• Journal of the korean society of oceanography
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• 제31권2호
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• pp.75-88
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• 1996

The analytic and numerical solution of the 1$\frac{1}{2}$-layer and 2$\frac{1}{2}$-layer models are derived. The large coastal-sea level drop and the fast westward speed of the anticyclonic gyre due to strong offshore winds using two ocean models are investigated. The models are forced by wind stress fields similar in structure to the intense mountain-pass jets(${\sim}$20 dyne/$cm^{2}$) that appear in the Gulfs of Tehuantepec and Papagayo in the Central America for periods of 3${\sim}$7 days. Analytic and numerical solutions compare favorably with observations, the large sea-level drop (${\sim}$30 cm) at the coast and the fast westward propagation speeds (${\sim}$13 km/day) of the gyres. The coastal sea-level drop is enhanced by several factors: horizontal mixing, enhanced forcing, coastal geometry, and the existence of a second active layer in the 2$\frac{1}{2}$-layer model. Horizontal mixing enhances the sea-level drop because the coastal boundary layer is actually narrower with mixing. The forcing ${\tau}$/h is enhanced near the coast where h is thin. Especially, in analytic solutions to the 2$\frac{1}{2}$-layer model the presence of two baroclinic modes increases the sea-level drop to some degree. Of theses factors the strengthened forcing ${\tau}$/h has the largest effect on the magnitude of the drop, and when all of them are included the resulting maximum drop is -30.0 cm, close to observed values. To investigate the processes that influence the propagation speeds of anticyclonic gyre, several test wind-forced calculations were carried out. Solutions to dynamically simpler versions of the 1$\frac{1}{2}$-layer model show that the speed is increased both by ${\beta}$-induced self-advection and by larger h at the center ofthe gyres. Solutions to the 2$\frac{1}{2}$-layer model indicate that the lower-layer flow field advects the gyre westward and southward, significantly increasing their propagation speed. The Papagayo gyre propagates westward at a speed of 12.8 km/day, close to observed speeds.

• East Asian mathematical journal
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• 제33권1호
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• pp.53-65
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• 2017

Numerical solutions of the Rosenau-Burgers equation based on the cubic B-spline finite element method are introduced. The backward Euler method is used for discretization in time, and the obtained nonlinear algebraic system is changed to a linear system by the Newton's method. We show that those methods are unconditionally stable. Two test problems are studied to demonstrate the accuracy of the proposed method. The computational results indicate that numerical solutions are in good agreement with exact solutions.

• 한국소음진동공학회논문집
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• 제11권9호
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• pp.462-474
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• 2001

In this paper, Generalized Differential Quadrature Method is applied to the buckling analysis of built-up columns without or with stay plates. numerical analysis using GDQM is carried out for various boundary conditions(simply supported conditions, fixed conditions, fixed-simply supported conditions), dimensionless stiffness parameter and dimensionless inertia moment parameter. The accuracy and convergence of solutions are compared with exact solutions of Gjelsvik to validate the results of GDQM. Results obtained by this method are as follows. 91) This method can yield the accurate numerical solutions using few grid points. (2) The buckling load of built-up column increases as the dimensionless stiffness parameter decreases. (3) The effects of boundary conditions on the buckling load are not considerable as the dimensionless stiffness parameter increases. (4) The buckling load of built-up column increases due to the stay plate.

• 한국공간구조학회논문집
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• 제14권2호
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• pp.59-68
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• 2014

A study on the vibration and buckling analyses of laminated composite plates is described in this paper. In order to carry out the analyses of laminated composite plates, a NURBS-based isogeometric general plate element based on Reissner-Mindlin (RM) theory is developed. The non-uniform rational B-spline (NURBS) is used to represent the geometry of plate and the unknown displacement field and therefore, all terms required in this element formulation are consistently derived by using NURBS basis function. Numerical examples are conducted to investigate the accuracy and reliability of the present plate element. From numerical results, the present plate element can produce the isogeometric solutions with sufficient accuracy. Finally, the present isogeometric solutions are provided as future reference solutions.

• 대한기계학회논문집
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• 제17권11호
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• pp.2773-2781
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• 1993

Laplace's equation is, perhaps, the most important equation, which governs various kinds of physical phenomena. Due to its importance, there have been several numerical techniques such as the finite element method, the finite difference method, and the boundary element method. However, these techniques do not appear very effective as they require a substantial amount of numerical calculation. In this paper, we develop a new most efficient technique based on analytic solutions for Laplace's equation in some convex polygons. Although a similar approach was used for the same problem, the present technique is unique as it solves directly Laplace's equation with the utilization of analytical solutions.

• Kyungpook Mathematical Journal
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• 제62권3호
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• pp.557-581
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• 2022

The anisotropic-diffusion convection equation with exponentially variable coefficients is discussed in this paper. Numerical solutions are found using a combined Laplace transform and boundary element method. The variable coefficients equation is usually used to model problems of functionally graded media. First the variable coefficients equation is transformed to a constant coefficients equation. The constant coefficients equation is then Laplace-transformed so that the time variable vanishes. The Laplace-transformed equation is consequently written as a boundary integral equation which involves a time-free fundamental solution. The boundary integral equation is therefore employed to find numerical solutions using a standard boundary element method. Finally the results obtained are inversely transformed numerically using the Stehfest formula to get solutions in the time variable. The combined Laplace transform and boundary element method are easy to implement and accurate for solving unsteady problems of anisotropic exponentially graded media governed by the diffusion convection equation.

• Geomechanics and Engineering
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• 제15권3호
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• pp.889-898
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• 2018

Backfilling of mine stopes with waste rocks or tailings is commonly done to enhance ground stability. It is also an alternative for mining wastes disposal. A successful application of underground backfilling requires an accurate evaluation of the stress distribution in stopes. Over the years, various analytical solutions have been proposed to assess these stresses. Most of them were based on the arching theory, considering uniform stresses across horizontal layer elements. The vertical and horizontal stresses in vertical stopes are principal stresses only along the vertical center line, but not close to the walls where there is rotation of the principal stresses. A few solutions use arc layer elements that follow the iso-contours of the minor principal stresses, based on numerical solutions. In this paper, a modified analytical solution is developed for the stresses in vertical backfilled stopes, considering a circular arc distribution. The proposed solution is calibrated with a few numerical modeling results and then validated by additional numerical simulations under different conditions.

• 대한원격탐사학회지
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• 제10권2호
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• pp.17-35
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• 1994

A semi-empirical model for microwave polarimetric radar backscattering from bare soil surfaces was developed using polarmetric radar measurements and the knowledge based on the theoretical and numerical solutions. The microwave polarimetric backscatter measurements were conducted for bare soil surfaces under a variety of roughness and moisture conditions at L-, C-, and X-band frequencies at incidence angles ranging from 10` to 70`. Since the accrate target parameters as well as the radar parameters are necessary for radar scattering modeling, a complete and accurate set of ground truth data were also collected using a laser profile meter and dielectric probes for each surface condition, from which accurate measurements were made of the rms height, correlation length, and dielectric constant. At first, the angular and spectral dependencies of the measured radar backscatter for a wide range of roughnesses and moisture conditions are examined. Then, the measured scattering behavior was tested using theoretical and numerical solutions. Based on the experimental observations and the theoretical and numerical solutions, a semi-empirical model was developed for backscattering coeffients in terms of the surface roughness parameters and the relative dielectric constant of the soil surface. The model was found to yield very good agreement with the backscattering measurements of this study as well as with independent measurements.

• Structural Engineering and Mechanics
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• 제68권6호
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• pp.721-733
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• 2018

The modal frequency responses of functionally graded (FG) sandwich doubly curved shell panels are investigated using a higher-order finite element formulation. The system of equations of the panel structure derived using Hamilton's principle for the evaluation of natural frequencies. The present shell panel model is discretised using the isoparametric Lagrangian element (nine nodes and nine degrees of freedom per node). An in-house MATLAB code is prepared using higher-order kinematics in association with the finite element scheme for the calculation of modal values. The stability of the opted numerical vibration frequency solutions for the various shell geometries i.e., single and doubly curved FG sandwich structure are proven via the convergence test. Further, close conformance of the finite element frequency solutions for the FG sandwich structures is found when compared with the published theoretical predictions (numerical, analytical and 3D elasticity solutions). Subsequently, appropriate numerical examples are solved pertaining to various design factors (curvature ratio, core-face thickness ratio, aspect ratio, support conditions, power-law index and sandwich symmetry type) those have the significant influence on the free vibration modal data of the FG sandwich curved structure.

• Structural Engineering and Mechanics
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• 제6권6호
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• pp.583-612
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• 1998

A unified third-order laminate plate theory that contains classical, first-order and third-order theories as special cases is presented. Analytical solutions using the Navier and L$\acute{e}$vy solution procedures are presented. The Navier solutions are limited to simply supported rectangular plates while the L$\acute{e}$vy solutions are restricted to rectangular plates with two parallel edges simply supported and other two edges having arbitrary combination of simply supported, clamped, and free boundary conditions. Numerical results of bending and vibration for a number of problems are discussed in the second part of the paper.