• Steel and Composite Structures
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• v.50 no.1
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• pp.63-75
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• 2024

In this paper, the modified couple stress theory (MCST) and first order shear deformation theory (FSDT) are employed to investigate the free vibration and bending analyses of a three-layered micro-shell sandwiched by piezoelectric layers subjected to an applied voltage and reinforced graphene nanoplatelets (GPLs) under external and internal pressure. The micro-shell is resting on an elastic foundation modeled as Pasternak model. The mixture's rule and Halpin-Tsai model are utilized to compute the effective mechanical properties. By applying Hamilton's principle, the motion equations and associated boundary conditions are derived. Static/ dynamic results are obtained using Navier's method. The results are validated with the previously published works. The numerical results are presented to study and discuss the influences of various parameters on the natural frequencies and deflection of the micro-shell, such as applied voltage, thickness of the piezoelectric layer to radius, length to radius ratio, volume fraction and various distribution pattern of the GPLs, thickness-to-length scale parameter, and foundation coefficients for the both external and internal pressure. The main novelty of this work is simultaneous effect of graphene nanoplatelets as reinforcement and piezoelectric layers on the bending and vibration characteristics of the sandwich micro shell.

• The Journal of the Acoustical Society of Korea
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• v.27 no.8
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• pp.411-417
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• 2008

An alternative formulation of the Helmholtz integral equation derived to express the pressure field explicitly in terms of the velocity vector of a radiating surface is used to solve acoustic radiation and fluid/structure interaction problems. This formulation, derived for arbitrary sources, is similar in form to the Rayleigh's formula for planar sources. Because the surface pressure field is expressed explicitly as a surface integral of the surface velocity, which can be implemented numerically using standard Gaussian quadratures, there is no need to use BEM to solve a set of simultaneous equations for the surface pressure at the discretized nodes. Furthermore the non-uniqueness problem inherent in methods based on Helmholtz integral equation is avoided. Validation of this formulation is demonstrated for some simple geometries.

• Journal of the Korean School Mathematics Society
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• v.9 no.1
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• pp.105-120
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• 2006

The Seventh Curriculum makes sure that those students who don't have a proper understanding of contents required at a certain stage take a remedial course. But a trend contrary to the intention is formed since there is no systematic education for such a course and thus more students get to fall into the group of low achievement. In particular, solving a simultaneous equation in a rote way without understanding influences negatively students' achievement. Schoenfeld introduced the basic elements of one's own mathematical problem solving process and behavior, referred to Polya's. Employing Schoenfeld's strategy, this study aimed to induce students' active participation in math classes, as well as to focus on a mathematical problem solving process during the study. Two students were selected from a remedial course at 00 Middle School and administered with a qualitative case study method over 17 lessons, each of which lasted for 30 minutes. In the beginning, they used such knowledge as facts and definitions a lot. There was a tendency of their resorting to intuitive knowledge more when they lacked basic knowledge or met with a difficult question. As the lessons were given, however, they improved their ability to implement algorithm procedures and used more familiar ones with the developed common procedures in the area of resources.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.6
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• pp.751-759
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• 2007

We have developed several methods for the optimization problem having large-scale and highly nonlinear system. First, step by step method in optimization process was employed to improve the convergence. In addition, techniques of furnishing good initial guesses for analysis using sensitivity information acquired from optimization iteration, and of manipulating analysis/optimization convergency criterion motivated from simultaneous technique were used. We applied them to flow control problem and verified their efficiency and robustness. However, they are based on quasi-Newton method that approximate the Hessian matrix using exact first derivatives. However solution of the Navier-Stokes equations are very cost, so we want to improve the efficiency of the optimization algorithm as much as possible. Thus we develop a true Newton method that uses exact Hessian matrix. And we apply that to the three-dimensional problem of flow around a sphere. This problem is certainly intractable with existing methods for optimal flow control. However, we can attack such problems with the methods that we developed previously and true Newton method.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.17 no.3
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• pp.149-157
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• 2005

Typical water quality (WQ) parameters defined in the governing equation of the WQ model are the pollutant loads from atmosphere and watersheds, pollutant release rates from sediment, diffusion coefficient and reaction coefficient etc. The direct measurement of these parameters is very difficult as well as requires high cost. In this study, the pollutant budget equation including these parameters was used to construct the linear simultaneous equations. Based on these equations, the inverse problems were constructed and WQ parameter estimation method minimizing the sum of squared errors between the computed and observed amounts of the mass changes was suggested. WQ parameters, i.e., the atmospheric pollutant loads, sediment release rates, diffusion coefficients and reaction coefficient, were estimated using .this method by utilizing the vertical concentration profile data which has been observed in Cheonsu Bay and Ulsan Port. Values of the estimated parameters show a large temporal variation. However, this technique is persuasive in that the RHS (root mean square) error was less than $5.0\%$ of the observed value ranges and the agreement index was greater than 0.95.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.31 no.4
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• pp.372-378
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• 1995

This study describes an analysis on the sinking characteristics in purse seine. The experiment was carried out using three simplified model seines in a flume tank under still water condition. The densities($\rho$) of netting materials were 0.91g/$cm^3$ for PP seine, 1.14g/$cm^3$ for PA seine and 1.38g/$cm^3$ for PES seine. Differential equations were derived from the conservation of momenta of the model seines and used to determine the sinking speeds of the depths of leadline and the other portions of seines. An analysis carried out by simultaneous differential equations for numerical method by subroutine Runge-Kutta-Gill. The results obtained were as follows: 1) Sinking speed of net margin was fastest for PP seine, followed by PA and PES seines. 2) The coefficient of resistance for netting of seine was estimated to be $K_D=0.061({\frac{\rho}{{\rho}_w}})^4$. 3) The coefficient of resistance for netting bundle of seine was estimated to be $C_R=0.91({\frac{\rho}{{\rho}_w}}$. 4) In all seines, the calculated depths of leadline closely agreed with the measured ones(meas.=0.99cal.).

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.2
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• pp.113-125
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• 2007

Improved numerical method to obtain the exact stiffness matrices is newly proposed to perform the spatially coupled elastic and stability analyses of non-symmetric and open/closed thin-walled beam on elastic foundation. This method overcomes drawbacks of the previous method to evaluate the exact stiffness matrix for the spatially coupled stability analysis of thin-walled beam-column This numerical technique is accomplished via a generalized eigenproblem associated with 14 displacement parameters by transforming equilibrium equations to a set of first order simultaneous ordinary differential equations. Next polynomial expressions as trial solutions are assumed for displacement parameters corresponding to zero eigenvalues and the eigenmodes containing undetermined parameters equal to the number of zero eigenvalues are determined by invoking the identity condition. And then the exact displacement functions are constructed by combining eigensolutions and polynomial solutions corresponding to non-zero and zero eigenvalues, respectively. Consequently an exact stiffness matrix is evaluated by applying the member force-deformation relationships to these displacement functions. In order to illustrate the accuracy and the practical usefulness of this study, the numerical solutions are compared with results obtained from the thin-walled beam and shell elements.

• Journal of KIISE:Software and Applications
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• v.27 no.1
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• pp.50-61
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• 2000

Recently the stereo vision based on conics has received much attention by many authors. Conics have many features such as their matrix expression, efficient correspondence checking, abundance of conical shapes in real world. Extensions to higher algebraic curves met with limited success. Although irreducible algebraic curves are rather rare in the real world, lines and conics are abundant whose products provide good examples of higher algebraic curves. We consider plane algebraic curves of an arbitrary degree $n{\geq}2$ with a fully calibrated stereo system. We present closed form solutions to both correspondence and reconstruction problems. Let $f_1,\;f_2,\;{\pi}$ be image curves and plane and $VC_P(g)$ the cone with generator (plane) curve g and vertex P. Then the relation $VC_{O1}(f_1)\;=\;VC_{O1}(VC_{O2}(f_2)\;∩\;{\pi})$ gives polynomial equations in the coefficient $d_1,\;d_2,\;d_3$ of the plane ${\pi}$. After some manipulations, we get an extremely simple polynomial equation in a single variable whose unique real positive root plays the key role. It is then followed by evaluating $O(n^2)$ polynomials of a single variable at the root. It is in contrast to the past works which usually involve a simultaneous system of multivariate polynomial equations. We checked our algorithm using synthetic as well as real world images.

• Wind and Structures
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• v.13 no.1
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• pp.57-82
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• 2010

The 486m-long roof of Shenzhen Citizens Centre is one of the world's longest spatial lattice roof structures. A comprehensive numerical study of wind effects on the long-span structure is presented in this paper. The discretizing and synthesizing of random flow generation technique (DSRFG) recently proposed by two of the authors (Huang and Li 2008) was adopted to produce a spatially correlated turbulent inflow field for the simulation study. The distributions and characteristics of wind loads on the roof were numerically evaluated by Computational Fluid Dynamics (CFD) methods, in which Large Eddy Simulation (LES) and Reynolds Averaged Navier-Stokes Equations (RANS) Model were employed. The main objective of this study is to explore a useful approach for estimations of wind effects on complex curved roof by CFD techniques. In parallel with the numerical investigation, simultaneous pressure measurements on the entire roof were made in a boundary layer wind tunnel to determine mean, fluctuating and peak pressure coefficient distributions, and spectra, spatial correlation coefficients and probability characteristics of pressure fluctuations. Numerical results were then compared with these experimentally determined data for validating the numerical methods. The comparative study demonstrated that the LES integrated with the DSRFG technique could provide satisfactory prediction of wind effects on the long-span roof with complex shape, especially on separation zones along leading eaves where the worst negative wind-induced pressures commonly occur. The recommended LES and inflow turbulence generation technique as well as associated numerical treatments are useful for structural engineers to assess wind effects on a long-span roof at its design stage.

• IEIE Transactions on Smart Processing and Computing
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• v.2 no.5
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• pp.302-309
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• 2013

This paper proposes a mathematical model of Caprine arthritis encephalitis (CAE), which is a disease causing significant economic damage to the goat farming industry, and reports the application of this model to the development of an information management system of animal quarantine to overcome this disease. The mathematical model of CAE was derived from the AIDs model in human case because epidemical characteristics of these diseases including infection pass are similar. This model can be expressed by simultaneous differential equations. Simulations using a new model were performed according Euler's and Runge-Kutta method using numerical analysis software. In each method, strong convergence was observed and the results were similar. The design of an information management system of animal quarantine was proposed as an application of the new model. System design was constructed on the assumption that in subtropical islands, the expected development of information infrastructure and utilization will become valuable in the future.