Dynamic analysis of 3-D beam elements including warping and shear deformation effects

International Journal of Solids and Structures

Volumn 43, Issue 22-23, 2006, Pages 6707-6726

  Sapountzakis, E J ^a   Mokos, V G ^a  

^a NATIONAL TECHNICAL UNIVERSITY OF ATHENS   (Greece)

Author keywords

Bar; Beam; Boundary element method; Damping; Dynamic analysis; Mass; Nonuniform torsion; Shear deformation; Stiffness matrix; Warping

Indexed keywords

BARS (METAL); BOUNDARY ELEMENT METHOD; DAMPING; SHEAR DEFORMATION; STIFFNESS MATRIX; TORSIONAL STRESS;

DYNAMIC ANALYSIS; MASS; NONUNIFORM TORSION; WARPING;

BEAMS AND GIRDERS;

EID: 33748978419     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2006.02.004     Document Type: Article

References (26)

1. Ahmed M.Z., and Weisgerber F.E. Torsion constant for matrix analysis of structures including warping effect. Int. J. Solids Struct. 33 (1996) 361-374
2. Bach C., and Baumann R. Elastizität und Festigkeit. ninth ed. (1924), Springer, Berlin
3. Barsoum R.S., and Gallagher R.H. Finite element analysis of torsional-flexural stability problems. Int. J. Numer. Meth. Engng. 2 (1970) 335-352
4. Cowper G.R. The shear coefficient in Timoshenko's beam theory. J. Appl. Mech., ASME 33 2 (1966) 335-340
5. Humar J.L. Dynamics of Structures. second ed. (2002), A.A. Balkema Publishers, Lisse, Abingdon, Exton (Pa), Tokyo
6. Hutchinson J.R. Shear coefficients for Timoshenko beam theory. ASME J. Appl. Mech. 68 (2001) 87-92
7. Katsikadelis J.T. Boundary Elements: Theory and Applications (2002), Elsevier, Amsterdam-London
8. Katsikadelis J.T., and Tsiatas G.C. Nonlinear dynamic analysis of beams with variable stiffness. J. Sound Vibr. 270 (2004) 847-863
9. MSC/NASTRAN for Windows, 1999. Finite element modeling and postprocessing system. Help System Index,Version 4.0, USA.
10. Murin J. Beam element with varying cross-section satisfying local and global equilibrium conditions. Mech. Engng. 49 3 (1998) 208-223
11. Murin J. 3D beam element with changing cross sectional area. Engng. Mech. 1 (1999) 25-35
12. Murin J., and Kutis V. 3D-beam element with continuous variation of the cross-sectional area. Comput. Struct. 80 (2002) 329-338
13. Prokić A. On triply coupled vibrations of thin-walled beams with arbitrary cross-section. J. Sound Vibr. 279 (2005) 723-737
14. Reilly R.J. Stiffness analysis of grid including warping. ASCE J. Struct. Dir. 7 (1972) 1511-1523
15. Sapountzakis E.J. Solution of nonuniform torsion of bars by an integral equation method. Comput. Struct. 77 (2000) 659-667
16. Sapountzakis E.J., and Mokos V.G. Warping shear stresses in nonuniform torsion by BEM. Comput. Mech. 30 2 (2003) 131-142
17. Sapountzakis E.J., and Mokos V.G. A BEM solution to transverse shear loading of beams. Comput. Mech. 36 (2005) 384-397
18. Schramm U., Kitis L., Kang W., and Pilkey W.D. On the shear deformation coefficient in beam theory. Finite Elements Anal. Des. 16 (1994) 141-162
19. Schramm U., Rubenchik V., and Pilkey W.D. Beam stiffness matrix based on the elasticity equations. Int. J. Numer. Meth. Engng. 40 (1997) 211-232
20. Stephen N.G. Timoshenko's shear coefficient from a beam subjected to gravity loading. ASME J. Appl. Mech. 47 (1980) 121-127
21. Stojek D. Zur Schubverformung im Biegebalken. Z. Angew. Math. Mech. 44 (1964) 393-396
22. Tanaka M., and Bercin A.N. Finite element modelling of the coupled bending and torsional free vibration of uniform beams with an arbitrary cross-section. Appl. Math. Model. 21 (1997) 339-344
23. Timoshenko S.P., and Goodier J.N. Theory of Elasticity. third ed. (1984), McGraw-Hill, New York
24. Waldron P. Elastic analysis of curved thin-walled girders including the effect of warping restraint. Engng. Struct. 7 (1985) 93-104
25. Waldron P. Stiffness analysis of thin-walled girders. ASCE J. Struct. Div. 6 (1986) 1366-1384
26. Yang Y., and McGuire W. A procedure for analyzing space frames with partial warping restraint. Int. J. Numer. Meth. Engng. 20 (1984) 1377-1398