• 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.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.22 no.3
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• pp.267-275
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• 2009

This paper presents the p-convergent coupling element on the basis of the ESSE(equivalent single layer shell element) and the PLLE(partial-linear layerwise element) to analyze laminated composite plates. The ESSE is formulated by the degenerated shell theory, on the other hand, the assumption of the PLLE is piecewise linear variation of the in-plane displacement and a constant value of lateral displacement across the thickness. The proposed finite element model is based on p-convergence approach. The integrals of Legendre polynomials and Gauss-Lobatto technique are chosen to interpolate displacement fields and to implement numerical quadrature, respectively. This study has been focused on the verification of p-convergent element. For this purpose, various finite element multiple models associated with the combination of ESSE and PLLE elements are tested to show numerical stability. The simple examples such as a cantilever beam subjected vertical load and a plate with tension are adopted to evaluate the performance of proposed element.

• Journal of Korean Association for Spatial Structures
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• v.8 no.4
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• pp.81-90
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• 2008

This paper presents a finite element formulation for the three-dimensional hierarchical solid element using Integrals of Legendre polynomials. The proposed hexahedral solid element is composed of four different modes including vertex, edge, face, and internal mode, respectively. The eigenvalue and patch test have been carried out to confirm the zero-energy mode and constant strain condition. In addition to these, a posteriori error estimation has been studied for the p-adaptive finite element analysis that is based on a smoothing technique to compute a post-processed solution from the finite element solution. The uniform p-refinement and non-uniform p-refinement are compared in terms of convergence rate as the number of degree of freedom is increased. The simple cantilever beam is tested to show the performance of the proposed solid element.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.9
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• pp.2331-2338
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• 1994

Experimental conditions of the optical shadow methods of caustics for measurement of the stress intensity factor and the J-integral in various materials(polycarbonate, PMMA, Al 5586D) are investigated. The necessary experimental requirements toe determine accurate values of the stress intensity factors and the J-integrals are described. The ratio of $r_o$ (radius of initial curve) to $r_p$ (plastic zone size) is selected as a parameter to verify the experimental limitation of the method of caustics in determination of fracture parameters. In this study, transmission caustics method was used for compact tension specimens made of polycarbonate and PMMA. while reflection caustics method was applied to c-shaped tension specimen made of Al 5586D. The appropriate ranges of $r_o/r_p$ tp determine accurate values of stress intensity factors were found to be 1.5~1.8. Existing experimental results have been obtained mainly by changing $r_p$ with different loads in $r_o/r_p$. However, in this study we could obtain varying $K_{caus}/K_{th}$ over the wide range of $r_o/r_p$ at fixed load conditions with newly designed optical arrangement. Thus, we could find the range in which theoretical and experimental results agree well each other by changing $r_o$ values only. In Al 5586D specimen, experimental caustics were located inside of the plastic zone, and $K_{caus}/K_{th}$ were found to be not unity in this range. It is found that $J_{caus}/J_{th}=1{\;}with{\;}r_o/t{\geq}0.8$ and the experimental plastic zone includes the contours of caustics.

• 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.

• The Journal of the Acoustical Society of Korea
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• v.18 no.8
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• pp.32-41
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• 1999

In this paper, an inversion method using chirp signals and two near field receivers is proposed. Inversion problems can be formulated into the probabilistic models composed of signals, a forward model and noise. Forward model to simulate chirp signals is chosen to be the source-wavelet-convolution planewave modeling method. The solution of the inversion problem is defined by a posteriori pdf. The wavelet matching technique, using weighted least-squares fitting, estimates the sediment sound-speed and thickness on which determination of the ranges for a priori uniform distribution is based. The genetic algorithm can be applied to a global optimization problem to find a maximum a posteriori solution for determined a priori search space. Here the object function is defined by an L₂norm of the difference between measured and modeled signals. The observed signals can be separated into a set of two signals reflected from the upper and lower boundaries of a sediment. The separation of signals and successive applications of the genetic algorithm optimization process reduce the search space, therefore improving the inversion results. Not only the marginal pdf but also the statistics are calculated by numerical evaluation of integrals using the samples selected during importance sampling process of the genetic algorithm. The examples applied here show that, for synthetic data with noise, it is possible to carry out an inversion for sedimentary layers using the proposed inversion method.

• 한국해양학회지
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• v.28 no.3
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• pp.192-201
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• 1993

To reduce tsunami hazards, it is necessary to develope the methods which can simulate tsunami wave signals of coastal areas. In the present paper, it is attempted t use Sign Method for analyzing and simulating recorded tsunami signals. A tsunami record Y(t) can be represented as the convolution integral of a source evolution function E(t') and a wave propagation function K(t-t') Y(t)=.int. E(t')K(t-t')dt' A source function contains the peculiarities of a tsunami generator. A wave function is a kind of transfer function which contains the characteristics of a wave propagation path. The source functions and the wave function and the wave functions of 9 Korean coast points and 6 Japan coast points are estimated, and the tsunami wave signals are simulated by the convolution integrals of the source functions and the wave functions. According to the results of analysis, the Sign Method is an effective method for simulating tsunami wave signals of Korean coast points which are located far from tsunami source areas. Furthermore, if the source function of a neighboring point ad the wave function of an another tsunami are given, unrecorded tsunami wave also can be estimated.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.12 no.4_1
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• pp.67-76
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• 1992

A hierarchical formulation based on p-version of the finite element method for linear elastic axisymmetric stress analysis is presented. This is accomplished by introducing additional nodal variables in the element displacement approximation on the basis of integrals of Legendre polynomials. Since the displacement approximation is hierarchical, the resulting element stiffness matrix and equivalent nodal load vectors are hierarchical also. The merits of the propoosed element are as follow: i) improved conditioning, ii) ease of joining finite elements of different polynomial order, and iii) utilizing previous solutions and computation when attempting a refinement. Numerical examples are presented to demonstrate the accuracy, efficiency, modeling convenience, robustness and overall superiority of the present formulation. The results obtained from the present formulation are also compared with those available in the literature as well as with the analytical solutions.

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1531-1548
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• 2016

Let C[0, t] denote the space of real-valued continuous functions on [0, t] and define a random vector $Z_n:C[0,t]{\rightarrow}\mathbb{R}^n$ by $Z_n(x)=(\int_{0}^{t_1}h(s)dx(s),{\ldots},\int_{0}^{t_n}h(s)dx(s))$, where 0 < $t_1$ < ${\cdots}$ < $ t_n=t$ is a partition of [0, t] and $h{\in}L_2[0,t]$ with $h{\neq}0$ a.e. Using a simple formula for a conditional expectation on C[0, t] with $Z_n$, we evaluate a generalized analytic conditional Wiener integral of the function $G_r(x)=F(x){\Psi}(\int_{0}^{t}v_1(s)dx(s),{\ldots},\int_{0}^{t}v_r(s)dx(s))$ for F in a Banach algebra and for ${\Psi}=f+{\phi}$ which need not be bounded or continuous, where $f{\in}L_p(\mathbb{R}^r)(1{\leq}p{\leq}{\infty})$, {$v_1,{\ldots},v_r$} is an orthonormal subset of $L_2[0,t]$ and ${\phi}$ is the Fourier transform of a measure of bounded variation over $\mathbb{R}^r$. Finally we establish various change of scale transformations for the generalized analytic conditional Wiener integrals of $G_r$ with the conditioning function $Z_n$.