• Advances in aircraft and spacecraft science
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• v.4 no.6
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• pp.679-699
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• 2017

The aim of this study is to perform a finite element analysis of the Von Mises stresses distribution in the adhesive layer and of the J-Integral for a damaged plate repaired by a composite patch. Firstly, we study the effect of the fiber orientation, especially the position of the layers that have orientation angle different of $0^{\circ}$ from the first layer which is in all cases of our study oriented at ($0^{\circ}$) on the J-Integral. Secondly, we evaluate the effects of the mechanical properties of the patch and the use of a hybrid patch on the reduction of stresses distribution and J-Integral. The results show clearly that the stacking sequence for the composite patch must be selected to absorb optimally the stresses from the damaged area and to position the various layers of the composite under the first layer whose fibers orientation will remain in all cases equal to $0^{\circ}$. The use of a hybrid composite reduces significantly the J-Integral and the stresses in both damaged plate and the adhesive layer.

• Industrial Engineering and Management Systems
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• v.15 no.2
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• pp.143-147
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• 2016

Uncertainty appears not only in real quantities but also in complex quantities. Complex uncertain process is essentially a sequence of complex uncertain variables indexed by time. In order to describe complex uncertain process, a formal definition of complex uncertain distribution is given in this paper, as well as the concepts of independence and variance. In addition, some properties of complex uncertain integral are presented.

• Journal of the Korean Statistical Society
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• v.13 no.1
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• pp.25-31
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• 1984

A technique which has been used for the evaluation of certain kinds of multiple integrals, viz., the technique of imcomplete gamma function operators, is employed and extended to the case where the parameters and arguments are non-equal and non-integer for the probability integral of the inverted Dirichlet distribution. Several types of recurrence formulas have been developed for the tail probabilities and a subset selection procedure in ranking variances is discussed as an application.

• Wind and Structures
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• v.34 no.5
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• pp.421-435
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• 2022

To investigate the non-Gaussian properties of fluctuating wind pressures and the error margin of extreme wind loads on a long-span curved roof with matching and mismatching ratios of turbulence integral scales to depth (L_u^x/D), a series of synchronized pressure tests on the rigid model of the complex curved roof were conducted. The regions of Gaussian distribution and non-Gaussian distribution were identified by two criteria, which were based on the cumulative probabilities of higher-order statistical moments (skewness and kurtosis coefficients, S_k and K_u) and spatial correlation of fluctuating wind pressures, respectively. Then the characteristics of fluctuating wind-loads in the non-Gaussian region were analyzed in detail in order to understand the effects of turbulence integral-scale. Results showed that the fluctuating pressures with obvious negative-skewness appear in the area near the leading edge, which is categorized as the non-Gaussian region by both two identification criteria. Comparing with those in the wind field with matching L_u^x/D, the range of non-Gaussian region almost unchanged with a smaller L_u^x/D, while the non-Gaussian features become more evident, leading to higher values of S_k, Ku and peak factor. On contrary, the values of fluctuating pressures become lower in the wind field with a smaller L_u^x/D, eventually resulting in underestimation of extreme wind loads. Hence, the matching relationship of turbulence integral scale to depth should be carefully considered as estimating the extreme wind loads of long-span roof by wind tunnel tests.

• Tribology and Lubricants
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• v.17 no.5
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• pp.373-379
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• 2001

The problem of interest is formulating elastic contact problem of a layered semi-infinite solid in terms of Fourier integral. The plane strain problem is considered for a solid composed of homogeneous isotropic two layers with different mechanical properties. General solutions for the subsurface stress and deformation field of frictionless elastic bodies under normal loading using of Fourier transformation technique are obtained. The numerical results for the stress distribution of coated solid for some particular cases are given.

• Bulletin of the Korean Mathematical Society
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• v.54 no.3
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• pp.917-933
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• 2017

In this paper, seven equivalent conditions of complete moment convergence and complete integral convergence for negatively orthant dependent (NOD, in short) sequences are shown under two cases: identical distribution and stochastic domination. The results obtained in the paper improve and generalize the corresponding ones of Liang et al. [10]). In addition, an extension of the Baum-Katz complete convergence theorem: six equivalent conditions of complete convergence is established.

• The Magazine of the Society of Air-Conditioning and Refrigerating Engineers of Korea
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• v.11 no.3
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• pp.1-8
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• 1982

When exact analytical solutions to certain type of heat conduction problems are quite cumbersome or not obtainable, it is important to introduce approximate analytical methods which are simple and useful compared with numerical methods. In this study, therefore, the Heat Balance Integral Method is applied to analysis of steady-state conduction in a straight fin of trapezoidal profile, and the two-dimensional temperature distribution in the fin and the approximate fin efficiency are obtained. Results are compared with those by the one- dimensional analysis and two-dimensional numerical analysis for a wide range of Biot numbers. It is shown that the two-dimensional temperature distribution obtained by the integral method is in good agreement with that by the finite element method at Biot numbers for which the result by the one-dimensional analysis is unreliable.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.125-136
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• 2020

In this article, we discuss classes of generalized functions for certain modified integral operator of Bessel-type involving Fox's H-function kernel. We employ a known differentiation formula of Fox's H-function to obtain the definition and properties of the distributional modified Bessel-type integral. Further, we derive a smoothness theorem for its kernel in a complete countably multi-normed space. On the other hand, using an appropriate class of convolution products, we derive axioms and establish spaces of modified Boehmians which are generalized distributions. On the defined spaces, we introduce addition, convolution, differentiation and scalar multiplication and further properties of the extended integral.

• School Mathematics
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• v.13 no.3
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• pp.423-446
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• 2011

In school mathematics, concepts of definite integral and integration by substitution have mathematical connection with introduction of probability density function, expectation of continuous random variable, and standardization of normal distribution. However, we have difficulty in finding mathematical connection between integration and continuous probability distribution in the curriculum manual, 13 kinds of 'Basic Calculus and Statistics' and 10 kinds of 'Integration and Statistics' authorized textbooks, and activity books applied to the revised curriculum. Therefore, the purpose of this study is to provide a teaching method connected with mathematical concepts of integral in regard to three concepts in continuous probability distribution chapter-introduction of probability density function, expectation of continuous random variable, and standardization of normal distribution. To find mathematical connection between these three concepts and integral, we analyze a survey of student, the revised curriculum manual, authorized textbooks, and activity books as well as 13 domestic and 22 international statistics (or probability) books. Developed teaching method was applied to actual classes after discussion with a professional group. Through these steps, we propose the result by making suggestions to revise curriculum or change the contents of textbook.

• Bulletin of the Society of Naval Architects of Korea
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• v.24 no.4
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• pp.19-36
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• 1987

In this research the coupling problem between the elastic structure and the fluid, specially the hydroelastic harmonic vibration problem, is studied. In order to couple the domains, i.e., the structural domain and the fluid domain, the boundary integral method(direct boundary integral formulation) is used in the fluid domain in combination with the finite element method for the structure. The boundary integral method has been widely developed to apply it to the hydroelastic vibration problem. The hybrid boundary integral method using eigenfunctions on the radiation boundaries and the boundary integral method using the series form image-functions to replace the even bottom and free surface boundaries in case of high frequencies have been developed and tested. According to the boundary conditions and the frequency ranges the different boundary integral methods with the different idealizations of the fluid boundaries have been studied. Using the same interpolation functions for the pressure distribution and the displacement the two domains have been coupled and using Hamilton principle the solution of the hydroelastic have been obtained through the direct minimizing process. It has become evident that the finite-boundary element method combining with the eigenfunction or the image-function method give good results in comparison with the experimental ones and the other numerical results by the finite element method.