• Communications for Statistical Applications and Methods
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• v.17 no.6
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• pp.811-827
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• 2010

This paper deals with a density estimation method in binary choice models that can be regarded as a statistical inverse problem. We use an orthogonal basis to estimate density function and consider the choice of an appropriate truncation parameter to reflect the model complexity and the prediction accuracy. We propose a data-dependent rule to choose the truncation parameter in the context of binary choice models. A numerical simulation is provided to illustrate the performance of the proposed method.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 1997.11a
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• pp.55-62
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• 1997

본 논문에서는 윤곽선의 다각근사화시 발생하는 오차신호를 표본화하고 표본화된 신호를 부호화하기 위한 새로운 변환을 제안한다. 제안하는 방법은 다각근사화시 발생하는 윤곽선의 단편들이 완만한 곡선의 형태를 갖고 양 끝점이 0이라는 특징을 고려해서 르장드르 다항식에 기반한 새로운 변환을 제안한다. 제안한 방법은, 기존의 방법인 이산여현변환, 이산정현변환 등과 변환부호화 이득면에서 비교해 볼 때 우수한 결과를 얻었다.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.14 no.6
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• pp.1289-1298
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• 1994

The new p-version crack model is proposed to estimate the stress intensity factors of the thick cracked plate under flexure. The proposed model is based on high order theory and $C^{\circ}$-plate element including shear deformation. The displacements fields are defined by integrals of Legendre polynomials which can be classified into three groups such as basic mode, side mode and internal mode. The computer implementation allows arbitrary variations of p-level Up to a maximum value of 10. The stress intensity factors are computed by virtual crack extention approach. The effects of ratios of thickness to crack length(h/a), crack length to width(a/W) and boundary conditions are investigated. Very good agreement with the existing solution in the literature are shown for the uncracked plate as well as the cracked plate.

• Aerospace Engineering and Technology
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• v.13 no.2
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• pp.60-65
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• 2014

In this paper, numerical integration method using operational matrix of integration is studied. Using the operational matrix of integration, modified fixed point iteration method is introduced in order to solve rapidly an initial value problem for non-linear equation of motion. As an example, an initial value problem for orbital motion is considered. Through the numerical example, it is shown that the algorithm is efficient from the computational time point of view.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.22 no.1
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• pp.117-124
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• 2009

The p-convergent boundary element method has been proposed to analyze two-dimensional potential problem on the basis of high order Legendre shape functions that have different property comparing with the shape functions in conventional boundary element method. The location of nodes corresponding to high order shape function are not defined along the boundary, called by nodeless node, similar to the p-convergent finite element method. As the order of shape function increases, the collocation point method is used to solve linear simultaneous equations. The collocation patterns of p-convergent boundary element method consist of non-symmetric hierarchial or symmetric non-hierarchical. As the order of shape function increases, the number of collocation point increases. The singular integral that appears in p-convergent boundary element has been calculated by special numeric quadrature technique and semi-analytical integration technique. The L-shape domain problem including singularity in the vicinity of reentrant comer is analyzed and the numerical results show that the relative error is smaller than $10^{-2}%$ range as compared with other results in literatures. In case of same condition, the symmetric p-collocation point pattern shows high accuracy of solution.

• Computational Structural Engineering
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• v.6 no.4
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• pp.57-66
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• 1993

The p-version crack model based on integrals of Legendre polynomial and virtual crack extension method is proposed with its potential for application to stress intensity factor computations in linear elastic fracture mechanics. The main advantage of this model is that the data preparation effort is minimal because only a small number of elements are used and high accuracy and the rapid convergence can be achieved in the vicinity of crack tip. There are two important findings from this study. Firstly, the limit value, the strain energy of the exact solution, can be estimated with successive three p-version approximations by ascertaining that the approximations enter the asymptotic range. Secondly, the rate of convergence of p-version model is almost twice that of h-version model on the basis of uniform or quasiuniform mesh refinement for the cracked panel problem subjected to tension.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.14 no.4
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• pp.729-740
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• 1994

In the shape optimal design based on h-version of FEM, the ideal mesh for the initial geometry most probably will not be suitable for the final analysis. Thus, it is necessary to remesh the geometry of the model at each stage of optimization. However, the p-version of FEM appears to be a very attractive alternative for use in shape optimization. The main advantages are as follows; firstly, the elements are not sensitive to distortion for interpolation polynomials of order $p{\geq}3$; secondly, even singular problems can be solved more efficiently with p-version than with the h-version by proper mesh design; thirdly, the initial mesh design are identical. The 2-D p-version model for shape optimization is presented on the basis of Bezier's curve fitting, gradient projection method, and integrals of Legendre polynomials. The numerical results are performed by p-version software RASNA.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.22 no.2
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• pp.189-196
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• 2009

This paper presents the subparametric finite element model formulated by partial-linear layerwise theory for the analysis of laminate composites. The proposed model is based on refined approximations of two dimensional plane for orthotropic thick laminate plate as well as thin case. Three dimensional problem can be reduced to two dimensional case by assuming piecewise linear variation of in-plane displacement and a constant value of out-of-plane displacement across the thickness. The integrals of Legendre polynomials are chosen to define displacement fields and Gauss-Lobatto numerical integration is implemented in order to directly obtain maximum values occurred at the nodal points of each layer without other extrapolation techniques. The validity and characteristics of the proposed model have been tested by using orthotropic multilayered plate problem as compared to the values available in the published references. In this study, the convergence test has been carried out to determine the optimal layer model in terms of central deflection and stresses. Also, the distribution of displacements and stresses across the thickness has been investigated as the number of layer is increased.

• Computational Structural Engineering
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• v.9 no.1
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• pp.33-45
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• 1996

A general stiffener element which includes transverse shear deformation is formulated using the p-version finite element method. Hierarchic C/sup o/-shape functions, derived from Integrals of Legendre polynomials, are used to define the assembled stiffness matrix of the stiffener with respect to the local reference frame is transformed to the plate reference system by applying the appropriate transformation matrices in order to insure compatibility of displacements at the junction of the stiffener and plate. The transformation matrices which account for the orientation and the eccentricity effects of the stiffener with respect to the plate reference axes are used to find local behavior at the junction of the stiffener and the relative contributions of the plate and stiffener to the strength of the composite system. The results obtained by the p-version finite element method are comared with the results in literatures, especially those by the h-version finite element analysis program, MICROFEAP-II.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.23 no.2
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• pp.191-198
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• 2010

This study investigated that the stress reduction of single edge cracked plates with patch repairs according to different type of patching such as material, size and thickness of patch and adhesive as well as single sided or double sided patches. As a numerical tool, the p-convergent partial layerwise model has been employed. The proposed model is formulated by assuming piecewise linear variation of in-plane displacement and a constant value of out-of-plane displacements across thickness. The integrals of Legendre polynomials are chosen to define displacement fields and Gauss-Lobatto numerical integration is implemented in order to directly obtain maximum values occurred at the nodal points of each layer without other extrapolation techniques. Also, total strain energy release rate method is adopted to obtain stress intensity factors. Numerical examples are presented not only to demonstrate the stress reduction effect in terms of non-dimensional stress intensity factor and deflection with respect to different type of patch repairs, but also the accuracy of proposed model.