• East Asian mathematical journal
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• v.22 no.2
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• pp.223-238
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• 2006

• Journal of the Korean Society for Precision Engineering
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• v.20 no.2
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• pp.154-161
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• 2003

The effects of specimen geometry, and loading conditions on the J-integral fur CCT (center cracked tension) specimens are investigated by using FEM. It is found that the J-integral tends to decrease according to the parallel tensile loading to crack line. Furthermore, it is verified that the compressive parallel loading to crack line is likely to increase the J-integral. A stress ratio of length to width of the center CCT specimen is confirmed to affect the J-integral significantly.

• Communications of the Korean Mathematical Society
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• v.12 no.4
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• pp.985-998
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• 1997

For n random strips chosen so as to meet a fixed bounded convex set K of the plane we let $\nu$ be the number of intersection regions that meet K. We develop the integral formula for the mean value of $\nu$ and $\nu^2$ involving the area and the perimeter of K and the breadths of the strips. We get some geometric inequalities in way of studying integral geometry.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.32 no.5
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• pp.411-418
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• 2008

In this work, the effect of strength mismatch on plastic limit loads is quantified for similar metal weld plates with cracks under tension load, via three-dimensional, small strain elastic-perfectly plastic finite element analyses. Relevant variables related to plate geometry and crack length are systematically varied, in addition to the weld width. An important finding is that mis-match limit loads can be uniquely quantified through strength mis-match ratio and one geometry-related parameter. Based on the proposed limit load solutions, reference stress based J-integral estimates is also investigated. When the reference stress is defined by the mis-match limit load, predicted J-integral values agree overall well with FE results.

• Journal of Industrial Technology
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• v.15
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• pp.153-168
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• 1995

The purpose of this study is to develop a method for predicting the aerodynamic performance of the subsonic airfoils in the 2-dimensional, steady and viscous flow. For this study, the airfoil geometry is specified by adopting the longest chord line system and by considering local surface curvature. In case of the inviscid-incompressible flow, the analysis is accomplished by the linearly varying strength vortex panel method and the Karman-Tsien correction law is applied for the inviscid-compressible flow analysis. The Goradia's integral method and the Truckenbrodt integral method are adopted for the boundary layer analysis of the laminar flow and the turbulent flow respectively. Viscous and inviscid solutions are converged by the Lockheed iterative calculating method using the equivalent airfoil geometry. And the analysis of the seperated flow is performed using the Dvorak and Maskew's method as the basic method. The wake effect is also considered and its geometry expressed by the formula of Summey & Smith when no seperation occurs. A computational efficiency is verified by the comparison of the computational results with experimental data and by the shorter execution time.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.1
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• pp.105-112
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• 2002

In recent years, the integrity of reactor Pressure Vessel(RPV) under pressurized thermal shock (PTS) accident has been treated as one of the most critical issues. Under PTS condition, the combination of thermal and mechanical stress by steep temperature gradient and internal pressure causes considerably high tensile stress at the inside of RPV wall. As a result, cracks on inner surface of RPV may experience elastic-plastic behavior which can be characterized by J-integral. In such a case, however, J-integral may possibly lose its vapidity due to the constraint effect. The degree of constraint effect is influenced by the loading mode, crack geometry and material properties. In this paper, in order to investigate the effect of clad thickness and crack geometry on constraint effect, three dimensional finite element analyses were performed for various surface cracks. Total of 27 crack geometries were analyzed and results were presented by a two-parameter characterization based on the J-integral and the f-stress.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.4
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• pp.617-624
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• 2002

An equation of J-integral for a penny-shaped crack at the end of the fiber embedded in rubber matrix is proposed. The values of J-integral for the specimens with various crack and specimen radius are obtained by FEA(Finite Element Analysis). The dimensional analysis is applied to derive an equation of J-integral as a nonlinear elastic energy release rate. The geometry and deformation calibration function in an equation of J can be expressed in a separated form. The geometry calibration function characterizing the effects of cord and specimen size is expressed in a polynomial form of fourth order. The deformation calibration function characterizes the effect of the overall level of strain. As approaching the infinitesimal strain, the value of the deformation calibration function approaches the results of LEFM(Linear Elastic Fracture Mechanics).

• Journal of the Korean Mathematical Society
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• v.56 no.2
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• pp.421-437
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• 2019

We establish some Hessian comparison theorems and volume comparison theorems for Riemann-Finsler manifolds under various line radial integral curvature bounds. As their applications, we obtain some results on first eigenvalue, Gromov pre-compactness and generalized Myers theorem for Riemann-Finsler manifolds under suitable line radial integral curvature bounds. Our results are new even in the Riemannian case.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.6
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• pp.701-708
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• 2004

This paper discusses applicability of the enhanced reference stress method to estimate J-integral along the semi-elliptical surface crack front. It is found that angular variations of normalized J­integral are strongly dependent on the geometry, loading mode and loading magnitude. As application of the reference stress approach to semi-elliptical surface cracks implies proportional increases in the normalized J-integral, the present results pose a question in applicability of the reference stress approach. However, investigation of the error in the estimated J-integral in the present work suggests that the enhanced reference stress approach, recently proposed by authors, provides an effective engineering tool fur estimating crack driving force along the semi-elliptical surface crack front.

• Communications for Statistical Applications and Methods
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• v.22 no.1
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• pp.69-80
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• 2015

In this paper, the probability that a given point is covered by a random convex hull generated by independent and identically-distributed random points in a plane is studied. It is shown that such probability can be expressed in terms of an integral that can be approximated numerically by function-evaluations over the grid-points in a 2-dimensional space. The new integral representation allows such probability be computed efficiently. The computational burdens under the proposed integral representation and those in the existing literature are compared. The proposed method is illustrated through numerical examples where the random points are drawn from (i) uniform distribution over a square and (ii) bivariate normal distribution over the two-dimensional Euclidean space. The applications of the proposed method in statistics are are discussed.