• Journal of the Computational Structural Engineering Institute of Korea
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• v.29 no.3
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• pp.237-244
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• 2016

This paper presents a nonlinear Moving Least Squares(MLS) difference method for material nonlinearity problem. The MLS difference method, which employs strong formulation involving the fast derivative approximation, discretizes governing partial differential equation based on a node model. However, the conventional MLS difference method cannot explicitly handle constitutive equation since it solves solid mechanics problems by using the Navier's equation that unifies unknowns into one variable, displacement. In this study, a double derivative approximation is devised to treat the constitutive equation of inelastic material in the framework of strong formulation; in fact, it manipulates the first order derivative approximation two times. The equilibrium equation described by the divergence of stress tensor is directly discretized and is linearized by the Newton method; as a result, an iterative procedure is developed to find convergent solution. Stresses and internal variables are calculated and updated by the return mapping algorithm. Effectiveness and stability of the iterative procedure is improved by using algorithmic tangent modulus. The consistency of the double derivative approximation was shown by the reproducing property test. Also, accuracy and stability of the procedure were verified by analyzing inelastic beam under incremental tensile loading.

• Geophysics and Geophysical Exploration
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• v.1 no.2
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• pp.127-135
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• 1998

The Born approximation is widely used for solving the complex scattering problems in electromagnetics. Approximating total internal electric field by the background field is reasonable for small material contrasts as long as scatterer is not too large and the frequency is not too high. However in many geophysical applications, moderate and high conductivity contrasts cause both real and imaginary part of internal electric field to differ greatly from background. In the extended Born approximation, which can improve the accuracy of Born approximation dramatically, the total electric field in the integral over the scattering volume is approximated by the background electric field projected to a depolarization tensor. The finite difference and elements methods are usually used in EM scattering problems with a 2D model and a 3D source, due to their capability for simulating complex subsurface conductivity distributions. The price paid for a 3D source is that many wavenumber domain solutions and their inverse Fourier transform must be computed. In these differential equation methods, all the area including homogeneous region should be discretized, which increases the number of nodes and matrix size. Therefore, the differential equation methods need a lot of computing time and large memory. In this study, EM modeling program for a 2D model and a 3D source is developed, which is based on the extended Born approximation. The solution is very fast and stable. Using the program, crosshole EM responses with a vertical magnetic dipole source are obtained and the results are compared with those of 3D integral equation solutions. The agreement between the integral equation solution and extended Born approximation is remarkable within the entire frequency range, but degrades with the increase of conductivity contrast between anomalous body and background medium. The extended Born approximation is accurate in the case conductivity contrast is lower than 1:10. Therefore, the location and conductivity of the anomalous body can be estimated effectively by the extended Born approximation although the quantitative estimate of conductivity is difficult for the case conductivity contrast is too high.

• Journal of Energy Engineering
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• v.9 no.4
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• pp.309-318
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• 2000

핀-관 열교환기의 효율을 증대시키기 위하여는 열저항을 결정하는 데 있어서 중요한 역할을 하는 공기측 열전달 특성의 향상이 필요하다. 본 연구에서는 핀-관 열교환기의 공리측 성능을 해석하기 위해서 3차원 비압축성 Navier-Stokes 코드를 개발하였으며 이 코드는 시간항에 스칼라 내재적 근사분해법(scalar implicit approximate factorization)절차, 공간항에 유한체적법과 2차의 풍상차분법(upwind differencing)을 사용한다. 서로 다른 3개의 핀형상(평판핀, 슬릿핀, 파형핀)을 고려하였고 이들의 유동 및 열전달 특성을 연구하였다.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.37B no.10
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• pp.912-920
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• 2012

In this paper, we derived a closed-form equation of a Best Linear Unbiased Estimator (BLUE) estimator for the 3 dimensional estimation of the position of the emitter based on the Time Difference of Arrival (TDOA) technique. The BLUE derived for the case of estimating 3 dimensional position of the emitter with 4 base stations or sensors, and for this purpose, we used an approximated equation of the TDOA hyperbola equation obtained from the first order Taylor-series after setting the reference points of the position. The derived equation can be used for any kind of noises which are uncorrelated in each other in the TOA measurement noises and for a white Gaussian noise also.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.32 no.5
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• pp.273-278
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• 2019

In this study, a new simple method for the estimation of hyperelastic material properties by indentation tests is proposed. Among hyperelastic material models, the Yeoh model with three material properties ($C_{10}$, $C_{20}$, $C_{30}$) is adopted to describe the strain energy density in terms of strain invariants. Finite element simulations of the spherical indentation of hyperelastic materials of the Yeoh model with different material properties are performed to establish a database of indentation force-displacement curves. The indentation force-displacement curves are fitted by cubic polynomials, which are approximated as a product of third-order polynomials of ($C_{10}$, $C_{20}$, $C_{30}$). A regression analysis is conducted to determine the coefficients of the equations for the indentation force-displacement curve approximations. A regression equation is used to estimate the hyperelastic material properties. The present method is verified by comparing the estimated material properties with true values.

• Journal of the Society of Naval Architects of Korea
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• v.47 no.3
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• pp.291-305
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• 2010

A three-dimensional time-domain calculation method is of crucial importance in prediction of the motions and wave loads of a ship advancing in a severe irregular sea. The exact solution of the free surface wave-ship interaction problem is very complicated because of the essentially nonlinear boundary conditions. In this paper, an approximate body nonlinear approach based on the three-dimensional time-domain forward-speed free-surface Green function has been presented. The Froude-Krylov force and the hydrostatic restoring force are calculated over the instantaneous wetted surface of the ship while the forces due to the radiation and scattering potentials over the mean wetted surface. The time-domain radiation and scattering potentials have been obtained from a time invariant kernel of integral equations for the potentials which are discretized according to the second-order boundary element method (Hong and Hong 2008). The diffraction impulse-response functions of the Wigley seakeeping model advancing in transient head waves at various Froude numbers have been presented. A simulation of coupled heave-pitch motion of a long rectangular barge advancing in regular head waves of large amplitude has been carried out. Comparisons between the linear and the approximate body nonlinear numerical results of motions and wave loads of the barge at a nonzero Froude number have been made.

• Journal of computational fluids engineering
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• v.3 no.2
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• pp.1-8
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• 1998

We make use of cubic B-spline interpolation function in two cases: heat conduction and fluid flow problems. Cubic B-spline test function is employed because it is superior to approximation of linear and non-linear problems. We investigated the accuracy of the numerical formulation and focused on the position of the breakpoints within the computational domain. When the domain is divided by partitions of equal space, the results show poor accuracy. For the case of a heat conduction problem this partition can not reflect the temperature gradient which is rapidly changed near the wall. To correct the problem, we have more grid points near the wall or the region which has a rapid change of variables. When we applied the unequally spaced breakpoints, the results show high accuracy. Based on the comparison of the linear problem, we extended to the highly non-linear fluid flow problems.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.10 no.3
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• pp.7-17
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• 1990

The objective of this paper is to provide a method of optimizing are as of the members as well as shape of both truss and arch structures. The design process includes satisfaction of stress and Euler buckling stress constraints for truss and combined stress constraints for arch structures. In order to reduce the number of detailed finite element analysis, the Force Approximation Method is used. A finite element analysis of the initial structure is performed and the gradients of the member end forces are calculated with respect to the areas and nodal coordinates. The gradients are used to form an approximate structural analysis based on first order Taylor series expansions of the member end forces. Using move limits, a numerical optimizer minimizes the volume of the structure with information from the approximate structural analysis. Numerical examples are performed and compared with other methods to demonstrate the efficiency and reliability of the Force Approximation Method for shape optimization. It is shown that the number of finite element analysis is greatly reduced and that it leads to a highly efficient method of shape optimization of structures.

• Proceedings of the KIEE Conference
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• 2008.10b
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• pp.441-442
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• 2008

본 논문에서는 비선형 시스템인 척추동물의 Inferior Olive 뉴론을 대상으로 center manifold와 normal form 해를 통하여 bifurcation해석을 한다. IO 모델에 고정점이 있음을 보이고, 3차 항까지 근사를 하며 행렬 기저벡터를 통하여 해를 구하는 과정을 제시한다.

• Proceedings of the Optical Society of Korea Conference
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• 2003.02a
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• pp.270-271
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• 2003

lens를 통과하는 두 광선(paraxial ray, marginal ray)이 lens의 축이나 focal plane과 만나는 지점이 서로 일치하지 않을 때, 두 개의 서로 다른 교차점 사이의 거리나 높이를 종, 횡 구면수차 (Lateral, Longitudinal Spherical aberration)이라 한다. 수차의 크기는 lens의 굽어짐 (bending)형태에 따라 달라지는데 3차 근사 lens 공식으로 유도한 식은 다음과 같으며, 그 결과의 그래프는 그림.1 과 같다. (중략)