Anisotropic bending-torsion coupling for warping in a non-linear beam

Computational Mechanics

Volumn 31, Issue 1-2 SPEC., 2003, Pages 78-87

  Klinkel, S ^a   Govindjee, S ^b  

^a UNIVERSITY OF KARLSRUHE   (Germany)

^b Berkeley   (United States)

Author keywords

Anisotropic beams; Anisotropic warping; MEMS modeling; Silicon beams

Indexed keywords

BENDING (DEFORMATION); BENDING MOMENTS; ELASTICITY; FINITE ELEMENT METHOD; MICROELECTROMECHANICAL DEVICES; SINGLE CRYSTALS; TORSIONAL STRESS;

ANISOTROPIC BENDING-TORSION COUPLING; ANISOTROPIC WARPING; NON-LINEAR BEAM;

SILICON;

EID: 0037481191     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00466-002-0395-y     Document Type: Article

References (18)

1. Battini J-M, Pacoste C (2002) Co-rotational beam elements with warping effects in instability problems. Comput. Meth. Appl. Mech. Eng. 191: 1755-2010
2. Crisfield MA (1990) A consistent co-rotational formulation for non-linear, three-dimensional, beam elements. Comput. Meth. Appl. Mech. Eng. 81: 131-150
3. Crisfield MA, Moita GF, Jelenić G, Lyons LPR (1995) Enhanced lower-order element formulations for large strains. Comput. Mech. 17: 62-73
4. 1 finite element including transverse shear and torsion warping for rectangular sandwich beams. Int. J. Numer. Meth. Eng. 45: 47-75
5. Gruttmann F, Sauer R, Wagner W (1998) A geometrical non-linear eccentric 3d-beam element with abitrary cross-section. Comput. Meth. Appl. Mech. Eng. 160: 383-400
6. Gruttmann F, Sauer R, Wagner W (1999) Shear stresses in prismatic beams with arbitray cross-sections. Int. J. Numer. Meth. Eng. 45: 865-889
7. Gruttmann F, Sauer R, Wagner W (2000) Theory and numerics of three-dimensional beams with elastoplastic material behaviour. Int. J. Numer. Meth. Eng. 48: 1675-1702
8. Jelenić G, Crisfield MA (1999) Geometrical exact 3d beam theory: Implementation of a strain-invariant finite element for statics and dynamics. Comput. Meth. Appl. Mech. Eng. 171: 141-171
9. Klinkel S, Wagner W (1997) A geometrical non-linear brick element based on the eas-method. Int. J. Numer. Meth. Eng. 40: 4529-4545
10. Krahula JL, Lauterbach GF (2001) A finite element solution for Saint-Venant torsion. AIAA Journal 7: 2200-2203
11. Maluf N (2000) An introduction to microelectromechanical systems engineering. Boston/London: Artech House
12. Savoia M, Tullini N (1993) Torsional response of inhomogeneous and multilayered composite beams. Composite Structures 25: 587-594
13. Senturia SD (2001) Microsystem design. Boston/Dordrecht/London: Kluwer Academic Publishers
14. Simo JC, Armero F (1992) Geometrically non-linear enhanced strain mixed methods and the method of incompatiable modes. Int. J. Numer. Meth. Eng. 33: 1431-1449
15. Simo JC, Vu-Quoc I (1991) A geometrically-exact rod model incorporating shear and torsion-warping deformations. Int. J. Sol. Struct. 27: 371-393
16. Sokolnikoff IS (1956) Methematical theory of elesticity. New York: McGraw-Hill
17. Timoshenko SP, Goodier JN (1970) Theory of elesticity (3 ed.). New York: McGraw-Hill
18. Voigt W (1928) Lehrbuch der Kristallphysik (Nachdruck der 1. Auflage). Leipzig/Berlin: Teubner-Verlag