A triangular plate element with drilling degrees of freedom,for large rotation analyses of built-up plate/shell structures, based on the reissner variational principle and the von karman nonlinear theory in the Co-Rotational reference frame

CMES - Computer Modeling in Engineering and Sciences

Volumn 61, Issue 3, 2010, Pages 273-312

  Cai, Y C ^a,b   Paik, J K ^c   Atluri, S N ^b  

^a Tongji University   (China)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c Pusan National University   (South Korea)

Author keywords

Drilling degrees offreedom; Explicit tangent stiffness; Large deformation; Reissner variational principle; Thin plate shell; Updated Lagrangian formulation

Indexed keywords

LARGE DEFORMATIONS; TANGENT STIFFNESS; THIN PLATE/SHELL; UPDATED LAGRANGIAN FORMULATIONS; VARIATIONAL PRINCIPLES;

BENDING (DEFORMATION); BENDING MOMENTS; DEGREES OF FREEDOM (MECHANICS); FINITE ELEMENT METHOD; LAGRANGE MULTIPLIERS; LINEAR TRANSFORMATIONS; MECHANICS; ROTATION; STIFFNESS; STIFFNESS MATRIX; STRUCTURES (BUILT OBJECTS); VARIATIONAL TECHNIQUES;

PLATES (STRUCTURAL COMPONENTS);

EID: 77957577059     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (30)

1. Allman, D.J. (1988): A quadrilateral finite element including vertex rotations for plane elasticity problems. International Journal for Numerical Methods in Engineering, Vol.26, pp. 717-739.
2. Atluri, S.N. (1975): On 'hybrid' finite element models in solid mechanics, Advances in computer methods for partial differential equations, R. Vichrevetsky, Ed., AICA, pp. 346-355.
3. Atluri, S.N. (1979): On rate principles for finite strain analysis of elastic and inelastic nonlinear solids, Recent research on mechanical behavior, University of Tokyo Press, pp. 79-107.
4. 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.
5. 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.
6. 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.
7. Atluri, S. N.; Gallagher, R. H.; Zienkiewicz, O. C. (Editors). (1983): Hybrid & Mixed Finite Element Methods, J. Wiley & Sons, 600 pages.
8. Atluri, S.N.; Murakawa, H. (1977): On hybrid finite element models in nonlinear solid mechanics, finite elements in nonlinear mechanics, P.G. Bergan et al, Eds., Tapir Press, Norway, Vol. 1, pp. 3-40.
9. Atluri, S.N.; Reissner, E. (1989): On the formulation of variational theorems involving volume constraints. Computational Mechanics, Vol.5, pp 337-344.
10. Chia, C.Y. (1980): Nonlinear Analysis of Plate. McGraw-Hill, New York.
11. 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.
12. Dhatt, G.S. (1970): Instability of thin shells by the finite element method. IASS Symposium for Folded Plates and Prismatic Structures, Vienna.
13. Huang, B.Z.; Shenoy, V.B.; Atluri, S.N. (1994): A quasi-comforming triangular laminated composite shell element based on a refined first-order theory. Computational Mechanics, Vol.13, pp.295-314.
14. 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
15. Iura, M.; Atluri, S.N. (1992):Formulation of a membrane finite element with drilling degrees of freedom. Computational Mechanics, Vol.9, pp.417-428.
16. Iura, M.; Atluri, S.N. (2003): Advances in finite rotations in structural mechanics. CMES:Computer Modeling in Engineering&Sciences, Vol.4, pp.213-215.
17. Kim, K.D.; Lomboy, G.R. (2006): A co-rotational quasi-conforming 4-node resultant shell element for large deformation elasto-plastic analysis .Computer Methods in Applied Mechanics and Engineering, Vol.195, pp. 6502-6522.
18. 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.
19. 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.
20. Nguyen-Van, H.; Mai-Duy, N.; Tran-Cong, T. (2009): An improved quadrilateral flat element with drilling degrees of freedom for shell structural analysis. CMES:Computer Modeling in Engineering&Sciences, Vol.49, pp.81-110.
21. Oral, S.; Barut, A. (1991): A shear-flexible facet shell element for large deflection and instability analysis. Computer Methods in Applied Mechanics and Engineering, Vol.93, pp. 415-431.
22. Pian, T.H.H. (1964):Derivation of element stiffness matrices by assumed stress distribution. Journal of AIAA, Vol.2, pp. 1332-1336.
23. 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
24. Reissner, E. (1953): On a variational theorem for finite elastic deformations, Journal of Mathematics&Physics, Vol.32, pp. 129-135.
25. Shi, G.; Atluri, S.N. (1988): Elasto-plastic large deformation analysis of spaceframes: a plastic-hinge and stress-based explict derivation of tangent stiffnesses. International Journal for Numerical Methods in Engineering, Vol.26, pp.589-615.
26. Shi, G.; Voyiadzis, G.Z. (1991): Geometrically nonlinear analysis of plate by assumed strain element with explicit tangent stiffness matrix. Computers&Structures, Vol.41, pp.759-763.
27. Simo, J.C. (1993): On a stress resultant geometrically exact shell model. Part VII: Shell intersections with 5/6-DOF finite element formulations. Computer Methods in Applied Mechanics and Engineering, Vol.108, pp.319-339.
28. Xue, W.M.; Karlovitz, L.A.; Atluri, S.N. (1985): On the existence and stablity conditions for mixed-hybrid finite-element solutions based on Reissners variational principle. International Journal of Solids and Structures, Vol.21, pp.97-116.
29. Yang, HTY.; Saigal, S.; Masud, A.; Kapania, R.K. (2000): A survey of recent shell finite elements. International Journal for Numerical Methods in Engineering, Vol.47, pp.101-127.
30. Zhang, Y.X.; Cheung, Y.K. (2003): Geometric nonlinear analysis of thin plates by a refined nonlinear non-conforming triangular plate element. Thin-Walled Structures, Vol.41, pp.403-418.