Large deformation analyses of space-frame structures, with members of arbitrary cross-section, using explicit tangent stiffness matrices, based on a von karman type nonlinear theory in rotated reference frames

CMES - Computer Modeling in Engineering and Sciences

Volumn 53, Issue 2, 2009, Pages 117-145

  Cai, Yongchang ^a,b   Paik, J K ^c   Atluri, Satya N ^c  

^a TONGJI UNIVERSITY   (China)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c Pusan National University   (South Korea)

Author keywords

Co rotational reference frame; Explicit tangent stiffness; Large deformation; Rod; Space frames; Unsymmetrical cross section; Updated Lagrangian formulation

Indexed keywords

LARGE DEFORMATIONS; REFERENCE FRAME; SPACE FRAMES; TANGENT STIFFNESS; UNSYMMETRICAL; UPDATED LAGRANGIAN FORMULATIONS;

BENDING (DEFORMATION); FINITE ELEMENT METHOD; LAGRANGE MULTIPLIERS; PLATES (STRUCTURAL COMPONENTS); ROTATION; STEEL BEAMS AND GIRDERS; STIFFNESS; STRUCTURAL FRAMES;

STIFFNESS MATRIX;

EID: 77949822726     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (31)

1. Atluri, S.N. (1980): On some new general and complementary energy theorems for the rate problems in finite strain, classical elastoplasticity. Journal of Structural Mechanics, Vol.8(1), pp. 61-92.
2. Atluri, S.N. (1984): Alternate stress and conjugate strain measures, and mixed variational formulations involving rigid rotations, for computational analyses of finitely deformed plates and shells: part-I: thoery. Computers & Structures, Vol.18(1), pp. 93-116.
3. Atluri, S.N.; Cazzani, A. (1994): Rotations in computational solid mechanics, invited feature article. Archives for Computational Methods in Engg., ICNME, Barcelona, Spain, Vol 2(1), pp. 49-138.
4. Atluri, S.N.; Iura, M.; Vasudevan, S. (2001): A consistent theory of finite stretches and finite rotations, in space-curved beams of arbitrary cross-section. Computational Mechanics, vol.27, pp.271-281
5. Auricchio, F.; Carotenuto, P.; Reali,A. (2008): On the geometrically exact beam model: A consistent, effective and simple derivation from three-dimensional finiteelasticity. International Journal of Solids and Structures, vol.45, pp. 4766-4781.
6. Bathe, K.J.; Bolourchi, S. (1979): Large displacement analysis of three- dimensional beam structures. International Journal for Numerical Methods in Engineering, vol.14, pp.961-986.
7. Chan, S.L. (1996): Large deflection dynamic analysis of space frames. Computers & Structures, vol.58, pp.381-387.
8. Crisfield, M.A. (1990): A consistent co-rotational formulation for non-linear, threedimensional, beam-elements. Computer Methods in Applied Mechanics and Engineering, vol.81, pp. 131-150.
9. Dinis, L.W.J.S.; Jorge, R.M.N.; Belinha, J. (2009): Large deformation applications with the radial natural neighbours interpolators. CMES: Computer Modeling in Engineering & Sciences, vol.44, pp. 1-34
10. Gendy, A.S.; Saleeb, A.F. (1992): On the finite element analysis of the spatial response of curved beams with arbitrary thin-walled sections. Computers & Structures, vol.44, pp.639-652
11. Han, Z.D.; Rajendran, A.M.; Atluri, S.N. (2005): Meshless Local Petrov- Galerkin (MLPG) approaches for solving nonlinear problems with large deformations and rotations. CMES: Computer Modeling in Engineering & Sciences, vol.10, pp. 1-12
12. Iura, M.; Atluri, S.N. (1988): Dynamic analysis of finitely stretched and rotated 3-dimensional space-curved beams. Computers & Structures, Vol.29, pp.875-889
13. Izzuddin, B.A. (2001): Conceptual issues in geometrically nonlinear analysis of 3D framed structures. Computer Methods in Applied Mechanics and Engineering, vol.191, pp. 1029-1053.
14. Kondoh, K.; Tanaka, K.; Atluri, S.N. (1986): An explict expression for the tangent-stiffness of a finitely deformed 3-D beam and its use in the analysis of space frames. Computers & Structures, vol.24, pp.253-271.
15. Kondoh, K.; Atluri, S.N. (1987): Large-deformation, elasto-plastic analysis of frames under nonconservative loading, using explicitly derived tangent stiffnesses based on assumed stresses. Computational Mechanics, vol.2,pp.1-25.
16. Lee, M.H.; Chen,W.H. (2009): A three-dimensional meshless scheme with background grid for electrostatic-structural analysis. CMC: Computers Materials & Continua, vol.11, pp. 59-77
17. Lee, S.Y.; Lin, S.M.; Lee, C.S.; Lu, S.Y.; Liu, Y.T. (2008): Exact large deflection of beams with nonlinear boundary conditions. CMES: Computer Modeling in Engineering & Sciences, vol.30, pp. 27-36
18. Lee, S.Y.; Lu, S.Y.; Liu, Y.R.; Huang, H.C. (2008): Exact large deflection solutions for Timoshenko beams with nonlinear boundary conditions. CMES: Computer Modeling in Engineering & Sciences, vol.33, pp. 293-312
19. Liu, C.S. (2007a): A modified Trefftz method for two-dimensional Laplace equation considering the domain's characteristic length. CMES: Computer Modeling in Engineering & Sciences, vol.21, pp. 53-66.
20. Liu, C.S. (2007b): A highly accurate solver for the mixed-boundary potential problem and singular problem in arbitrary plane domain. CMES: Computer Modeling in Engineering & Sciences, vol.20, pp. 111-122.
21. Liu, C.S.; Atluri, S.N. (2008): A novel time integration method for solving a large system of non-linear algebraic equations. CMES:Computer Modeling in Engineering & Sciences, vol.31, pp. 71-83.
22. Lo, S.H. (1992): Geometrically nonlinear formulation of 3D finite strain beam element with large rotations. Computers & Structures, vol.44, pp.147-157
23. Mata, P.; Oller, S.; Barbat A.H. (2007): Static analysis of beam structures under nonlinear geometric and constitutive behavior. Computer Methods in Applied Mechanics and Engineering, vol.196, pp. 4458-4478.
24. Mata, P.; Oller, S.; Barbat A.H. (2008): Dynamic analysis of beam structures considering geometric and constitutive nonlinearity. Computer Methods in Applied Mechanics and Engineering, vol.197, pp. 857-878.
25. Punch, E.F.; Atluri, S.N. (1984): Development and testing of stable, invariant, isoparametric curvilinear 2-D and 3-D hybrid-stress elements. Computer Methods in Applied Mechanics and Engineering ,Vol.47, pp.331-356
26. Simo, J.C. (1985): A finite strain beam formulation. The three-dimensional dynamic problem. Part I. Computer Methods in Applied Mechanics and Engineering, vol.49, pp.55-70.
27. Shi, G.; Atluri, S.N. (1988): Elasto-plastic large deformation analysis of spaceframes: a plastic-hinge and strss-based explict derivation of tangent stiffnesses. International Journal for Numerical Methods in Engineering, vol.26, pp.589-615.
28. Wu, T.Y.; Tsai, W.G.;Lee, J.J. (2009): Dynamic elastic-plastic and large deflection analyses of frame structures using motion analysis of structures. Thin-Walled Structures, vol.47, pp. 1177- 1190.
29. Xue, Q.; Meek J.L. (2001): Dynamic response and instablity of frame structures. Computer Methods in Applied Mechanics and Engineering, vol.190, pp. 5233-5242.
30. Zhou, Z.H.; Chan,S.L. (2004a): Elastoplastic and Large Deflection Analysis of Steel Frames by One Element per Member. I: One Hinge along Member. Journal of Structural Engineering, vol.130, pp.538-544.
31. Zhou, Z.H.; Chan,S.L. (2004b): Elastoplastic and Large Deflection Analysis of Steel Frames by One Element per Member. II: Three Hinges along Member. Journal of Structural Engineering, vol.130, pp.545-5553.