Computational Structural Engineering (전산구조공학)

Computational Structural Engineering Institute of Korea (한국전산구조공학회)
권호 표지

A Finite Element Nonlinear Formulation for Large Deformations of Plane Frames

평면 뼈대구조물의 큰 변형에 대한 비선형 유한요소의 정식화

  • Published : 1994.12.01
Download PDF
⟨ Previous Next ⟩

Abstract

An explicit finite element nonlinear formulation for very large deformations of plane frame structures is developed. The formulation is based on an updated material reference frame and hence a true stress-strain relationship can be directly applied to characterize the properties of material which is subjected to very large deformations. In the formulation, a co-rotational approach is applied to deal with the large rotations but small strain problems. Straight beam element is considered when the strain of an element is large. The element formulation is based on the small deflection beam theory but with the inclusion of the effect of axial force. The element equations are constructed in an element local coordinate system which rotates and translates with the element, and then transformed to the global coordinate system. Several numerical examples are analyzed to validate the presented formulation.

평면 뼈대구조물의 매우 큰 변형에 대하여 정확한 비선형 유한요소의 정식화 과정을 나타내었다. 유한요소의 구성은 변화되는 재료의 기준 물성치에 근거를 두고 형성하였으며 매우 큰 변형을 받는 재료의 성질을 명확하게 특정지어 진응력-변형율 관계식을 직접 적용할 수 있도록 하였다. 큰회전과 작은 변형율을 받는 문제들을 형성하기 위하여 Co-rotation 접근 방법을 사용하였다. 큰 변형을 일으키는 요소의 문제를 해결하기 위하여 직선보 형태의 유한요소를 사용하였으며 개개의 유한요소의 정식화는 축방향력의 영향을 고려하여 미소 처짐보이론을 바탕으로 형성하였다. 본 연구에서 형성된 큰 변형에 대한 비선형 유한요소의 타당성을 확인하기 위해 몇몇 수치해들을 해석하고 검토하였다.

Keywords

References

  1. Int. J. Solids Structures v.6 A Finite Element Formulation for Problems of Large Strain and Large Displacement Hibbit,H.D.;Marcal,P.V.;Rice,J.R.
  2. In Formulations and Computational Algorithms in Finite Element Analysis A Plate / Shell Element for large Deflections and Rotations Ramm,E.;K.J.Bathe(ed.);J.T.Oden(ed.);W.Wunderich(ed.)
  3. Comput. Struct v.7 Geometrically Nonlinear Finite Element of Beams, Frames, Arches and Axisymmetric shells Wood, Arches;Zienkiewicz,O.C.
  4. Int. J. Numer. Meth. Engng. v.14 Large Displacement Analysis of Three-Dimensional Beam Structures Bathe,K.J.;Bolourchi,S.
  5. Comput. Struct v.10 Nonlinear Static and Dynamic Analysis of Framed Structures Remseth,S.N.
  6. Int. J. Numer. Meth. Engng. v.23 A Total Lagrangian Formulation for the Geometrically Nonlinear Analysis of Structures Using Finite Elements. Part Ⅱ: Arches, Frames and Axisymmetric Shells Oliver,J.;Onate,E.
  7. Int. J. Numer. Meth. Engng. v.28 Geometrically Non-linear Formulation for Three Dimensional Curved Beam Elements with Large Rotations Surana,K.S.;Sorem,R.M.
  8. J. Struct. Engng. v.109 Nonlinear Elastic Frame Analysis by Finite Element Wen,R.K.;Rahimzadeh,J.
  9. Comput. Meth. Appl. Mech. Engng. v.51 On finite Element Analysis of geometrically Nonlinear Problems Peterson,A.;Petersson,H.
  10. Comput. Struct. v.34 Geometrically Nonlinear Analysis of Elastic Framed Structures Wong,M.B.;Tin-Loi, F.
  11. Int. J. Solids Structures v.6 Finite Elements, Finite Roatations and Small Strains of Flexible Shells Wempner,G.
  12. comput. Struct. v.6 Large Deformations of Framed Structures under Stratic and Dynamic Loads Oran,C.;Kassimali,A.
  13. Comput. Meth. Appl. Mech. Engng. v.16 Nonlinear Analysis of Free-form Shells by Flat Finite Elements Horrigmoe,G.;Bergan,P.G.
  14. Compt. Struct. v.10 Applications of Higher Order Co-rotational Stretch Theories to Nonlinear Finite Element Analysis Belytschko,T.;Glaw,m L.W.
  15. Publication 83: 1, Dept. of Structural Machanics On the Co-rotational Finite Element Formulatiion for Large Deformation Problems Mattiason,K.
  16. Comput. Struct v.26 Nonlinear Finite Element Analysis of Elastic Frames Hsiao,K.M.;Hou,F.Y.
  17. J. Press. Vessel Technol v.108 An Element Independent Co-rotational Procedure for the Treatment of Large Rotations Rankin,C.C.;Brogan,F.A.
  18. Comput. Struct. v.27 A Corotational Procedure that Handles Large Rotations of Spatial Beam Structures Hsiao,K.K.;Horng,H.J.;Chen,Y.R.
  19. Discretisation Meth. in Strut. Mech. Co-rotational Beam Elements for Two-and Three Dimensional Non-linear Analysis Crisfield,M.A.;Cole,G.;G.Kuhn(ed.)(et al.)
  20. Comput. Mech. Appl. Mech. Eng. v.81 A Consistent Co-ratational Formulation for Non-linear, Three Dimensional Beam Elements Crisfield,M.A.
  21. Int. J. Solids Structures v.2 Large Deflections of Diamond Shaped Frames Jenkins,J.A.;Seitz,T.B.;Przemieniecki,J.S.
  22. Finite Elements in Analysis and Design v.13 Am Explicit Finite Element Formulation for Very Large Deformations Based on Updated Material reference Frame Yun,Y.M.