• Transactions of the Korean Society of Mechanical Engineers
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• v.10 no.5
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• pp.787-797
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• 1986

An implicit approach is employed to obtain a general boundary integral formulation of axisymmetric elastic problems in terms of a pair of singular integral equations. The corresponding kernel functions from the solutions of Navier's equation are derived by applying a three dimensional integral and a direct axisymmetrical approach. A numerical discretization schem including the evaluation of Cauchy principal values of the singular integral is described. Finally the typical axisymmetric elastic models are analyzed, i.e. the hollow sphere, the constant thickness and the V-notched round bar.

• The Journal of the Acoustical Society of Korea
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• v.28 no.2E
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• pp.51-59
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• 2009

Mutual radiation impedance becomes more important in the design and analysis of acoustic transducers for higher power, better beam pattern, and wider bandwidth at low frequency sonar systems. This review paper focused on literature survey about the researches of mutual radiation impedance in the acoustic transducer arrays over 60 years. The papers of mutual radiation impedance were summarized in terms of transducer array structures on various baffle geometries such as planar, cylindrical, spherical, conformal, spheroidal, and elliptic cylindrical arrays. Then the computation schemes of solving conventional quadruple integral in the definition of mutual radiation impedance were surveyed including spatial convolution method, which reduces the quadruple integral to a double integral for efficient computation.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.04a
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• pp.41-52
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• 1998

A volume integral equation method and a mixed volume and boundary integral equation method are presented for the solution of plane elastostatic problems in solids containing orthotropic inclusions and voids. The detailed analysis of the displacement and stress fields are developed for orthotropic cylindrical and elliptic-cylindrical inclusions and voids. The accuracy and effectiveness of the new methods are examined through comparison with results obtained from analytical and boundary integral equation methods. Through the analysis of plane elastostatic problems in unbounded isotropic matrix containing orthotropic inclusions and voids, it is established that these new methods are very accurate and effective for solving plane elastostatic and elastodynamic problems in unbounded solids containing general anisotropic inclusions and voids or cracks.

• Journal of Ocean Engineering and Technology
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• v.25 no.2
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• pp.62-66
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• 2011

In this paper, a liquid-filled long membrane container resting on a horizontal foundation is considered. All of the quantities are normalized to obtain similarity solutions. A system of nonlinear ordinary differential equations with undetermined boundary conditions is solved analytically. The integration of the curvature gives the solutions, which are expressed in terms of the elliptic integrals. A method for finding the shape and characteristic values is proposed for a given cross-sectional volume. The validity of these solutions is confirmed, and some results are shown for characteristic values and shapes.

• Structural Engineering and Mechanics
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• v.4 no.1
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• pp.49-59
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• 1996

This paper considers large deflection problem of a simply supported beam with variable are length subjected to a point load. The beam has one of its ends hinged and at a fixed distance from this end propped by a frictionless support over which the beam can slide freely. This highly nonlinear flexural problem is solved by elliptic-integral method and shooting-optimization technique, thereby providing independent checks on the new solutions. Because the beam can slide freely over the frictionless support, there is a maximum or critical load which the beam can carry and it is dependent on the position of the load. Interestingly, two possible equilibrium configurations can be obtained for a given load magnitude which is less than the critical value. The maximum arc-length was found to be equal to about 2.19 times the fixed distance between the supports and this value is independent of the load position.

• The Pure and Applied Mathematics
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• v.1 no.1
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• pp.29-33
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• 1994

There are various aspects of the solution of boundary-value problems for second-order linear elliptic equations in two independent variables. One useful method of solving such boundary-value problems for Laplace's equation is by means of suitable integral representations of solutions and these representations are obtained most directly in terms of particular singular solutions, termed Green's functions.(omitted)

• Journal of Biomedical Engineering Research
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• v.5 no.2
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• pp.161-166
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• 1984

In this paper, we describe an effective technique for computing the steady-state motion in a two-dimensional cochlear model. With the cochlear fluid assumed incompressible and invisid, the problem reduces to solving an integral equation for a region with yielding boundary. Using the conformal mapping, Jacobian elliptic function and hyperbolic function, a pair of second-order differential equation is derived. What we will show in this paper is that by appropriately transforming integral equation, the same computation can be performed with comparable accuracy in a short time.

• Structural Engineering and Mechanics
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• v.4 no.5
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• pp.469-484
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• 1996

Green's functions are obtained in exact closed-forms for the elastic fields in bi-material elastic solids with slipping interface and differing transversely isotropic properties induced by concentrated point and ring force vectors. For the concentrated point force vector, the Green functions are expressed in terms of elementary harmonic functions. For the concentrated ring force vector, the Green functions are expressed in terms of the complete elliptic integral. Numerical results are presented to illustrate the effect of anisotropic bi-material properties on the transmission of normal contact stress and the discontinuity of lateral displacements at the slipping interface. The closed-form Green's functions are systematically presented in matrix forms which can be easily implemented in numerical schemes such as boundary element methods to solve elastic problems in computational mechanics.

• Journal of the Society of Naval Architects of Korea
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• v.54 no.4
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• pp.335-343
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• 2017

The Newman-Raju formula and contour integral-based finite element analyses(FEAs) have been widely used to assess crack growth rates and residual lives at crack locations in ships or offshore structures, but the Newman-Raju formula is known to be less accurate for the complicated weld details and the conventional FEA-based contour integral approach needs concentrated efforts to construct FEA models. Recently, an extended finite element method(XFEM) has been proposed to reduce those modeling efforts with reliable accuracy. Stress intensity factors(SIFs) from the approaches such as the Newman-Raju formula, conventional FEA-based J-integral, and XFEM-based J-integral were compared for an infinitely long plate with a propagating elliptic crack. It was concluded that the XFEM approach was far reliable in terms of prediction ability of SIFs. Assuming a 25 year-aged coast guard patrol ship had the prescribed cracks at the bracket toes attached to longitudinal stiffeners in way of deck and bottom, SIFs were derived based on the three approaches. To obtain axial tension loads acting on the longitudinal stiffeners, long term hull girder bending moments were assumed to obey Weibull distribution of which two parameters were decided from a reference (DNV, 2014). For the complicated weld details, it was concluded that the XFEM approach could cost-effectively and accurately estimate the crack growth rates and residual lives of ship structures.

• Nuclear Engineering and Technology
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• v.36 no.3
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• pp.248-262
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• 2004

Turbulence models are separately assessed for a three dimensional thermal-hydraulic analysis of the integral reactor SMART. Seven models (mixing length, k-l, standard $k-{\epsilon},\;k-{\epsilon}-f{\mu},\;k-{\epsilon}-v2$, RRSM, and ERRSM) are investigated for flat plate channel flow, rotating channel flow, and square sectioned U-bend duct flow. The results of these models are compared to the DNS data and experiment data. The results are assessed in terms of many aspects such as economical efficiency, accuracy, theorization, and applicability. The standard $k-{\epsilon}$ model (high Reynolds model), the $k-{\epsilon}-v2$ model, and the ERRSM (low Reynolds models) are selected from the assessment results. The standard $k-{\epsilon}$ model using small grid numbers predicts the channel flow with higher accuracy in comparison with the other eddy viscosity models in the logarithmic layer. The elliptic-relaxation type models, $k-{\epsilon}-v2$, and ERRSM have the advantage of application to complex geometries and show good prediction for near wall flows.