• Journal of the Korean earth science society
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• v.33 no.1
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• pp.11-31
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• 2012

Kaula's theory of satellite orbit and Kepler's law are re-visited. All the mathematical steps of derivation are thoroughly shown including the ones, which had been omitted in Kaula's original publication. Particularly in evaluations of the 15 independent Lagrange brackets, simplicity and clarity are attained by using orthogonal property of transformation matrix. Explanations of important physical concepts are included as well in the midway of derivation. One conceptual blunder of Kaula's is corrected.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.16 no.2
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• pp.253-258
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• 2012

A computationally efficient interpolation filter with a low-distortion performance is a key component to utilize the naturally-sampled pulse width modulation (NPWM) in a digital domain. To realize the efficient interpolation filter, we propose a novel design based on the recently-proposed modified Farrow filter. The proposed filter shows a better pass-band distortion performance maintaining similar degree of complexity compared with the conventional Lagrange interpolation filter. We achieve the maximum distortion deviation of 10-3 dB to 20-kHz audible frequency range and distortion reduction of 1/6 times compared with the Lagrange interpolation filter.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.3 s.174
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• pp.803-809
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• 2000

For the effective analysis of an engineering problem, meshless methods which require only positioning finite points without the element meshing recently have been proposed and being studied extensively. Meshless methods have difficulty in imposing essential boundary conditions directly, because non-interpolate shape functions originated from an approximation process are used. So some techniques, which are Lagrange multiplier method, modified variational principles and coupling with finite elements and so on, were introduced in order to impose essential boundary conditions. In spite of these methods, imposition of essential boundary conditions have still many problems like as non-positive definiteness, inaccuracy and negation of meshless characteristics. In this paper, we propose a new method which modifies shape function. Through numerical tests, convergence, accuracy and validity of this method are compared with the standard EFGM which uses Lagrange multiplier method or modified variational principles. According to this study, the proposed method shows the comparable accuracy and efficiency.

• Nuclear Engineering and Technology
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• v.24 no.3
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• pp.319-328
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• 1992

The Galerkin formulation of the finite element method is applied to the integral law of the first-order form of the one-group neutron transport equation in one-dimensional spherical geometry. Piecewise linear or quadratic Lagrange polynomials are utilized in the integral law for the angular flux to establish a set of linear algebraic equations. Numerical analyses are performed for the scalar flux distribution in a heterogeneous sphere as well as for the criticality problem in a uniform sphere. For the criticality problems in the uniform sphere, the results of the finite element method, with the use of continuous finite elements in space and angle, are compared with the exact solutions. In the heterogeneous problem, the scalar flux distribution obtained by using discontinuous angular and spatical finite elements is in good agreement with that from the ANISN code calculation.

• Tunnel and Underground Space
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• v.21 no.3
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• pp.174-180
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• 2011

An anisotropic version of Mohr-Coulomb failure criterion is proposed in order to provide a strength criterion for transversely isotropic rock. The concept of fabric tensor introduced by Pietruszczak & Mroz (2001) is employed to define the friction angle and cohesion as scalar functions of the fabric tensors. The anisotroy in these two strength parameters are calculated in association with the consideration of the relative rotation between the principal stress coordinate and the principal material triad. The critical plane on which the anisotropic function maximized is found by an optimization technique based on the Lagrange multiplier method. To demonstrate the performance of the anisotropic failure criterion, conventional triaxial tests on the samples having various inclinations of weakness plane are simulated and the resulting triaxial strength and dip angle of failure plane are discussed.

• Structural Engineering and Mechanics
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• v.65 no.4
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• pp.369-380
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• 2018

In this paper, a multi-layered finite element model for laminated glass plates is introduced. A layer-wise theory is applied to the analysis of laminated glass due to the combination of stiff and soft layers; the independent layers are connected via Lagrange multipliers. The von $K{\acute{a}}rm{\acute{a}}n$ large deflection plate theory and the constant Poisson ratio for constitutive equations are assumed to capture the possible effects of geometric nonlinearity and the time/temperature-dependent response of the plastic foil. The linear viscoelastic behavior of a polymer foil is included by the generalized Maxwell model. The proposed layer-wise model was implemented into the MATLAB code and verified against detailed three-dimensional models in ADINA solver using different hexahedral finite elements. The effects of temperature, load duration, and creep/relaxation are demonstrated by examples.

• The KIPS Transactions:PartD
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• v.10D no.7
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• pp.1145-1148
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• 2003

We show the mixed finite element method which induces solutions that has the same order of errors for both the gradient of the solution and the solution itself. The technique to construct an efficient reusable matrix is suggested. Two families of mixed finite element methods are introduced with an automatic generating technique for matrix with my order of basis. The generated matrix by this technique has more accurate values and is a sparse matrix. This new technique is applied to solve a minimal surface problem.

• Water for future
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• v.27 no.2
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• pp.155-166
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• 1994

Various Eulerian-Lagrangian numerical models for the one-dimensional longitudinal dispersion equation are studied comparatively. In the model studied, the transport equation is decoupled into two component parts by the operator-splitting approach ; one part governing adveciton and the other dispersion. The advection equation has been solved using the method of characteristics following fluid particles along the characteristic line and the results are interpolated onto an Eulerian grid on which the dispersion equation is solved by Crank-Nicholson type finite difference method. In solving the advection equation, various interpolation schemes are tested. Among those, Hermite interpolation polynomials are superior to Lagrange interpolation polynomials in reducing dissipation and dispersion errors in the simulation.

• Communications of Mathematical Education
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• v.22 no.1
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• pp.53-63
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• 2008

In this paper we study a new proof method of equalities and inequalities using moment of inertia. We analyze proof method using moment of inertia, and describe how to prove equalities and inequalities using moment of inertia.

• International Journal of Aeronautical and Space Sciences
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• v.14 no.3
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• pp.237-246
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• 2013

It is of great significance to utilize a landing mechanism to explore an asteroid. A landing mechanism named ALISE (Asteroid Landing and In Situ Exploring) for asteroid with soft surface is presented. The landing dynamic in the first turning stage, which represents the landing performance of the landing mechanism, is built by a Lagrange equation. Three key parameters can be found influencing the landing performance: the retro-rocket thrust T, damping element damping $c_1$, and cardan element damping $c_2$. In this paper, the retro-rocket thrust T is solved with considering that the landing mechanism has no overturning in extreme landing conditions. The damping element damping c1 is solved by a simplified dynamic model. After solving the parameters T and $c_1$, the cardan element damping $c_2$ is calculated using the landing dynamic model, which is built by Lagrange equation. The validities of these three key parameters are tested by simulation. The results show a stable landing, when landing with the three estimated parameters T, $c_1$, and $c_2$. Therefore, the landing dynamic model and methods to estimate key parameters are reasonable, and are useful for guiding the design of the landing mechanism.