Transactions of the Korean Society of Mechanical Engineers A (대한기계학회논문집A)

The Korean Society of Mechanical Engineers (대한기계학회)
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A New Anisoparametric Out-of-Plane Deformable Curved Beam Element

새로운 부등매개변수 면회변형 곡선보 요소

  • Published : 2001.04.01
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Abstract

It is known that the reduced integration, modified shape function, anisoparametric and non-conforming element can reduce the error induced by stiffness locking phenomenon in the finite element analysis. In this study, we propose new anisoparametric curved beam element. The new element based on reduced minimization theory is composed of different shape functions in each displacement field. By the substitution of this modified shape function, the unmatched coefficient that cause stiffness locking in the constraint energy is eliminated. To confirm the availability of this new model, we performed numerical tests for a simple model. As a result of numerical test, the undulate stress patterns are disappeared in static analysis, and displacements and stresses are close to exact solution. Not only in the static analysis but also in the eigen analysis of free vibrated curved beam model, this element shows successful convergent results.

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References

  1. Prathap, G., 1985, 'The Curved Beam/Deep Arch/Finite Ring Element Revisted,' Int. J. Num. Meth. Engng., Vol. 21, pp. 389-407 https://doi.org/10.1002/nme.1620210302
  2. Prathap, G. and Babu, C. R., 1986, 'An Isoparametric Quadratic Thick Curved Beam Element,' Int. J. Num. Meth. Engng., Vol. 23, pp. 1973-1984 https://doi.org/10.1002/nme.1620231102
  3. Day, R. A. and Potts, D. M., 1990, 'Curved Mindlin Beam and Axi-Symmetric Shell Elements - A New Approach,' Int. J. Num. Meth. Engng., Vol. 30, pp. 1263-1274 https://doi.org/10.1002/nme.1620300704
  4. 김용우, 1991, '유한요소의 가성구속과 가성모드에 의한 오차유발에 관한 통합이론,' 연세대학교 대학원, 박사학위 논문
  5. 문원주, 1997, '면내변형 곡선보 요소의 강체 변위장에 관한 연구,' 연세대학교 대학원, 박사학위 논문
  6. Zienkiewicz, O.C. and Taylor, R. L., 1989, The Finite Element Method, 4th edition, McGraw-Hill
  7. Min Oak-key and Kim Yong-woo, 1994, 'Reduced Minimization Theory in Beam Elements,' Int. J. Num. Meth. Engng., Vol. 37, pp. 2125-2145 https://doi.org/10.1002/nme.1620371208
  8. Min Oak-key and Kim Yong-woo, 1994, 'Numeritical Reduced Minimization Theory for Beam Elements Under Non-Uniform Isoparametric Mapping,' Int. J. Num. Meth. Engng., Vol. 39, pp. 1357-1382 https://doi.org/10.1002/(SICI)1097-0207(19960430)39:8<1357::AID-NME908>3.0.CO;2-Y
  9. 문원주, 김용우, 민옥기, 이강원, 1996, '공간 곡선보 요소에서의 감차최소화 이론,' 대한기계학회 논문집, 제20권, 제12호, pp. 3792-3803
  10. Kim Moon-joon, Min Oak-key, Kim Yong-woo and Moon Won-joo, 2000 'New Anisoparametric 3-Node Elements for Out-of-Plane Deformable Curved Beam,' KSME International Journal, Vol. 14, No. 3, pp. 131-141
  11. Tessler, A. and Spiridigliozzi, L., 1986, 'Curved Beam Elements with Penalty Relaxation,' Int. J. Num. Meth. Engng., Vol. 23, pp. 2245-2262 https://doi.org/10.1002/nme.1620231207
  12. 권영두, 임범수, 박윤호, 1999, '가우스 적분 가중치 수정에 의한 디제너레이트 쉘요소의 굽힘 특성 개선,' 대한기계학회논문집, 제23권, 제8호, pp. 1328-1337
  13. 민옥기, 김용우, 유동규, 1990, '곡선보의 강성과잉현상과 고유치에 관한 연구,' 대한기계학회논문집, 제14권, 제2호, pp. 445-454
  14. 문원주, 김용우, 민옥기, 1993, '면외변형 링요소를 이용한 고유해석,' 대한기계학회논문집, 제17권, 제7호, pp. 1719-1730
  15. 최창근, 1989, '유한요소해석,' 집문당
  16. Dasgupta, S. and Sengupta, D., 1997, 'Static and Dynamic Application of a Five Noded Horizontally Curved Beam Element with Shear Deformation,' Int. J. Num. Mech. Engng., Vol. 40, pp. 1801-1819 https://doi.org/10.1002/(SICI)1097-0207(19970530)40:10<1801::AID-NME138>3.0.CO;2-V
  17. 김용우, 문원주, 권해성, 민옥기, 1993, '면외 변형이 가능한 평면 곡선보의 선형 유한요소,' 대한기계학회논문집, 제16권, 제3호, pp. 419-429
  18. Moon Won-joo, Kim Yong-woo, Min Oak-key, 1998, 'Rigid Body Displacement Fields of an In-plane-deformable Curved Beam Based on Conventional Strain Definition,' KSME Int.J., vol.12, No.3, pp. 461-472
  19. 유승원, 문원주, 민옥기, 1999, '면외변형 곡선보 요소의 강체변위 특성,' 대한기계학회논문집, 제23권, 제8호, pp. 1388-1398