Work-conjugacy between rotation-dependent moments and finite rotations

International Journal of Solids and Structures

Volumn 40, Issue 11, 2003, Pages 2851-2873

  Ritto Corrêa, Manuel ^a   Camotim, Dinar ^a  

^a INSTITUTO SUPERIOR TÉCNICO   (Portugal)

Author keywords

Conservative moments; Finite rotations; Rotation dependent moments; Semi tangential rotations

Indexed keywords

DEGREES OF FREEDOM (MECHANICS); FINITE DIFFERENCE METHOD; METHOD OF MOMENTS; RANGE FINDING;

FINITE ROTATIONS;

ROTATION;

ROTATION;

EID: 0037902148     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7683(03)00078-7     Document Type: Article

References (25)

1. Argyris J. An excursion into large rotations Computer Methods in Applied Mechanics and Engineering 32 1982 85 155
2. Argyris J.H. Balmer H. Doltsinis J.S. Dunne P.C. Haase M. Kleiber M. Malejannakis G.A. Mlejnek H.-P. Muller M. Scharpf D.W. Finite element method--the natural approach Computer Methods in Applied Mechanics and Engineering 17-18 1979 1 106
3. Argyris J.H. Dunne P.C. Scharpf D.W. On large displacement-small strain analysis of structures with rotational degrees of freedom Computer Methods in Applied Mechanics and Engineering 14 1978 405 451
4. Argyris J.H. Hilbert O. Malejakannis G. Scharpf D.W. On the geometrical stiffness of a beam in space--a consistent V.W. approach Computer Methods in Applied Mechanics and Engineering 20 1979 105 131
5. Buechter N. Ramm E. Shell theory versus degeneration--a comparison in large rotation finite element analysis International Journal for Numerical Methods in Engineering 34 1992 39 59
6. Cardona A. Geradin M. A beam finite element non-linear theory with finite rotations International Journal for Numerical Methods in Engineering 26 1988 2403 2438
7. Christoffersen J. When is a moment conservative? Journal of Applied Mechanics ASME 56 1989 299 301
8. Crisfield, M.A., 1997. Non-Linear Finite Element Analysis of Solids and Structures, vol. 2: Advanced Topics. John Wiley, Chichester, UK
9. Goldstein H. Classical Mechanics second ed. 1980 Addison-Wesley Reading, MA
10. Ibrahimbegović, A., Frey, F., Kozar, I., 1995. Computational aspects of vector-like parametrization of three-dimensional finite rotations. International Journal for Numerical Methods in Engineering 38, 3653-3673.
11. Izzuddin B.A. Conceptual issues in geometrically nonlinear analysis of 3D framed structures Computer Methods in Applied Mechanics and Engineering 191 2001 1029 1053
12. Kim M.-Y. Chang S.-P. Park H.G. Spatial postbuckling analysis of nonsymmetric thin-walled frames. I-Theorethical considerations based on semitangential property Journal of Engineering Mechanics ASCE 127 8 2001 769 778
13. Lanczos C. The Variational Principles of Mechanics 1970 University of Toronto Press Toronto, Canada republished by Dover, New York, 1986
14. Pietraszkiewicz W. Badur J. Finite rotations in the description of continuum deformation International Journal of Engineering Science 21 9 1983 1097 1115
15. Ritto-Corrêa, M., Camotim, D., 2002. On the di.erentiation of the Rodrigues formula and its signi.cance for the vector-like parameterization of Reissner-Simo beam theory. International Journal for Numerical Methods in Engineering 55, 1005-1032.
16. Saleeb A. Chang T. Gendy A. Effective modelling of spatial buckling of beam assemblages, accounting for warping constraints and rotation-dependency of moments International Journal for Numerical Methods in Engineering 33 1992 469 502
17. Simo J. Vu-Quoc L. A three-dimensional finite strain rod model. Part II: Computational aspects Computer Methods in Applied Mechanics and Engineering 58 1986 79 116
18. Stuelpnagel J. On the parameterization of the three-dimensional rotation group SIAM Review 6 1964 422 430
19. Teh L.H. Clarke M.J. New definition of conservative internal moments in space frames Journal of Engineering Mechanics ASCE 123 2 1997 97 106
20. Teh L.H. Clarke M.J. Symmetry of tangent stiffness matrices of 3D elastic frame Journal of Engineering Mechanics ASCE 125 2 1999 248 251
21. Wang C.-C. A new representation theorem for isotropic functions: an answer to Professor G.F. Smith's criticism of my papers on representations for isotropic functions. Part 2. Vector-valued isotropic functions, symmetric tensor-valued isotropic functions and skew-symmetric tensor-valued isotropic functions Archive for Rational Mechanics and Analysis 36 1970 166 197
22. Yang Y.-B. Kuo S.-R. Theory and Analysis of Nonlinear Framed Structures 1994 Prentice-Hall New York
23. Yang Y.-B. McGuire W. Joint rotation and geometric nonlinear analysis Journal of Structural Engineering ASCE 112 4 1986 879 905
24. Yang Y.-B. McGuire W. Stiffness matrix for geometric nonlinear analysis Journal of Structural Engineering ASCE 112 4 1986 853 877
25. Ziegler H. Principles of Structural Stability second ed. 1968 Blaisdell Waltan, MA