. Because the composite material has relatively low elastic moduli, the design of pultruded compression members may not be governed by the material strength limit state but by the stability limit state such as the local buckling or the global buckling. Therefore, the stability limit state must be checked to design pultruded columns. In this research, the local buckling analysis of pultruded I-shape column was conducted for various composite materials using the closed-form solution. To establish the design guidelines for the local buckling of pultruded I-shape compression members, the simplified form of equation to find the local buckling coefficient of pultruded I-shape column was proposed as a function of mechanical properties and the width ratio of plate components using the results obtainde by the closed-form solution. In order to verify the validity of proposed solution, the results obtained by the proposed approximate solution were compared with those of the closed-form solution and the experimental results.

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