Journal of Korean Society of Steel Construction (한국강구조학회 논문집)

Korean Society of Steel Construction (한국강구조학회)
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Analytical Investigation on Elastic Behaviors of Isotropic Annular Sector Plates Subjected to Uniform Loading

등분포하중을 받는 등방성 환형 섹터판의 탄성 거동에 대한 해석적 연구

  • 김경식 (청주대학교 토목환경공학과)
  • Received : 2010.03.02
  • Accepted : 2010.05.10
  • Published : 2010.06.27
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Abstract

This paper presents the development of a new analytical solution to the governing differential equation for isotropic annular sector plates subjected to uniform loading in a three-dimensional polar coordinate system. The 4th order governing partial differential equation (PDE) was converted to an ordinary differential equation (ODE) by assuming the Levy-type series solution form and the subsequent mathematical operations. Finally, a series-type solution was assembled with homogeneous and nonhomogeneous solution parts after operating real values and complex conjugates derived from the characteristic equation. To demonstrate the convergence rate and the accuracy of the featured method, several examples with various sector angles were selected and solved. The deflections and internal moments in the example annular sector plates that were obtained from the proposed solution were compared with those obtained from other analytical studies and numerical analyses using the finite element analysis package program, ABAQUS. Very good agreement with the results of other analytical and numerical methodologies was shown.

본 논문에서는 등분포 하중을 받는 등방성 환형 섹터판의 지배방정식에 대한 새로운 해석적 해가 3차원 극좌표계에서 개발된다. 4차의 편미분방정식 형태를 가지는 지배방정식은 레비 타입 시리즈 해에 대한 가정과 그 후속적인 수학적 처리를 통해 4차의 상미분방정식으로 전환된다. 전환된 상미분방정식의 특성방정식에 대한 실수 영역 및 복소수 영역의 해를 해석적으로 구한 후 제차 및 비제차 방정식의 각 해의 조합으로 최종적인 지배방정식의 해가 완성된다. 개발된 해의 수렴성 및 정확성을 보여주기 위해 다양한 경계조건 및 내부 중심 각도를 가지는 판에 대한 예제 해석을 수행하였고 그 결과를 다른 해석적 연구결과와 비교하였다. 또한 개발된 해의 정확성을 확인하기 위하여 유한요소 프로그램인 ABAQUS를 이용한 탄성해석을 추가로 수행하여 그 결과를 비교하였다. 제안된 해로부터 결정된 환형 섹터판의 변위 및 모멘트 값은 여타의 해석적 및 수치적 접근방법으로 구한 값들과 비교해 본 결과 매우 높은 수준에서 일치하고 있음이 확인되었다.

Keywords

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