• Title/Summary/Keyword: Approximate Equation

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Removal Characteristics of Heavy Metals by Continuous Neutralization of Plating Wastewater with Waste-Oyster Shells (폐굴껍질에 의한 산성도금폐수의 연속 중화시 중금속제거 특성)

  • 김형석;송동근;성낙창
    • Resources Recycling
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    • v.7 no.3
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    • pp.36-41
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    • 1998
  • Objective of the research is to deteonine the praeLic따 running parameters for neutralization and removal of heavy metals from plating wastewater with waste-oyster shells by the Bohart$.$Adams equation. Waste-oyster shells discharged from the d domestic oyster cultnring fields cause a serious ocean environmental pollution. However, it is expected that those are able to b be recycled for removal of heavy metals through neutralization of plating wastewater because the shells contain approximate 93% $CaCO_3$, and have multi-pore voids. By applying the results of the continuous experiments to Bohart-Adams equation, s service time decreases in the order of Cr>Fe>Cu while removal efficiencies of metals become less in the order of Fe>Cr>Cu.

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The study for Six Sigma Robust Design of Column part for LCD Transfer system (LCD이송장치 Column부의 식스 시그마 강건설계를 위한 연구)

  • Jung D.W.;Chung W.J.;Song T.J.;Bang D.J.;Yoon Y.M.
    • Proceedings of the Korean Society of Precision Engineering Conference
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    • 2005.10a
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    • pp.869-872
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    • 2005
  • This research studied robust design of column part for LCD transfer system. $1^{st}$ DOE(Design of Experiment)was conducted to find out main effect factors. 36 experiments were performed and their results were shows that the geometric parameters(Low-length, Side-length, Upper-thickness, Middle-thickness)are more important than other factors. The main effect plots shows that the maximum deflection of column is minimized with increasing Low-length, Side-length, under-thickness and Middle-thickness. $2^{nd}$ DOE was conducted to obtain RMS(Response Surface Method)equation 25 experiments were conducted. The CCD(Central Composite Design)technique with four factors were used. The coefficient of determination $(R^2)$ for the calculated RSM equation was 0.986. Optimum design was conducted using the RSM equation Multi-island genetic algorithm was used to optimum design. Optimum value for Low-length. Side-length, Upper-thickness and Middle-thickness were 299.8mm, 180.3mm, 21.7mm, 21.9mm respectively. An approximate value of 5.054mm in deflection was expected to be a maximum under the optimum conditions. Six sigma robust design was conducted to find out guideline for control range of design parameter. To acquire six sigma level reliability, the standard deviation of design parameter should be controlled within 2% of average design value.

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Dynamic Analysis of MLS Difference Method using First Order Differential Approximation (1차 미분 근사를 이용한 MLS차분법의 동적해석)

  • Kim, Kyeong-Hwan;Yoon, Young-Cheol;Lee, Sang-Ho
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.31 no.6
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    • pp.331-337
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    • 2018
  • This paper presents dynamic algorithm of the MLS(moving least squares) difference method using first order differential Approximation. The governing equations are only discretized by the first order MLS derivative approximation. The system equation consists of an assembly of the approximate function, so the shape of system equation is similar to FEM(finite element method). The CDM(central difference method) is used for time integration of dynamic equilibrium equation. The natural frequency analyses of the MLS difference method and FEM are performed, and two analysis results are compared. Also, the accuracy of the proposed numerical method is verified by displaying the dynamic analysis results together with the results by the existing second order differential approximation. In the process of assembling the first order MLS derivative approximation, the oscillation error was suppressed and the stress distribution was interpreted as relatively uniform.

Application of Hamilton variational principle for vibration of fluid filled structure

  • Khaled Mohamed Khedher;Muzamal Hussain;Rizwan Munir;Saleh Alsulamy;Ayed Eid Alluqmani
    • Advances in nano research
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    • v.15 no.5
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    • pp.401-410
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    • 2023
  • Vibration investigation of fluid-filled three layered cylindrical shells is studied here. A cylindrical shell is immersed in a fluid which is a non-viscous one. Shell motion equations are framed first order shell theory due to Love. These equations are partial differential equations which are usually solved by approximate technique. Robust and efficient techniques are favored to get precise results. Employment of the wave propagation approach procedure gives birth to the shell frequency equation. Use of acoustic wave equation is done to incorporate the sound pressure produced in a fluid. Hankel's functions of second kind designate the fluid influence. Mathematically the integral form of the Lagrange energy functional is converted into a set of three partial differential equations. It is also exhibited that the effect of frequencies is investigated by varying the different layers with constituent material. The coupled frequencies changes with these layers according to the material formation of fluid-filled FG-CSs. Throughout the computation, it is observed that the frequency behavior for the boundary conditions follow as; clamped-clamped (C-C), simply supported-simply supported (SS-SS) frequency curves are higher than that of clamped-simply (C-S) curves. Expressions for modal displacement functions, the three unknown functions are supposed in such way that the axial, circumferential and time variables are separated by the product method. Computer software MATLAB codes are used to solve the frequency equation for extracting vibrations of fluid-filled.

A Study on the proposal of Strength Presumption Equation of Concrete Using Admixture by Nondestructive Testing (비파괴 시험에 의한 혼화재를 사용한 콘크리트의 강도 추정식 제안에 관한 연구)

  • Kim Jeong-Sup;Shin Yong-Seok;Kim Koung-Ok
    • Journal of the Korea Institute of Building Construction
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    • v.6 no.3 s.21
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    • pp.59-66
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    • 2006
  • This study aims to estimate strength approximate to actual concrete strength by presenting appropriate non-destructive strength estimation expression with admixtures such as fly ash, blast furnace slag and silica fume which are used as cement substitute and owing to theirs of cement owing to their equal conditions to blending characteristics of concrete used for domestic structures and their recyclable properties. As a result of comparing error rate of existing expressions and this estimation expression, error rate of this estimation is reduced compared to existing expressions and has higher reliability. When conventional concrete expression is applied to admixture concrete, error rate occurs and then this study suggests the following estimation expressions depending on types of admixture concrete.

Bottom Friction on Mobile Coastal Beach (이동장 해저면에서의 마찰력)

  • 유동훈;이동수
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.4 no.2
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    • pp.63-71
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    • 1992
  • A solution method is developed for computing the bed shear stress driven by combined wave and current flow on a natural mobile coastal beach. An empirical equation is introduced to determine the shape of ripples formed on the natural sandy beach. The model being based on the Prandtl's mixing length theory, the effect of arbitrarily-angled interaction is included in the estimation of current velocity reduction and all numerical integrations are expressed by explicit approximate equations to improve the computation speed. In addition the computed sediment transport rates were compared with the measured values reported in literature. using the refined bottom friction model considering the ripple formation.

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Two-dimensional rod theory for approximate analysis of building structures

  • Takabatake, Hideo
    • Earthquakes and Structures
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    • v.1 no.1
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    • pp.1-19
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    • 2010
  • It has been known that one-dimensional rod theory is very effective as a simplified analytical approach to large scale or complicated structures such as high-rise buildings, in preliminary design stages. It replaces an original structure by a one-dimensional rod which has an equivalent stiffness in terms of global properties. If the structure is composed of distinct constituents of different stiffness such as coupled walls with opening, structural behavior is significantly governed by the local variation of stiffness. This paper proposes an extended version of the rod theory which accounts for the two-dimensional local variation of structural stiffness; viz, variation in the transverse direction as well as longitudinal stiffness distribution. The governing equation for the two-dimensional rod theory is formulated from Hamilton's principle by making use of a displacement function which satisfies continuity conditions across the boundary between the distinct structural components in the transverse direction. Validity of the proposed theory is confirmed by comparison with numerical results of computational tools in the cases of static, free vibration and forced vibration problems for various structures.

Thermal vibration analysis of thick laminated plates by the moving least squares differential quadrature method

  • Wu, Lanhe
    • Structural Engineering and Mechanics
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    • v.22 no.3
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    • pp.331-349
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    • 2006
  • The stresses and deflections in a laminated rectangular plate under thermal vibration are determined by using the moving least squares differential quadrature (MLSDQ) method based on the first order shear deformation theory. The weighting coefficients used in MLSDQ approximation are obtained through a fast computation of the MLS shape functions and their partial derivatives. By using this method, the governing differential equations are transformed into sets of linear homogeneous algebraic equations in terms of the displacement components at each discrete point. Boundary conditions are implemented through discrete grid points by constraining displacements, bending moments and rotations of the plate. Solving this set of algebraic equations yields the displacement components. Then substituting these displacements into the constitutive equation, we obtain the stresses. The approximate solutions for stress and deflection of laminated plate with cross layer under thermal load are obtained. Numerical results show that the MLSDQ method provides rapidly convergent and accurate solutions for calculating the stresses and deflections in a multi-layered plate of cross ply laminate subjected to thermal vibration of sinusoidal temperature including shear deformation with a few grid points.

Estimating the Region of Attraction via collocation for autonomous nonlinear systems

  • Rezaiee-Pajand, M.;Moghaddasie, B.
    • Structural Engineering and Mechanics
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    • v.41 no.2
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    • pp.263-284
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    • 2012
  • This paper aims to propose a computational technique for estimating the region of attraction (RoA) for autonomous nonlinear systems. To achieve this, the collocation method is applied to approximate the Lyapunov function by satisfying the modified Zubov's partial differential equation around asymptotically stable equilibrium points. This method is formulated for n-scalar differential equations with two classes of basis functions. In order to show the efficiency of the suggested approach, some numerical examples are solved. Moreover, the estimated regions of attraction are compared with two similar methods. In most cases, the proposed scheme can estimate the region of attraction more efficient than the other techniques.

Nonlinear vibration of thin circular sector cylinder: An analytical approach

  • Pakar, Iman;Bayat, Mahmoud;Bayat, Mahdi
    • Steel and Composite Structures
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    • v.17 no.1
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    • pp.133-143
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    • 2014
  • In this paper, we try to prepare an accurate analytical solution for solving nonlinear vibration of thin circular sector cylinder. A new approximate solution called variational approach is presented and correctly applied to the governing equation of thin circular sector cylinder. The effect of important parameters on the response of the problem is considered. Some comparisons have been presented between the numerical solution and the present approach. The results show an excellent agreement between these methods. It has been illustrated that the variational approach can be a useful method to solve nonlinear problems by considering the effects of important parameters.