Non-uniform warping including the effects of torsion and shear forces. Part I: A general beam theory

International Journal of Solids and Structures

Volumn 44, Issue 18-19, 2007, Pages 5912-5929

  El Fatmi, Rached ^a  

^a UNIVERSITY OF TUNIS EL MANAR   (Tunisia)

Author keywords

Axial stress; Coupling effect; Exact beam theory; Non symmetrical cross section; Non uniform warping; Saint Venant solution; Shear; Shear force; Torsion; Warping parameter

Indexed keywords

AXIAL STRESS; BEAM THEORY; DISPLACEMENT MODELS; SHEAR BENDING; SHEAR FORCE; TORSION FORCE; WARPING PARAMETERS;

AXIAL COMPRESSION; BENDING (DEFORMATION); ELASTICITY; KINEMATICS; NUMERICAL ANALYSIS; TORSIONAL STRESS;

CANTILEVER BEAMS;

EID: 34447555693     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2007.02.006     Document Type: Article

References (35)

1. Batoz J.L., and Dhatt G. Modélisation des structures par éléments finis vol. 2 (1990), Hermes Edition, Paris
2. Benscoter S. A theory of torsion bending for multicell beams. Journal of Applied Mechanics 21 1 (1954) 25-34
3. Calgaro J.A. Poutres à parois minces (1998), Hermes, Paris
4. Dufort L., Drapier S., and Grédiac M. Closed-form solution for the cross-section warping in short beams under three-point bending. Composite Structures 52 (2001) 233-246
5. Eisenberger M. An exact high order beam element. Computers and Structures 81 (2003) 147-152
6. El Fatmi R. Non-uniform warping including the effects of torsion and shear forces. Part II: analytical and numerical applications. International Journal of Solids and Structures 44 (2007) 5930-5952
7. El Fatmi R., and Zenzri H. On the structural behavior and the saint venant solution in the exact beam theory. Application to laminated composite beams. Computers and Structures 80 (2002) 1441-1456
8. El Fatmi R., and Zenzri H. A numerical method for the exact elastic beam theory. Applications to homogeneous and composite beams. International Journal of Solids and Structures 41 (2004) 2521-2537
9. Ferrero J.F., Barrau J.J., Segura J.M., Castanie B., and Sudre M. Torsion of thin-walled composite beams with midplane symmetry. Composite Structures 54 (2001) 111-120
10. Gruttmann F., Sauer R., and Wagner W. Shear stresses in prismatic beams with arbitrary cross-section. International Journal of Numerical Methods in Engineering 45 7 (1999) 865-889
11. Kim N., and Kim M. Exact dynamic/static stifness matrices of non symmetric thin-walled beams considering coupled shear deformation effects. Thin-Walled Structures 43 (2005) 701-734
12. Ladevèze P., and Simmonds J. New concepts for linear beam theory with arbitrary geometry and loading. European Journal of Mechanics 17 3 (1998) 377-402
13. Ladevèze P., Sanchez P., and Simmonds J.C. On application of the exact theory of elastic beams. In: Durban S.J., and Givoli D. (Eds). Advances in the Mechanics of Plates and Shells (2001), Kluwer Academy Publishers
14. Le Fichoux, E., 1998. Présentation et utilisation de CASTEM. Rapport, DMT/SEMT/LAMS/RT/98-014-A. CEA, France.
15. Loughlan J., and Ata M. The analysis of carbon fibre composite box beams subjected to torsion with varaiable twist. Computer Methods in Applied Mechanics and Engineering 152 (1998) 373-391
16. Maddur S.S., and Chaturvedi S.K. Laminated composite open profile sections: non-uniform torsion of I-sections. Composite Structures 50 (2000) 159-169
17. Martinez F., Ségura J., and Gay D. Effets locaux liés au gauchissement variable dans les poutres homogénes et composites soumises à la flexion. Compte Rendu de l'Académie des Sciences, Mécanique des solides et des structures 327 II-b (1999) 653-658
18. Mentrasti L. Torsion of box girders with deformable cross sections. Journal of Engineering Mechanics 117 10 (1991) 2179-2199
19. Mokos V.G., and Sapountzakis E.J. A beam solution of transverse shear loading of composite beams. International Journal of Solids and Structures 42 (2005) 3261-3287
20. Pavazza R. Torsion of thin-walled beams of open cross-section with influence of shear. International Journal of Mechanical Sciences 47 (2005) 1099-1122
21. Prokic̀ A. Thin walled beams with open or closed cross section. Computers and Structures 47 6 (1993) 1065-1070
22. Reddy J.N., Wang C.M., and Lee K.H. Relationships between bending solutions of classical and shear deformation beam theories. International Journal of Solids and Structures 34 26 (1997) 3373-3384
23. Reddy J.N., Wang C.M., Lim G.T., and Ng K.H. Bending solutions of levinson beams and plates in term of the classical theories. International Journal of Solids and Structures 38 (2001) 4701-4720
24. Roberts T.M., and Al-Ubaidi H. Influence of shear deformation on restrained torsional warping of pultruded frp bars of open cross-section. Thin-Walled Structures 39 (2001) 395-414
25. Saadé, K., 2004. Finite element modelling of shear in thin walled beams with a single warping function. Ph.D. thesis, Faculté des Sciences Appliquées, Université Libre de Bruxelles.
26. Saadé K., Espion B., and Warzée G. Non-uniform torsional behavior and stability of thin walled elastic beams with arbitrary cross sections. Thin-Walled Structures 42 (2004) 857-881
27. Sapountzakis E.J. Solution of non-uniform torsion of bars by an integral equation method. Computers and Structures 77 (2000) 659-667
28. Sapountzakis E.J., and Mokos V.G. Warping shear stresses in nonuniform torsion of composite bars by bem. Computer Methods in Applied Mechanics and Engineering 192 (2003) 4337-4353
29. Sapountzakis E.J., and Mokos V.G. Nonuniform torsion of composite bars of variable thickness by bem. International Journal of Solids and Structures 41 7 (2004) 1753-1771
30. Sapountzakis E.J., and Mokos V.G. Dynamic analysis of 3-d beam elements including warping and shear deformation effects. International Journal of Solids and Structures 43 (2006) 6707-6726
31. Touratier M. An efficient standart plate theory. International Journal of Engineering Sciences 29 8 (1991) 901-916
32. Tsai H., and Kelly J.M. Buckling of short beams with warping effect included. International Journal of Solids and Structures 42 (2005) 239-253
33. Vlasov, V., 1961. Thin Walled Elastic Beams, second ed. English translation published for US Science Foundation by Israel Program for Scientific Tranlations, Jerusalem.
34. Wang C.M., Reddy J.N., and Lee K.H. Shear Deformable Beams and Plates (2000), Elsevier, NewYork
35. Yu W., Hodges D.H., Volovoi V.V., and Fuchs E.D. A generalized Vlasov theory for composite beams. Thin-Walled Structures 43 (2005) 1493-1511