DOI QR코드

DOI QR Code

An Estimation on the Stiffness Matrix of Three Dimensional Solid-Flat Shell Transition Element

3차원 솔리드-평면 쉘 변환요소의 강성행렬 추정

  • Received : 2014.04.16
  • Accepted : 2014.07.08
  • Published : 2014.07.30

Abstract

A structural model consists of many types of finite elements, such as truss, beam, plate, shell and solid element, and so on. With the aid of commercial computer programs, field engineers comfortably use these finite elements at the same time for the modelling and analysis of real structure in their new projects. However, it is still difficult to model the connections and interfaces between different types of finite elements because of mutually ill-matched node numbers and degrees of freedom(d.o.f). To settle these problems, Many researchers studied and proposed various solution methods in literatures on FEA(Finite Element Analysis) and the use of transition elements is considered as one of the solutions. This pater presents an isoparametric formulation for three dimensional transition finite element, especially the solid-flat shell transition element. The proposed solid-flat shell transition element is composed of the solid element with 8 nodes, 3 d.o.f and the flat shell element with 4 nodes, 6 d.o.f for the simple formula derivation and the usefulness of practical applications. Basic theories for solid element and flat shell element are studied at first and a possible method for realizing the solid-flat shell transition element is suggested. On the basis of these theoretical backgrounds, the formula which calculates the stiffness matrix of the solid-flat shell transition element is derived in detail and an algorithm available for computer programming is investigated lastly.

Keywords

Acknowledgement

Supported by : 한국과학재단

References

  1. 김호수,홍성목, 변환요소 및 분할구조법에 의한 병렬전단벽의 해석에 관한 연구, 대한건축학회논문집, 8권, 4호, p.p.97-108, 1992
  2. Harold C. Martin, Introduction to Matrix Method of Structural Analysis, McGraw-Hill, 1966
  3. K.J. Bathe, Finite Element Procedures, Prentice Hall, 1996
  4. O.C. Zienkiewicz, R.L. Taylor & J.Z. Zhu, The Finite Element Method-Its Basis & Fundamentals, Elsevier Butterworth-Heinemann, 2005
  5. K. S. Surana 'Transition finite elements for three dimensional stress analysis', International Journal for Numerical Methods in Engineering., v.15 (1980) 991-1020 https://doi.org/10.1002/nme.1620150704
  6. K. S. Surana "Geometrically non-linear formulation for the three dimensional solid-shell transition finite elements", Computers & Structures., v.15 (1982) 549-566 https://doi.org/10.1016/0045-7949(82)90007-4
  7. 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)
  8. A. Ibrahimbegovic ' A novel membrane element with enhanced displacement interpolation', J, Finite Elem. Anal. Design, (1990)
  9. 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)
  10. 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
  11. 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
  12. Computers and Structures, Inc., SAP2000-ANALYSIS REFERENCE, Ver. 7.0, 1998
  13. ADINA ENGINEERING, "ADINA-System verification manual", REPORT AE 83-5, June 1983