• 제목/요약/키워드: Boussinesq's solution

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탄성지반 위에 놓인 평판의 접촉영역 결정에 관한 연구 (A Study on the Determination of Contact Area of a Plate on Elastic Half-Space)

  • 정진환;이외득;김동석
    • 한국전산구조공학회:학술대회논문집
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    • 한국전산구조공학회 1998년도 가을 학술발표회 논문집
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    • pp.405-412
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    • 1998
  • According to the relative stiffness between the half-space and plate or loading condition, some parts of the plate can be separated from the half-space. The finite element procedure to determine the contact area by considering the distribution of contact pressure between plate and the elastic half-space is developed. The vertical surface displacements of the elastic half-space can be obtained through the integrations of the Boussinesq's solution for a point load. The rectangular plate on the elastic half-space is modeled by the 8-node rectangular and 6-node triangular elements and the Mindlin plate theory is used in oder to consider the transverse shear effect. In this study, the contact area may be determined approximately by the analysis with rectangular elements. From this results, the mesh pattern is modified by using triangular and rectangular elements. The contact area can be determined by the new mesh pattern with a relatively sufficient accuracy.

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Analysis of Harbor Tranquility due to Port Expansion

  • Moon, SeungHyo;Lee, JoongWoo;Kwon, SeongMin;Song, HyunWoo
    • 한국항해항만학회지
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    • 제43권5호
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    • pp.320-327
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    • 2019
  • This study examined the port expansion plan for the fishery port at the east coast of Korea, in accordance with permission conditions for coastal ports such as a limit on the cargo volume and passenger demand for the coastal tourism belt formation. The site was chosen as a municipal coastal port attracting the new ocean industry and building waterfront zone as a hub of new marine tourism. Two different numerical models (Swan and Bouss 2D) were used. Before applying to the target sea area, some numerical tests were conducted for the variation according to Bouss-2D's strong/weak and nonlinear technique compared to the irregular diffraction of semi-infinite breakwater with a theoretical solution. As a result, there was a difference in strong nonlinearity with breaking waves and it was necessary to experiment with a strong nonlinear analysis technique for the actual site. Two numerical models were applied to the fishery port site and the tranquility of some alternatives were analyzed. The numerical results show the most suitable plan was ALT-1, with satisfied harbor tranquility and reasonable economic sense. The extension of the east breakwater and enlarged turning basin of the F-Land plan have brought generally more stable harbor tranquility than the ALT-1. The result can be used as a reference for the port expansion plan in the future.

유한요소법에 의한 PC 농업용 사이로의 해석에 관한 연구 -제2보 탄성지반에 놓인 경우- (-An Analysis of Pre-Stressed Concrete Farn Sild by the Finite Element Method-)

  • 조진구;조현영;박병기
    • 한국농공학회지
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    • 제24권3호
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    • pp.73-83
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    • 1982
  • study aims to derive a rational method for the analysis of the farm silo supported on an elastic foundation in which it is assumed that the reaction pressure of the soil at a point is proportional to the deflection at that point. In order to investigate the effects of an elastic foundation on the behaviour of the structures on it, the analysis of the farm silo resting on an elastic foundation was compared with the solution that the ground support may be assumed uniform (which was obtained from part I of this paper). To calculate the deformation of an elastic foundation, Boussinesq's solution which allows an interaction of the various parts of ground was adopted. In this case, the foundation was treated as a superparametric element additionally. In the evaluation of an element stiffness matrix, Gauss quadrature' was used. In above numerical integration, 3-point rule for the farm silo wall and the footing was introduced and 2-point rule for the evaluation of a reaction between the footing and the elastic foundation was adopted. The stresses of a farm silo on an elastic foundation were smaller than those which the distribution of contact pressure between the footing and the soil is assumed uniformly. Since the differences of stresses were remarkable in PS structures than RC structures, it is desirable that designers take into account the effect of an elastic foundation for the case of PS structures. It can be noted that while the effect of an elastic foundation was more conspicuously observed in near of the ground, the value of stresses at far from the soil was little affected by an supported soil.

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Elastic solutions for shallow tunnels excavated under non-axisymmetric displacement boundary conditions on a vertical surface

  • Wang, Ling;Zou, Jin-Feng;Yang, Tao;Wang, Feng
    • Geomechanics and Engineering
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    • 제19권3호
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    • pp.201-215
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    • 2019
  • A new approach of analyzing the displacements and stress of the surrounding rock for shallow tunnels excavated under non-axisymmetric displacement boundary conditions on a vertical surface is investigated in this study. In the proposed approach, by using a virtual image technique, the shear stress of the vertical ground surface is revised to be zero, and elastic solutions of the surrounding rock are obtained before stress revision. To revise the vertical normal stress and shear stress of horizontal ground surface generated by the combined action of the actual and image sinks, the harmonic functions and corresponding stress function solutions were adopted. Based on the Boussinesq's solutions and integral method, the horizontal normal stress of the vertical ground surface is revised to be zero. Based on the linear superposition principle, the final solution of the displacements and stress were proposed by superimposing the solutions obtained by the virtual image technique and the stress revision on the horizontal and vertical ground surfaces. Furthermore, the ground settlements and lateral displacements of the horizontal and vertical ground surfaces are derived by the proposed approach. The proposed approach was well verified by comparing with the numerical method. The discussion based on the proposed approach in the manuscript shows that smaller horizontal ground settlements will be induced by lower tunnel buried depths and smaller limb distances. The proposed approach for the displacement and stress of the surrounding rocks can provide some practical information about the surrounding rock stability analysis of shallow tunnels excavated under non-axisymmetric displacement boundary conditions on a vertical surface.

Saint-Venant 공식(公式)에 의한 개수로(開水路)의 지하수성분(地下水性分) 추적(追跡) (Routing of Groundwater Component in Open Channel)

  • 김재한
    • 대한토목학회논문집
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    • 제8권4호
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    • pp.23-32
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    • 1988
  • 미계측유성(未計測流城)에서의 시간별 강우(降雨)로부터 부분침투천하(部分浸透川下)의 비피압대수층내(非被壓帶水層內)의 지하수(地下水)흐름에 기여하는 침투량과, 이로 인(因)하여 발생되는 하천수로상(河川水路上)에서의 시간별 기저유량(基底流量)의 동시적(同時的) 결합(結合)이 지형도(地形圖)나 토양도(土壤圖)부터 획득된 수리(水理) 및 수문(水文) 특성인자(特性因子)들에 의하여 수행(遂行)되었다. 지하수(地下水)흐름과 이의 개수로상(開水路上)의 흐름추적은 Boussinesg의 비선형방정식(非線形方程式)을 선형화(線形化)한 기법(技法)과 St. Venant의 간편화 공식을 각각 이용하므로써 결정되어졌다. 이의 해(解)를 위한 유출모형(流出模型)은 전류성(全流城)을 분할한 분포모형(分布模型)을 사용하였으며, 수치해법(數値解法)은 운동파방정식(運動波方程式)의 유한차분법(有限差分法)을 이용하였다. 그 결과로서, 수문지질(水文地質)의 다변성(多變性)에 따른 수문곡선분리(水文曲線分離)의 합리성(合理性)은 물리적(物理的)으로 바탕을 둔 지하지표수(地下地表水)의 모형을 개발하므로써 이루어져야 한다고 제안(提案)된다. 본 연구의 실하천유역(實河川流域)에 대한 적용 예로서는, 금강수계내(錦江水系內) 지류(支流)인 보청천유역(報靑川流域)을 선정(選定)하였으며, 그 결과로부터 본(本) 기법(技法)은 미계측유역에서의 강우의 지하침투량에 의한 기저유량을 모의발생(模擬發生)시킬 수 있으리라 판단된다.

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