• Korean Journal of Mathematics
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• v.31 no.3
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• pp.323-337
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• 2023

In this paper, we have defined bicomplex valued functions of bounded variations and rectifiable hyperbolic path. We have studied the integration of product-type bicomplex valued functions on rectifiable hyperbolic path. Also we have established bicomplex analogue of the Fundamental Theorem of Calculus for hyperbolic line integral.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.11 no.1
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• pp.17-27
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• 1991

The determination of the stress intensity factors is investigated by means of a surface integral defined around the crack tip of the structure. It has been shown in this work that this integral is derived from the standard path integral J. The use of the surface integral has also been extended to the case where body forces act. Computer program obtaining the stress intensity factors $K_I$ and $K_{II}$ is developed, which prepares input variables from the result of the conventional finite element analysis. This paper provides a parabolic smooth curve function. By the use of the function and conventional element meshes in which the aspect ratio (element length/crack length)is about 25 percent, relatively correct $K_I$ and $K_{II}$ values can be obtained for the exterior radius ranging from 1/3 to 1 of the crack length.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.11
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• pp.3498-3506
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• 1996

A loading device to be used in fracture experiment is presented. It's loading angle can be adjusted from $-45^{\circ}$ to $105^{\circ}$ at intervals of $15^{\circ}$ for a CTS ( compact tension-shear) specimen, so that it is to be useful to measure mixed mode toughness. The equations to give the $K_ I$, $K_ I1$ and J-integral for the experiment are evluated though finite elemetn analysis in which the loading procedure is simulated and the behaviors of the specimen such as load-displacement curve are estimated. In the course of the evaluation the values $K_ I$, $K_ I1$ and J-integral calculated through recentrly released numerical methods are employed as the reference ones.

• Journal of the Society of Naval Architects of Korea
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• v.29 no.1
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• pp.14-28
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• 1992

For a planar curve-sided paned with constant or linear density distributions of source or doublet in the singularity methods, Cantaloube and Rehbach(1986) show that the surface integral can be transformed into contour integral by using Stokes' formulas. As an extension of their formulations, this paper deals with a planar polygonal panel for which we derive the closed-forms of the potentials and the velocities induced by the singularity distributions. Test calculations show that the analytical evaluation of the closed-forms is superior to numerical integration(suggested by Cantaloube and Rehbach) of the contour integral. The compact and explicit expressions may produce accurate values of matrix elements of simultaneous linear equations in the singularity methods with much reduced computer tiome.

• Korean Journal of Computational Design and Engineering
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• v.13 no.6
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• pp.440-449
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• 2008

This paper deals with a method calculating various hull form parameters which are required in numerical analysis for ship performance such as motion, maneuverability, resistance and propulsion, etc. After the hull form is designed, before the model tests the ship's performances are evaluated by various analysis tools in which the hull form parameters are used with many kinds of forms aside from offset data. Here, The hull form parameters characterize the properties of hull form and contain positional, differential and integral information implicitly. Generally, the commercial CAD-system has not functions enough for supporting these form parameters and therefore each shipyard uses its own in-house analysis program as well as commercial analysis software. To overcome these limitations, modules for supporting these analysis programs have developed. The modules contain cubic composite spline cure using local curve fairing, intersect algorithm, Gaussian integral, and other geometric techniques needed in calculating hull form parameters. Using our analysis-supporting modules, a complex hull form can be remodeled exactly to the hull form designed by CAD-system and any hull form parameter required in various performance analyses can be calculated.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.12 no.2
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• pp.3-10
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• 2002

For efficient implementation of scalar multiplication in Kobliz elliptic curves, Frobenius endomorphism is useful. Instead of binary expansion of scalar, using Frobenius expansion of scalar we can speed up scalar multiplication and so fast scalar multiplication is closely related to the expansion length of integral multipliers. In this paper we propose a new idea to reduce the length of Frobenius expansion of integral multipliers of scalar multiplication, which makes speed up scalar multiplication. By using the element whose norm is equal to a prime instead of that whose norm is equal to the order of a given elliptic curve we optimize the length of the Frobenius expansion. It can reduce more the length of the Frobenius expansion than that of Solinas, Smart.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.2 s.173
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• pp.378-385
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• 2000

Fracture resistance (J-R) curves, which are used for elastic-plastic fracture mechanics analyses, decreased under tension-compression loading condition. This phenomenon was proved by several former researches, but the causes have not been clear yet. The objective of this paper is to investigate the cause of this phenomenon. On the basis of fracture resistance curve test results, strain hardening hypothesis, stress redistribution hypothesis and crack opening hypothesis were built. In this study, hardness tests, Automated Ball Indentation(ABI) tests, theoretical stress field analyses, and crack opening analyses were performed to prove the hypotheses. From this study, strain-hardening of material, generation of tensile residual stress at crack tip, and crack opening effects are proved as the causes of the decrease hypothesis.

• Transactions of the Korean Society of Mechanical Engineers
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• v.7 no.4
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• pp.441-450
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• 1983

A reasonable J-resistance curve determination procedure is suggested by correcting the amount of overestimation in J-value whose effect becomes significant when crack grows. Experiments using compact tension specimens of an alloy steel (SCM4, K.S. Designation) are performed. The value of J estimated according to this procedure is compared with that as obtained from the method by Merkle and Corten. The conditions for J controlled crack growth proposed by Hutchinson and Paris are examined for the material used here. It appears that J resistance curve, which is independent of crack ratio can be obtained for those specimens satisfying the conditions of J controlled crack growth.

• Transactions of the Korean Society of Mechanical Engineers
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• v.8 no.5
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• pp.469-475
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• 1984

In dual phase steel composed of martensite and ferrite which are different in deformation behavior, the quantitative estimation of fracture toughness is investigated by the R-curve method and the stretched zone method of JSME Sool. In the homogeneous material J$_{IC}$ value measured by the R-curve method and the stretched zone method are almost equivalent each other, but in the inhomogeneous material J$_{IC}$ value by the stretched zone method is overestimated than that by the R-curve method. Such a overestimation for the J$_{IC}$ is due to the continuous plastic blunting of ferrite after the stretched zone width in martensite reached critical value which overmeasures the critical stretched zone width.width.

• Proceedings of the KIEE Conference
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• 1997.11a
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• pp.171-173
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• 1997

This study proposes a method for evaluating composite power system effective load duration curve(CMELDC) al load points. The concept of ELDC in power system planning is very useful and important in HLI as well as HLII. Effective load duration curve of composite power system can be obtained from convolution integral processing or both probability function of unarrival power and load duration curve at load points. The characteristics and effectiveness of this methodology arc illustrated by case studyings of simple system.