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4변형 평면요소를 컴퓨터 프로그램으로 구현하기 위한 알고리즘

A Computer Program Algorithm for Realizing Quadrilateral Plane Element

  • 투고 : 2012.01.05
  • 발행 : 2012.04.25

초록

Many types of quadrilateral plane element are studied in literatures on FEA and implemented in various computer programs. Field engineers use these elements in their new projects according to the manual which is supplied with the program purchased, such as SAP2000, MIDAS, and so on. However, since these computer programs only present the concept and the way of using the commands and give different results in the same structural analysis model according to the element provided by each program, it is difficult to understand the basic theories and differences between these elements. So, it is necessary to establish the basic theories and the programming techniques in common use to consider these elements. In this study, basic theories for the consideration of quadrilateral plane elements with several degrees of freedom are studied first, where some of possible methods are investigated. On the basis of these theoretical backgrounds, an algorithm available in computer program is derived, which calculates the stiffness matrix of these elements in one process, and then a computer program(sNs) is developed based on the theory and algorithm studied. Lastly, some examples using these computerized elements are performed and the analysis results are compared with other commercial-use structural analysis programs used in field engineering for the verification of its fitness and validity.

키워드

과제정보

연구 과제 주관 기관 : 한국과학재단

참고문헌

  1. K.J. Bathe, Finite Element Procedures, Prentice Hall, 1996
  2. Harold C. Martin, Introduction to Matrix Method of Structural Analysis, McGraw-Hill, 1966
  3. O.C. Zienkiewicz, R.L. Taylor & J.Z. Zhu, The Finite Element Method - Its Basis & Fundamentals, Elsevier Butterworth-Heinemann, 2005
  4. E. L. Wilson and A. Ibrahimbegovic, 'Use of incompatible displacement modes for the calculation of element stiffnesses and stresses', J. Finite Elem. Anal. Design, (1990)
  5. A. Ibrahimbegovic 'A novel membrane element with enhanced displacement interpolation', J, Finite Elem. Anal. Design, (1990)
  6. A. Ibrahimbegovic and E. L. Wilson 'Unified formulation for triangular and quadrilateral flat shell finite elements with six nodal degrees of freedom', Int. j. numer. methods eng.,(1991)
  7. A. Ibrahimbegovic, R. L. Taylor and E. L. Wilson 'A robust membrane quadrilateral flat shell finite elements with six nodal degrees of freedom', Commun. Appl. Numer. Methods 7 (1991) 1-9
  8. A. Ibrahimbegovic 'Quadrilateral finite elements for analysis of thick and thin plates', Computer methods in applied mechanics and engineering., v.110 (1993) 195-209 https://doi.org/10.1016/0045-7825(93)90160-Y
  9. J. L. Batoz and M. B. Tahar, 'Evaluation of a new quadrilateral thin plate bending element', Int. j. numer. methods eng., 18, 1644-1677 (1982)
  10. Computers and Structures, Inc., SAP2000-ANALYSIS REFERENCE, Ver. 6.1
  11. ADINA ENGINEERING, "ADINA - System verification manual", REPORT AE 83-5, June 1983
  12. 마이다스아이티, MIDAS/GEN(Integrated Design System for Buildings and General Structures), Ver.7.8.5
  13. Computer and Structures, Inc., SAFE-USER'S MANUAL, Ver. 5.5, January 1995
  14. Computer and Structures, Inc., ETABS-Software Verification Exmaples, Ver. 8, June 2003
  15. Chun, K.S. and Kassegne, S.K., Park, W.T., Static assessment of quadratic hybrid plane stress element using non-conforming displacement modes and modified shape functions, Structural Engineering and Mechanics, Vol. 29, No. 6, 2008
  16. D. HAMADI and A.ZATAR, A New Analytical Integration Expression Applied To Quadrilateral Finite Elements, Proceeding of the World Congress on Engineering 2008, Vol. 2, 2008
  17. Choo, Y.S. and Choi, N., Lee, B.C., Quadrilateral and triangular plane elements with rotational degrees of freedom based on the hybrid Trefftz method, Finite Elements in Analysis and Design, Vol. 42, 2006
  18. Kaushalkumar Kansara, Development of Membrane, Plate and Flat Shell Elements in Java, Virginia Polytechnic Institute & State University, 2004