• Title/Summary/Keyword: half-plane

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TOEPLITZ OPERATORS ON WEIGHTED ANALYTIC BERGMAN SPACES OF THE HALF-PLANE

  • Kang, Si-Ho;Kim, Ja-Young
    • Bulletin of the Korean Mathematical Society
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    • v.37 no.3
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    • pp.437-450
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    • 2000
  • On the setting of the half-plane H={x+iy$\mid$y>0} of the complex plane, we study some properties of weighted Bergman spaces and their duality. We also obtain some characterizations of compact Toeplitz operators.

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Elastic Analysis of a Half-Plane Containing Multiple Inclusions Using Volume Integral Equation Method (체적 적분방정식법을 이용한, 다수의 함유체를 포함한 반무한 고체에서의 탄성해석)

  • Lee, Jung-Ki;Ku, Duck-Young
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.32 no.2
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    • pp.148-161
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    • 2008
  • A volume integral equation method (VIEM) is used to calculate the plane elastostatic field in an isotropic elastic half-plane containing multiple isotropic or anisotropic inclusions subject to remote loading. A detailed analysis of stress field at the interface between the matrix and the central inclusion in the first column of square packing is carried out for different values of the distance between the center of the central inclusion in the first column of square packing of inclusions and the traction-free surface boundary in an isotropic elastic half-plane containing multiple isotropic or anisotropic inclusions. The method is shown to be very accurate and effective for investigating the local stresses in an isotropic elastic half-plane containing multiple isotropic or anisotropic inclusions.

An Experimental Study on In-Plane Shear Strength of the Interface between Half PC Plate and Cast-in-Place Concrete Plate (하프 PC판과 후타설콘크리트 접합면의 면내전단강도에 관한 실험적 연구)

  • 신동원;고만영;이동우;김용부
    • Proceedings of the Korea Concrete Institute Conference
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    • 1998.10a
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    • pp.513-518
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    • 1998
  • In Half Precast Concrete Method, such as composite slab and composite wall, Interface between half PC plate and cast-in-place concrete is occurred. And this interface endure lastly in-plane shear which is occurred by external force. Therefore, test was executed to study in-plane shear strength of interface between half PC plate and cast-in-place concrete. In this test, Experimental parameters are finishing condition of the interface, cohesion of concrete, existence and nonexistence of re-bar truss, and angle and direction of lattice of re-bar truss. Comparing and analyzing experimental results, conclusions are obtained as follows. (1) In-plane shear strength of wide interface in composite plate is more affected by the roughness of interface than re-bar truss. And cohesion of concrete contribute to increasing in-plane shear strength. Therefore it seems that the interface should be roughen and kept clean to improve in-plane shear strength. (2) It seems that shear friction equation in ACI code can be sagely available for design of in-plane shear of composite plate.

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Investigation of continuous and discontinuous contact cases in the contact mechanics of graded materials using analytical method and FEM

  • Yaylaci, Murat;Adiyaman, Gokhan;Oner, Erdal;Birinci, Ahmet
    • Computers and Concrete
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    • v.27 no.3
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    • pp.199-210
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    • 2021
  • The aim of this paper was to examine the continuous and discontinuous contact problems between the functionally graded (FG) layer pressed with a uniformly distributed load and homogeneous half plane using an analytical method and FEM. The FG layer is made of non-homogeneous material with an isotropic stress-strain law with exponentially varying properties. It is assumed that the contact at the FG layer-half plane interface is frictionless, and only the normal tractions can be transmitted along the contacted regions. The body force of the FG layer is considered in the study. The FG layer was positioned on the homogeneous half plane without any bonds. Thus, if the external load was smaller than a certain critical value, the contact between the FG layer and half plane would be continuous. However, when the external load exceeded the critical value, there was a separation between the FG layer and half plane on the finite region, as discontinuous contact. Therefore, there have been some steps taken in this study. Firstly, an analytical solution for continuous and discontinuous contact cases of the problem has been realized using the theory of elasticity and Fourier integral transform techniques. Then, the problem modeled and two-dimensional analysis was carried out by using ANSYS package program based on FEM. Numerical results for initial separation distance and contact stress distributions between the FG layer and homogeneous half plane for continuous contact case; the start and end points of separation and contact stress distributions between the FG layer and homogeneous half plane for discontinuous contact case were provided for various dimensionless quantities including material inhomogeneity, distributed load width, the shear module ratio and load factor for both methods. The results obtained using FEM were compared with the results found using analytical formulation. It was found that the results obtained from analytical formulation were in perfect agreement with the FEM study.

Elastic Analysis of a Half-Plane Containing an Inclusion and a Void Using Mixed Volume and Boundary Integral Equation Method (혼합 체적-경계 적분방정식법을 이용한, 함유체와 공동을 포함한 반무한 고체에서의 탄성해석)

  • Lee, Jung-Ki;Yoon, Koo-Young
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.32 no.12
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    • pp.1072-1087
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    • 2008
  • A mixed volume and boundary integral equation method (Mixed VIEM-BIEM) is used to calculate the plane elastostatic field in an isotropic elastic half-plane containing an isotropic or anisotropic inclusion and a void subject to remote loading parallel to the traction-free boundary. A detailed analysis of stress field at the interface between the isotropic matrix and the isotropic or orthotropic inclusion is carried out for different values of the distance between the center of the inclusion and the traction-free surface boundary in an isotropic elastic half-plane containing three different geometries of an isotropic or orthotropic inclusion and a void. The method is shown to be very accurate and effective for investigating the local stresses in an isotropic elastic half-plane containing multiple isotropic or anisotropic inclusions and multiple voids.

Scaled Boundary Finite Element Methods for Non-Homogeneous Half Plane (비동질 반무한 평면에서의 비례경계유한요소법)

  • Lee, Gye-Hee
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.20 no.2
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    • pp.127-136
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    • 2007
  • In this paper, the equations of the scaled boundary finite element method are derived for non-homogeneous half plane and analyzed numerically In the scaled boundary finite element method, partial differential equations are weaken in the circumferential direction by approximation scheme such as the finite element method, and the radial direction of equations remain in analytical form. The scaled boundary equations of non-homogeneous half plane, its elastic modulus varies as power function, are newly derived by the virtual work theory. It is shown that the governing equation of this problem is the Euler-Cauchy equation, therefore, the logarithm mode used in the half plane problem is not valid in this problem. Two numerical examples are analysed for the verification and the feasibility.