The helicoidal modeling in computational finite elasticity. Part II: Multiplicative interpolation

International Journal of Solids and Structures

Volumn 41, Issue 18-19, 2004, Pages 5383-5409

  Merlini, T ^a   Morandini, M ^a  

^a POLITECNICO DI MILANO   (Italy)

Author keywords

Dual algebra; Exponential map; Finite rotations; Interpolation; Rototranslations

Indexed keywords

ALGEBRA; APPROXIMATION THEORY; COMPUTER SIMULATION; INTERPOLATION; LINEARIZATION; TENSORS;

DUAL ALGEBRA; EXPONETIAL MAP; FINITE ROTATIONS; ROTOTRANSLATIONS;

ELASTICITY;

EID: 10644226837     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2004.02.026     Document Type: Article

References (22)

1. Angeles, J., 1998. The application of dual algebra to kinematic analysis. In: Angeles, J., Zakhariev, E. (Eds.), Computational Methods in Mechanical Systems, vol. 161. Springer-Verlag, Heidelberg, pp. 1-31.
2. Bauchau, O.A., Trainelli, L., 2003. The vectorial parametrization of rotation. Nonlinear Dyn. 32, 71-92.
3. Borri, M., Bottasso, C., 1994a. An intrinsic beam model based on a helicoidal approximation - Part I: Formulation. Int. J. Numer. Meth. Eng. 37, 2267-2289.
4. Borri, M., Bottasso, C., 1994b. An intrinsic beam model based on a helicoidal approximation - Part II: Linearization and finite element implementation. Int. J. Numer. Meth. Eng. 37, 2291-2309.
5. Borri, M., Bottasso, C.L., 1998. The exponential map of motion-theory and applications. In: Idelsohn, S.R., Oñate, E., Dvorkin, E. (Eds.), Computational Mechanics. New trends and applications. ©CIMNE, Barcelona, Spain.
6. Borri, M., Trainelli, L., Bottasso, C.L., 2000. On representations and parameterizations of motion. Multibody Syst. Dyn. 4, 129-193.
7. Cardona, A., Geradin, M., 1988. A beam finite element non-linear theory with finite rotations. Int. J. Numer. Meth. Eng. 26, 2403-2438.
8. Crisfield, M., Jelenić, G., 1999. Objectivity of strain measures in the geometrically exact three dimensional beam theory and its finite-element implementation. Proc. R. Soc. Lond. A 455, 1125-1147.
9. de Souza Neto, E.A., 2001. The exact derivative of the exponential of an unsymmetric tensor. Comput. Methods Appl. Mech. Eng. 190, 2377-2383.
10. Ibrahimbegović, A., Frey, F., Kožar, I., 1995. Computational aspects of vector-like parametrization of three-dimensional finite rotations. Int. J. Numer. Methods Eng. 38, 3653-3673.
11. Ibrahimbegović, A., Taylor, R.L., 2002. On the role of frame-invariance in structural mechanics models at finite rotations. Comput. Methods Appl. Mech. Eng. 191, 5159-5176.
12. Itskov, M., 2000. On the theory of fourth-order tensors and their applications in computational mechanics. Comput. Methods Appl. Mech. Eng. 189, 419-438.
13. Itskov, M., 2002. The derivative with respect to a tensor: some theoretical aspects and applications. ZAMM Z. Angew. Math. Mech. 82, 535-544.
14. Itskov, M., Aksel, N., 2002. A closed-form representation for the derivative of non-symmetric tensor power series. Int. J. Solids Struct. 39, 5963-5978.
15. Jelenić, G., Crisfield, M.A., 1999. Geometrically exact 3D beam theory: implementation of a strain-invariant finite element for statics and dynamics. Comput. Methods Appl. Mech. Eng. 171, 141-171.
16. Merlini, T., 2002. Differentiation of rotation and rototranslation. DIA-SR 02-16, Dip. Ing. Aerospaziale, Politecnico di Milano.
17. Merlini, T., 2003. Recursive representation of orthonormal tensors. DIA-SR 03-02, Dip. Ing. Aerospaziale, Politecnico di Milano.
18. Merlini, T., Morandini, M., 2003. Interpolation of the orientation and oriente-position fields. DIA-SR 03-03, Dip. Ing. Aerospaziale, Politecnico di Milano.
19. Ortiz, M., Radovitzky, R.A., Repetto, E.A., 2001. The computation of the exponential and logarithmic mappings and their first and second linearizations. Int. J. Numer. Meth. Eng. 52, 1431-1441.
20. Ring, M.C., 2003. MAPM Version 4.8 (Mike's Arbitrary Precision Math Library). Available from «http://www.tc.umn.edu/~ringx004/ mapm-main.html».
21. Ritto-Corrêa, M., Camotim, D., 2002. On the differentiation of the Rodrigues formula and its significance for the vector-like parameterization of Reissner-Simo beam theory. Int. J. Numer. Methods Eng. 55, 1005-1032.
22. Rosati, L., 1999. Derivatives and rates of the stretch and rotation tensors. J. Elast. 56, 213-230.