KSCE Journal of Civil and Environmental Engineering Research (대한토목학회논문집)

Korean Society of Civil Engeneers (대한토목학회)
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Development of an Enhanced 8-node Hybrid/Mixed Plane Stress Element : HQ8-14βElement

8절점 Hybrid/Mixed 평면응력요소

  • 천경식 ((주)바우컨설탄트 기술연구소) ;
  • 박원태 (국립공주대학교 환경건설공학부) ;
  • 임성순 (서울시립대학교 토목공학과)
  • Received : 2005.09.22
  • Accepted : 2006.01.20
  • Published : 2006.03.30
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Abstract

A new enhanced 8-node hybrid/mixed plane stress elements based on assumed stress fields and modifed shape functions has been presented. The assumed stress fields are derived from the non-conforming displacement modes, which are less sensitive to geometric distortion. Explicit expression of shape functions is modifed so that it can represent any quadratic fields in Cartesian coordinates under the same condition as 9-node isoparametric element. The newly developed element has been designated as 'HQ8-$14{\beta}$'. The presented element is compared with existing elements to establish its accuracy and efficiency. Over a wide range of mesh distortions, the element presented here is found to be exceptionally accurate in predicting displacements.

본 논문에서는 가정응력장과 수정된 형상함수를 이용한 새로운 8절점 hybrid/mixed 평면응력요소를 제시하였다. 가정응력장은 비적합 변위모드로부터 유도하였으며, 이는 요소의 찌그러짐에 대한 민감도를 완화시켜준다. 그리고 Cartesian 좌표계에서 9절점 등매개변수 요소와 동일한 조건하에서 2차 변위를 정확히 보간하도록 수정한 형상함수를 사용하였다. 제시한 8절점 hybrid/mixed 평면응력요소(HQ8-$14{\beta}$)의 수치해석에 대한 정확성과 효율성을 검증하기 위해 기존의 참고문헌들과 비교, 분석하였다. 그 결과 본 논문에서 제시한 요소는 요소가 왜곡된 경우를 포함하여 우수한 성능을 보였다.

Keywords

References

  1. 박원태, 천경식, 임성순(2004) 직접수정된 8절점 가정변형률 유한 요소를 이용한 복합적층판의 정적, 좌굴 및 자유진동 해석, 한국구조물진단학회 논문집, 제8권 4호, pp. 107-114
  2. 천경식, 임성순, 장석윤(2004) 등방성 및 복합적층판 해석을 위한 개선된 8절점 Serendipity 유한요소, 대한토목학회 논문집, 대한토목학회, 제24권 제2A호, pp. 401-409
  3. 천경식, 장석윤(2004) 8절점 Serendipity 가정변형률 평판휨요소의 효율적인 성능개선을 위한 간단한 직접수정방안, 한국강구조학회 학술발표대회 논문집, pp. 330-337
  4. 최장근(2003), 유한요소법, 테크노 프레스
  5. Chun K.S. and Kassegne S.K. (2005) A new, efficient 8-node Serendipity element with explicit and assumed strain formulations, International Journal for Computational Methods in Engineering Science and Technology, Vol. 6(4), pp. 285-292 https://doi.org/10.1080/155022891009486
  6. Chun K.S., Kassegne S.K. and Park W.T. (2005) A quadratic hybrid assumed stress plane element using non-conforming displacement modes and modified shape functions, Journal of Applied Mechanics. ASME. submitted
  7. Choi C.K. and Park Y.M. (1999) Quadratic NMS Mindlin-platebending element, International Journal for Numerical Methods in Engineering. Vol. 46, pp. 1273-1289 https://doi.org/10.1002/(SICI)1097-0207(19991120)46:8<1273::AID-NME754>3.0.CO;2-N
  8. Chen W. and Cheung Y.K. (1995) A robust refined quadrilateral plane element, International Journal for Numerical Methods in Engineering, Vol. 38, pp. 649-666 https://doi.org/10.1002/nme.1620380409
  9. Di S. and Ramm E. (1994) On alternative hybrid stress 20 and 3D elements, Engineering Computations, Vol. II, pp. 49-68
  10. Feng W., Hoa S.V. and Huang Q. (1997) Classification of stress modes in assumed stress fields of hybrid finite elements, International Journal for Numerical Methods in Engineering, Vol. 40, pp. 4313-4339 https://doi.org/10.1002/(SICI)1097-0207(19971215)40:23<4313::AID-NME259>3.0.CO;2-N
  11. Groenwold A.A. and Stander N. (1995) An efficient 4-node 24 D.O.F. thick shell finite element with 5-point quadrature, Engineering Computations. Vol. 12, pp. 723-747 https://doi.org/10.1108/02644409510104686
  12. Geyer S. and Groenwold A.A. (2002) Two hybrid stress membrane finite element families with drilling rotations, International Journal for Numerical Methods in Engineering, Vol. 53, pp. 583-601 https://doi.org/10.1002/nme.287
  13. Kim S.H. and Choi C.K. (1992) Improvement of quadratic finite element for Mindlin plate bending, International Journal for Numerical Methods in Engineering, Vol. 34, pp. 197-208 https://doi.org/10.1002/nme.1620340112
  14. Kikuchi F., Okabe M. and Fujio H. (1999) Modification of the 8node serendipity element, Computer Methods in Applied Mechanics and Engineering, Vol. 179, pp. 91-109 https://doi.org/10.1016/S0045-7825(99)00031-6
  15. MacNeal R.H. and Harder R.L. (1985) A proposed standard set of problems to test finite elementaccuracy, Finite Elements in Analysis and Design, Vol. I, pp. 3-20
  16. MacNeal R.H. and Harder R.L. (1992) Eight nodes or nine', International Journal for Numerical Methods in Engineering, Vol. 33, pp. 1049-1058 https://doi.org/10.1002/nme.1620330510
  17. Pian T.H.H (1964) Derivation of element stiffness matrices by assumed stress distributions, AIAA Journal, Vol. 2, pp. 1333-1376 https://doi.org/10.2514/3.2546
  18. Pian T.H.H and Sumihara K. (1984) Rational approach for assumed stress finite elements, International Journal for Numerical Methods in Engineering, Vol. 20, pp. 1685-1695 https://doi.org/10.1002/nme.1620200911
  19. Pian T.H.H. and Tong P. (1986) Relation between incompatible displacement model and hybrid stress model, International Journal for Numerical Methods in Engineering, Vo. 22, pp. 173-181 https://doi.org/10.1002/nme.1620220112
  20. Pian T.H.H. and Wu C.C. (1988) A rational approach for choosing stress terms for hybrid finite element formulations, International Journal for Numerical Methods in Engineering, Vol. 26, pp.2331-2343 https://doi.org/10.1002/nme.1620261014
  21. Sze K.Y. (1992) Efficient formulation of robust mixed element using orthogonal stress/strain interpolants and admissible matrix formulation, International Journal for Numerical Methods in Engineering, Vol. 35, pp. 1-20 https://doi.org/10.1002/nme.1620350102
  22. Simo J.C., Fox D.D. and Rifai M.S. (1989) On stress resultant geometrically exact shell model. Part II: the linear theory; computational aspects, Computer Methods in Applied Mechanics and Engineering, Vol. 73, pp. 53-92 https://doi.org/10.1016/0045-7825(89)90098-4
  23. Wu C.C. and Cheung Y.K. (1995) On optimization approaches of hybrid stress elements, Finite Elements Analysis and Design, Vol. 21, pp. 111-128 https://doi.org/10.1016/0168-874X(95)00023-0
  24. Wu C.C. and Cheung Y.K. (1996) Penalty-equilibrating approach and an innovation of 4-noded hybrid stress elements, Communications in Numerical Methods in Engineering. Vol. 12, pp. 707-717 https://doi.org/10.1002/(SICI)1099-0887(199611)12:11<707::AID-CNM4>3.0.CO;2-K
  25. Yeo S. and Lee B.C. (1997) New stress assumption for hybrid stress elements and refined four-node plane and eight-node brick elements, International Journal for Numerical Methods in Engineering, Vol. 40, pp. 2933-2952 https://doi.org/10.1002/(SICI)1097-0207(19970830)40:16<2933::AID-NME198>3.0.CO;2-3