• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.647-654
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• 2017

Duality methods based on modified Lagrangian functional for solving a model crack problem is considered. Without additional assumptions of regularity of the solution of an initial problem duality ratio is established for initial and dual problem.

• Journal of the Korean Society for Precision Engineering
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• v.27 no.3
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• pp.80-88
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• 2010

A simple computational model for modeling of subsurface crack growth under cyclic contact loading is presented. In this model, it is assumed that the initial fatigue crack will initiate in the region of the maximum equivalent stress at certain depth under the contacting surface. The position and magnitude of the maximum equivalent stress are determined by using the equivalent contact model, which is based on the Hertzian contact conditions with frictional forces. The virtual crack extension method is used for simulation of the fatigue crack growth from the initial crack up to the formation of the surface pit due to contact fatigue. The relationships between the stress intensity factor and crack length are then determined for various combinations of equivalent contact radii and loadings.

• Journal of Welding and Joining
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• v.14 no.5
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• pp.69-77
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• 1996

This study aims to analyze the S. I. F. K value upon Mode I cracks in a finite-width plate of varying thickness, which is expressed in terms of width ratio ($\omega$), thickness ratio ($\beta$) and non-dimensional crack length (λ) by using the 2-dimensional finite element method. Then, by comparing the effectiveness of the results obtained by the two finite element methods, it is seen that the 2-dimensional finite element method can be used in order to analyse the S. I. F. K values upon a various thickness model. A model is developed in order to analyze the effects of initial residual stress upon the fatigue crack growth behavior in various thickness welded specimens. In this model, crack growth rate da/dN appears to be come small as the thickness ratio with the same ΔK is increased. Also, in the initial step, as ΔK is increased with crack growth rate is decreased and then increased because the repeated compressive residual stress retards crack growth rate.

• Nuclear Engineering and Technology
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• v.55 no.12
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• pp.4561-4569
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• 2023

A correct understanding of vibration-based degradation is crucial from the standpoint of maintenance for Steam Generators (SG) as crucial mechanical equipment in nuclear power plants. This study has established a novel approach to developing a model for investigating tube bundle degradation according to crack growth caused by two-phase Flow-Induced Vibration (FIV). An important step in the approach is to calculate the two-phase flow field parameters between the SG tube bundles in various zones using the porous media model to determine the velocity and vapor volume fraction. Afterward, to determine the vibration properties of the tube bundles, the Fluid-Solid Interaction (FSI) analysis is performed in eighteen thermal-hydraulic zones. Tube bundle degradation based on crack growth using the sixteen most probable initial cracks and within each SG thermal-hydraulic zone is performed to calculate useful lifetime. Large Eddy Simulation (LES) model, Paris law, and Wiener process model are considered to model the turbulent crossflow around the tube bundles, simulation of elliptical crack growth due to the vibration characteristics, and estimation of SG tube bundles degradation, respectively. The analysis shows that the tube deforms most noticeably in the zone with the highest velocity. As a result, cracks propagate more quickly in the tube with a higher height. In all simulations based on different initial crack sizes, it was observed that zone 16 experiences the greatest deformation and, subsequently, the fastest degradation, with a velocity and vapor volume fraction of 0.5 m/s and 0.4, respectively.

• Journal of the Society of Naval Architects of Korea
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• v.31 no.2
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• pp.86-90
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• 1994

This paper attempts to incorporate the initial crack damage effect into the existing idealized plate unit. For this purpose, a new concept which indicates the equivalent, reduced material properties due to initial cracks at the structural unit level, not at he microscopic aspect, is suggested, and a simplified mechanical plate model for the initially cracked plate in axial tension is formulated as a function of initial crack length, based on the finite-element solutions obtained by crack propagation analysis.

• Structural Engineering and Mechanics
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• v.41 no.1
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• pp.25-41
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• 2012

Kriging surrogate model provides explicit functions to represent the relationships between the inputs and outputs of a linear or nonlinear system, which is a desirable advantage for response estimation and parameter identification in structural design and model updating problem. However, little research has been carried out in applying Kriging model to crack identification. In this work, a scheme for crack identification based on a Kriging surrogate model is proposed. A modified rectangular grid (MRG) is introduced to move some sample points lying on the boundary into the internal design region, which will provide more useful information for the construction of Kriging model. The initial Kriging model is then constructed by samples of varying crack parameters (locations and sizes) and their corresponding modal frequencies. For identifying crack parameters, a robust stochastic particle swarm optimization (SPSO) algorithm is used to find the global optimal solution beyond the constructed Kriging model. To improve the accuracy of surrogate model, the finite element (FE) analysis soft ANSYS is employed to deal with the re-meshing problem during surrogate model updating. Specially, a simple method for crack number identification is proposed by finding the maximum probability factor. Finally, numerical simulations and experimental research are performed to assess the effectiveness and noise immunity of this proposed scheme.

• Tunnel and Underground Space
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• v.10 no.3
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• pp.301-308
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• 2000

Non-linear behavior of rock under compression can be predicted by a crack model. Crack growth in rock renders rock anisotropic. The degree of anisotropy is explained in terms of elastic moduli as a function of load level. In this study, we calculate the changes of elastic moduli due to crack growth numerically by using a crack model and compare these values with experimental results obtained from the measurement of ultrasonic wave velocities. Image processing technique is used to obtain the initial crack information needed for the numerical calculation of elastic moduli.

• Proceedings of the Korean Society for Rock Mechanics Conference
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• 2000.09a
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• pp.47-55
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• 2000

Non-linear behavior of rock under compression can be predicted by a crack model. Crack growth in rock renders rock anisotropic. The degree of anisotropy is explained in terms of elastic moduli as a function of load level. In this study, we calculate the changes of elastic moduli due to crack growth numerically by using a crack model and compare these values with experimental results obtained from the measurement of ultrasonic wave velocities. Image processing technique is used to obtain the initial crack information needed for the numerical calculation of elastic moduli.

• Computers and Concrete
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• v.9 no.1
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• pp.1-19
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• 2012

The size-effect study of various fracture parameters obtained from two parameter fracture model, effective crack model, double-K fracture model and double-G fracture model is presented in the paper. Fictitious crack model (FCM) for three-point bend test geometry for cracked concrete beam of laboratory size range 100-400 mm is developed and the different fracture parameters from size effect model, effective crack model, double-K fracture model and double-G fracture model are evaluated using the input data obtained from FCM. In addition, the fracture parameters of two parameter fracture model are obtained using the mathematical coefficients available in literature. From the study it is concluded that the fracture parameters obtained from various nonlinear fracture models including the double-K and double-G fracture models are influenced by the specimen size. These fracture parameters maintain some definite interrelationship depending upon the specimen size and relative size of initial notch length.

• Journal of Welding and Joining
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• v.29 no.2
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• pp.64-71
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• 2011

In this paper, crack propagation analyses in the inner diameter (ID) repair weld of the dissimilar metal weldment of a nozzle were performed using a finite element alternating method (FEAM). To calculate the theoretical solution for the crack tip stress intensity factor, a weak type singular integral equation consisted of crack surface traction and dislocation density function was constructed and solved in conjunction with the FEAM. A two-dimensional axisymmetric finite element nozzle model was prepared and ID repair welding was simulated. An initial crack, 10% depth of weld thickness, was assumed and crack propagation trajectory from the initial crack to the 75% depth of thickness was calculated using the FEAM. Crack growth versus time curve was also calculated and compared with the curves obtained from ASME code method. With the method constructed in this paper, crack propagation trajectory and crack growth time were calculated automatically and effectively.