A co-rotational formulation for 3D beam element using vectorial rotational variables

Computational Mechanics

Volumn 39, Issue 3, 2007, Pages 309-322

  Li, Z X ^a  

^a ZHEJIANG UNIVERSITY   (China)

Author keywords

3D beam element; Co rotational procedure; Large displacement; Large rotation; Vectorial rotational variable

Indexed keywords

DERIVATIVES; FINITE ELEMENT METHOD; RELIABILITY; ROTATION; STIFFNESS MATRIX; VECTORS;

3D BEAM ELEMENT; CO ROTATIONAL PROCEDURE; LARGE DISPLACEMENT; LARGE ROTATION; VECTORIAL ROTATIONAL VARIABLES;

THREE DIMENSIONAL COMPUTER GRAPHICS;

EID: 36148953771     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00466-006-0029-x     Document Type: Article

References (36)

1. Bathe KJ, Bolourchi S (1979) Large displacement analysis of three-dimensional beam structures. Int J Numer Methods Eng 14:961-986
2. Battini JM, Pacoste C (2002) Co-rotational beam elements with warping effects in instability problems. Comput Methods Appl Mech Eng 191:1755-1789
3. Cardona A, Geradin M (1988) Beam finite element non-linear theory with finite rotations. Int J Numer Methods Eng 26:2403-2438
4. Chen H, Blandford GE (1991) Thin-walled space frames. I. Large-deformation analysis theory. J Struct Eng ASCE 117:2499-2520
5. Crisfield MA (1990) Consistent co-rotational formulation for non-linear, three-dimensional, beam-elements. Comput Methods Appl Mech Eng 81:131-150
6. Crisfield MA (1996) Nonlinear finite element analysis of solid and structures, vol 2. Wiley, Chichester
7. Crisfield MA, Moita GF (1996) A unified co-rotational framework for solids, shells and beams. Int J Solids Struct 33:2969-2992
8. Hsiao KM, Horng HJ, Chen YR (1987) A co-rotational procedure that handles large rotations of spatial beam structures. Comput Struct 27:769-781
9. Hsiao KM, Lin WY (2000a) A co-rotational finite element formulation for buckling and postbuckling analyses of spatial beams. Comput Methods Appl Mech Eng 188:567-594
10. Hsiao KM, Lin WY (2000b) Co-rotational formulation for thin-walled beams with monosymmetric open section. Comput Methods Appl Mech Eng 190:1163-1185
11. Izzuddin BA (2001.) Conceptual issues in geometrically nonlinear analysis of 3D framed structures. Comput methods Appl Mech Eng 191:1029-1053
12. Izzuddin BA, LI Z (2004) A co-rotational formulation for large displacement analysis of curved shell. In: Deeks, Hao (eds) The 18th Australasian conference on the mechanics of structures & materials. Taylor & Francis Group, London, pp 1247-1253
13. Jiang L, Chernuka MW (1994) Co-rotational formulation for geometrically nonlinear finite element analysis of spatial beams. Trans Can Soc Mech Eng 18:65-88
14. Kwak HG, Kim DY, Lee HW (2001) Effect of warping in geometric nonlinear analysis of spatial beams. J Construct Steel Res 57:729-751
15. Lee K (1997) Analysis of large displacements and large rotations of three-dimensional beams by using small strains and unit vectors. Commun Numer Methods Eng 13:987-997
16. Li ZX, Izzuddin BA (2005) Application of vectorial rotational variables in large displacement analysis of structures. In: Shen ZY, Li GQ, Chan SL (eds) The fourth international conference on advances in steel structures. Elsevier, Oxford, pp 1501-1506
17. Lin WY, Hsiao KM (2001) Co-rotational formulation for geometric nonlinear analysis of doubly symmetric thin-walled beams. Comput Methods Appl Mech Eng 190:6023-6052
18. Meek JL, Tan HS (1984) Geometrically nonlinear analysis of space frames by an incremental iterative technique. Comput Methods Appl Mech Eng 47:261-282
19. Misra A, Behdinan K, Cleghorn WL (2000) Implementation of consistent updated Lagrangian formulation for static analysis of geometrically nonlinear beam. Trans Can Soc Mech Eng 24:135-142
20. Pai PF, Anderson TJ, Wheater EA (2000) Large-deformation tests and total-Lagrangian finite-element analyses of flexible beams. Int J Solids Struct 37:2951-2980
21. Schulz M, Filippou FC (2001) Non-linear spatial timoshenko beam element with curvature interpolation. Int J Numer Methods Eng 50:761-785
22. Simo JC (1992) (Symmetric) Hessian for geometrically nonlinear models in solid mechanics. Intrinsic definition and geometric interpretation. Comput Methods Appl Mech Eng 96:189-200
23. Simo JC, Vu-Quoc L (1986a) On the dynamics of flexible beams under large overall motions - the plane case: part I. J Appl Mech ASME 53:849-854
24. Simo JC, Vu-Quoc L (1986b) On the dynamics of flexible beams under large overall motions - the plane case: part II. J Appl Mech ASME 53:855-863
25. Simo JC, Vu-Quoc L (1986c) A three-dimensional finite-strain rod model. Part II: computational aspects. Comput Methods Appl Mech Eng 58:79-116
26. Simo JC, Vu-Quoc L (1988) On the dynamics in space of rods undergoing large motions - a geometrically exact approach. Comput Methods Appl Mech Eng 66:125-161
27. Simo JC, Vu-Quoc L (1991) A geometrically-exact rod model incorporating shear and torsion-warping deformation. Int J Solids Struct 27:371-393
28. Teh LH, Clarke MJ (1998) Co-rotational and Lagrangian formulations for elastic three-dimensional beam finite elements. J Construct Steel Res 48:123-144
29. Teh LH, Clarke MJ (1999) Symmetry of tangent stiffness matrices of 3D elastic frame. J Eng Mech ASCE 125:248-251
30. Urthaler Y, Reddy JN (2005) A corotational finite element formulation for the analysis of planar beams. Commun Numer Methods Eng 21:553-570
31. Vu-Quoc L, Deng H (1995) Galerkin projection for geometrically exact sandwich beams allowing for ply drop-off. J Appl Mech ASME 62:479-488
32. Vu-Quoc L, Ebcioglu IK (1995) Dynamic formulation for geometrically-exact sandwich beam and 1-plates. J Appl Mech ASME 62:756-763
33. Vu-Quoc L, Ebcioglu IK (1996) General multilayer geometrically-exact beams and 1-D plates with piecewise linear section deformation. Zeitschrift fuer Angewandte Math Mech 76:391-409
34. Vu-Quoc L, Simo JC (1987) Dynamics of earth-orbiting flexile satellites with multibody components. J Guid Control Dyn 10:549-558
35. Wen RK, Rahimzadeh J (1983) Nonlinear elastic frame analysis by finite element. J Struct Eng ASCE 109:1951-1971
36. Yang YB, Shieh MS (1990) Solution method for nonlinear problems with multiple critical points. AIAA J 28:2110-2116