• Title/Summary/Keyword: Interpolation Function

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Development of three dimensional variable-node elements and their applications to multiscale problems (삼차원 다절점 유한요소의 개발과 멀티스케일 문제의 적용)

  • Lim, Jae-Hyuk;Sohn, Dong-Woo;Im, Se-Young
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 2008.04a
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    • pp.172-176
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    • 2008
  • In this paper, three dimensional linear conforming variable-finite elements are presented with the aid of a smoothed integration (a class of stabilized conforming nodal integration), for mnltiscale mechanics problems. These elements meet the desirable properties of an interpolation such as the Kronecker delta condition, the partition of unity condition and the positiveness of interpolation function. The necessary condition of linear exactness is fully relaxed by employing the smoothed integration, which renders us to meet the linear exactness in a straightforward manner. This novel element description extend the category of the conventional finite elements space to ration type function space and give the flexibility on the number of nodes of element which are fixed in the conventional finite elements. Several examples are provided to show the convergence and the accuracy of the proposed elements, and to demonstrate their potential with emphasis on the multiscale mechanics problems such as global/local analysis, nonmatching contact problems, and modeling of composite material with defects.

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Charted Depth Interpolation: Neuron Network Approaches

  • Shi, Chaojian
    • Journal of Navigation and Port Research
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    • v.28 no.7
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    • pp.629-634
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    • 2004
  • Continuous depth data are often required in applications of both onboard systems and maritime simulation. But data available are usually discrete and irregularly distributed. Based on the neuron network technique, methods of interpolation to the charted depth are suggested in this paper. Two algorithms based on Levenberg-Marquardt back-propaganda and radial-basis function networks are investigated respectively. A dynamic neuron network system is developed which satisfies both real time and mass processing applications. Using hyperbolic paraboloid and typical chart area, effectiveness of the algorithms is tested and error analysis presented. Special process in practical applications such as partition of lager areas, normalization and selection of depth contour data are also illustrated.

Extension of Rational Interpolation Functions for FE Analysis of Rotating Beams (회전하는 보의 유한요소해석을 위한 유리형상함수의 확장)

  • Kim, Yong-Woo;Jeong, Jae-Ho
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2009.04a
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    • pp.573-578
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    • 2009
  • Starting from the rotating beam finite element in which the interpolating shape functions satisfies the governing static homogeneous differential equation of Euler-Bernoulli rotating beams, we derived new shape functions that satisfies the governing differential equation which contains the terms of hub radius and setting angle. The shape functions are rational functions which depend on hub radius, setting angle, rotational speed and element position. Numerical results for uniform and tapered cantilever beams with and without hub radius and setting angle are compared with the available results. It is shown that the present element offers an accurate method for solving the free vibration problems of rotating beam.

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The solution of single-variable minimization using neural network

  • Son, Jun-Hyug;Seo, Bo-Hyeok
    • Proceedings of the KIEE Conference
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    • 2004.07d
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    • pp.2528-2530
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    • 2004
  • Neural network minimization problems are often conditioned and in this contribution way to handle this will be discussed. It is shown that a better conditioned minimization problem can be obtained if the problem is separated with respect to the linear parameters. This will increase the convergence speed of the minimization. One of the most powerful uses of neural networks is in function approximation(curve fitting)[1]. A main characteristic of this solution is that function (f) to be approximated is given not explicitly but implicitly through a set of input-output pairs, named as training set, that can be easily obtained from calibration data of the measurement system. In this context, the usage of Neural Network(NN) techniques for modeling the systems behavior can provide lower interpolation errors when compared with classical methods like polynomial interpolation. This paper solve of single-variable minimization using neural network.

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Analysis of a Shaped Dual Offset Reflector Antenna-I : Subreflector Analysis (수정곡면 옵셉 복 반사판 안테나의 복사특성 해석-I : 부반사판 해석)

  • 임규태;이상설
    • Journal of the Korean Institute of Telematics and Electronics A
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    • v.32A no.9
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    • pp.106-113
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    • 1995
  • The radiation characteristics of the subreflector of a shaped dual offset reflector antenna are analyzed by the uniform theory of diffraction(UTD). The discrete shaped subreflector profile is transformed into an analytic function by the global interpolation. To obtain the first and the second derivative terms on the surface, the local interpolation method is used. The reflection point needed for the geometrical optics(GO) is found by using the multi-dimensional function minimizing algorithm. The radiation pattern of a Gregorian type shaped subreflector is presented. The characteristics of the radiation patterns for various feed edge taperings and frequencies are examined.

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Extension of Rational Interpolation Functions for FE Analysis of Rotating Beams (회전하는 보의 유한요소해석을 위한 유리형상함수의 확장)

  • Kim, Yong-Woo;Jeong, Jae-Ho
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.19 no.6
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    • pp.591-598
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    • 2009
  • Starting from the rotating beam finite element in which the interpolating shape functions satisfy the governing static homogeneous differential equation of Euler-Bernoulli rotating beams, we derived new shape functions that satisfy the governing differential equation which contains the terms of hub radius and setting angle. The shape functions are rational functions which depend on hub radius, setting angle, rotational speed and element position. Numerical results for uniform and tapered cantilever beams with and without hub radius and setting angle are compared with the available results. It is shown that the present element offers an accurate method for solving the free vibration problems of rotating beams.

Towards improving finite element solutions automatically with enriched 2D solid elements

  • Lee, Chaemin;Kim, San
    • Structural Engineering and Mechanics
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    • v.76 no.3
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    • pp.379-393
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    • 2020
  • In this paper, we propose an automatic procedure to improve the accuracy of finite element solutions using enriched 2D solid finite elements (4-node quadrilateral and 3-node triangular elements). The enriched elements can improve solution accuracy without mesh refinement by adding cover functions to the displacement interpolation of the standard elements. The enrichment scheme is more effective when used adaptively for areas with insufficient accuracy rather than the entire model. For given meshes, an error for each node is estimated, and then proper degrees of cover functions are applied to the selected nodes. A new error estimation method and cover function selection scheme are devised for the proposed adaptive enrichment scheme. Herein, we demonstrate the proposed enrichment scheme through several 2D problems.

Reconstruction of 3D Volume of Talairach Brain Atlas (Talairach 뇌지도의 3차원 볼륨 재구성)

  • 백철화;김태우
    • Journal of Biomedical Engineering Research
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    • v.20 no.4
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    • pp.409-417
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    • 1999
  • Talairach atlas consists of three orthogonal sets of coronal, sagittal, and axial slices. This atlas has recently an important role as a standard brain atlas in diagnosing disease related with brain function and analyzing cause of brain disease. The 3D digital volume data set reconstructed from the atlas is widely applied to visualization and quantitative analysis of results processed in the digital computer. This paper represented application method of bi-linear interpolation technique, proposed tri-planar interpolation algorithm for 3D volume data reconstruction of Talairach atlas. And we implemented Talairach atlas editor and discussed problems in volume reconstruction of Talairach atlas. The bi-linear method was applied to only one set of the slices and considered the on intensity value in the interpolation process. The tri-planar technique concurrently uses three orthogonal sets of slices with the same information of brain structures. Talairach atlas editor visualized three sets. of atlas slices on the same coordinate and had editing function. Using the atlas editor, we represented problems in volume reconstruction by showing inconsistency of brain structures among three sets of atlas slices.

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Macroblock-based Adaptive Interpolation Filter Method for Improving Coding Efficiency in H.264/AVC (H.264/AVC에서 부호화 효율 개선을 위한 매크로 블록 기반 적응 보간 필터 방법)

  • Yoon, Kun-Su;Kim, Jae-Ho
    • Journal of the Institute of Electronics Engineers of Korea SP
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    • v.44 no.5
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    • pp.73-83
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    • 2007
  • In this paper, we propose macroblock(MB)-based adaptive interpolation filter method for improving coding efficiency in H.264/AVC. In the proposed method, nine separable two-dimensional(2D) interpolation filters are applied for precisely compensating motions in various directions. The optimal cost function which considers the bit rate and distortion for coding the MB is defined. The filter is adaptively selected per MB for minimizing the defined cost function. In the experimental results, the proposed method shows more excellent in coding efficiency than the conventional methods for the various standard $QCIF(176{\times}144)/CIF(352{\times}288)$ video test sequences. It leads to about 6.25%(1 reference frame) and 3.46%(5 reference frames) bit rate reduction on average compared to the H.264/AVC.

Development of the Best Spherical Interpolation Method for Estimating Potential Natural Vegetation Distribution of the Globe (지구(地球)의 잠재자연식생분포(潜在自然植生分布)를 추정(推定)하기 위한 최적구면보간법(最適球面補間法)의 개발(開發))

  • Cha, Gyung Soo;Ochiai, Kamiya
    • Journal of Korean Society of Forest Science
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    • v.86 no.1
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    • pp.17-24
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    • 1997
  • As the first step to estimate the potential natural vegetation distribution of the globe, the best spherical interpolation method was developed to the temperature and precipitation which have close relation to the distribution pattern of world natural vegetation. For developing the interpolation method, a named Light Climatic Dataset composed of 1,060 stations around the globe was randomly divided into halves of feeding side and target side. The discrepancy between the observed and estimated values at the target stations was compared with combinations of parameters and methods. The estimated values were calculated to each combination which is all-out, constant radius and constant station methods in the selection of the feeding stations, n square reciprocal and negative exponential functions in weighting function of distance between feeding stations and each target, and oval weighting in direction of the feeding stations from each target. As a result, it turned out that the spherical interpolation with negative exponential weighting function fed from the constant radius stations ovally weighed yields the best estimates both for temperature and for precipitation. The parameters for temperature are $30^{\circ}$ in constant radius, 0.78 in negative exponential function and 0.4 in oval weighting, and for precipitation are $30^{\circ}$, 0.53 and 0.4, respectively.

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