• Structural Engineering and Mechanics
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• v.45 no.4
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• pp.495-519
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• 2013

This paper investigates properties of integral operators in complex variable boundary integral equation in plane elasticity, which is derived from the Somigliana identity in the complex variable form. The generalized Sokhotski-Plemelj's formulae are used to obtain the BIE in complex variable. The properties of some integral operators in the interior problem are studied in detail. The Neumann and Dirichlet problems are analyzed. The prior condition for solution is studied. The solvability of the formulated problems is addressed. Similar analysis is carried out for the exterior problem. It is found that the properties of some integral operators in the exterior boundary value problem (BVP) are quite different from their counterparts in the interior BVP.

• Advances in Computational Design
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• v.9 no.1
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• pp.73-80
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• 2024

The aim of this paper is to remove the rigid body motion in the interior boundary value problem (BVP) of plane elasticity by solving the interior and exterior BVPs simultaneously. First, we formulate the interior and exterior BVPs simultaneously. The tractions applied on the contour in two problems are the same. After adding and subtracting the two boundary integral equations (BIEs), we will obtain a couple of BIEs. In the coupled BIEs, the properties of relevant integral operators are modified, and those integral operators are generally invertible. Finally, a unique solution for boundary displacement of interior region can be obtained.

• The Pure and Applied Mathematics
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• v.25 no.2
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• pp.59-71
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• 2018

We consider the boundary value problem with a Dirichlet condition for a second order linear uniformly elliptic operator in a non-divergence form. We study some properties of a barrier at infinity which was introduced by Meyers and Serrin to investigate a solution in an exterior domains. Also, we construct a modified barrier for more general domain than an exterior domain.

• Journal of the Korean Mathematical Society
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• v.39 no.3
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• pp.439-460
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• 2002

We prove the multiplicity of ordered positive radial solutions for a semilinear elliptic problem defined on an exterior domain. The key argument is to prove the existence of the third solution in presence of two known solutions. For this, we obtain some partial results related to three solutions theorem for certain singular boundary value problems. Proof are mainly based on the upper and lower solutions method and degree theory.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.127-140
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• 2007

We present the boundary value problem (BVP) for the heave motion due to a vertical circular cylinder in water of finite depth. The BVP is presented in terms of velocity potential function. The velocity potential is obtained by considering two regions, namely, interior region and exterior region. The solutions for these two regions are obtained by the method of separation of variables. The analytical expressions for the hydrodynamic coefficients are derived. Computational results are presented for various depth to radius and draft to radius ratios.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 1999.10a
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• pp.83-90
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• 1999

This paper presents a method of seismic analysis for a cylindrical liquid storage structure on horizontally layered half-space considering the effects of the interior fluid and exterior soil medium in the frequency domain. the horizontal and rocking motions of the structures are included in this study. The fluid motion is expressed in terms of analytical velocity potential function which can be obtained by solving the boundary value problem including the sloshing behavior of the fluid as well as deformed configuration of the structure. The effect of the fluid is included in the equation of motion as the impulsive added mass and a frequency-dependent convective added mass along the nodes on the wetted boundary with structure. The soil medium is presented using the 3-D axisymmetric finite elements and dynamic infinite elements. The present method can be applied to the structures embedded in ground as well as on ground since it models the soil medium directly as well as the structure. For the purpose of vertification dynamci characteristics of a tank on homogeneous half-space is analyzed. Comparison of the present results with those by others shows good agreement.

• Structural Engineering and Mechanics
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• v.13 no.6
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• pp.615-638
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• 2002

This paper presents a method of seismic analysis for a cylindrical liquid storage structure considering the effects of the interior fluid and exterior soil medium in the frequency domain. The horizontal and rocking motions of the structure are included in this study. The fluid motion is expressed in terms of analytical velocity potential functions, which can be obtained by solving the boundary value problem including the deformed configuration of the structure as well as the sloshing behavior of the fluid. The effect of the fluid is included in the equation of motion as the impulsive added mass and the frequency-dependent convective added mass along the nodes on the wetted boundary of the structure. The structure and the near-field soil medium are represented using the axisymmetric finite elements, while the far-field soil is modeled using dynamic infinite elements. The present method can be applied to the structure embedded in ground as well as on ground, since it models both the soil medium and the structure directly. For the purpose of verification, earthquake response analyses are performed on several cases of liquid tanks on a rigid ground and on a homogeneous elastic half-space. Comparison of the present results with those by other methods shows good agreement. Finally, an application example of a reinforced concrete tank on a horizontally layered soil with a rigid bedrock is presented to demonstrate the importance of the soil-structure interaction effects in the seismic analysis for large liquid storage tanks.