Characteristic behavior of prismatic anisotropic beam via generalized eigenvectors

International Journal of Solids and Structures

Volumn 47, Issue 10, 2010, Pages 1327-1337

  Morandini, Marco ^a   Chierichetti, Maria ^b   Mantegazza, Paolo ^a  

^a POLITECNICO DI MILANO   (Italy)

^b Georgia Institute of Technology   (United States)

Author keywords

Anisotropic beam; Beam warping; Cross section; De Saint Venant's principle; Mechanical property

Indexed keywords

ANISOTROPIC BEAMS; BEAM WARPING; COMPOSITE BEAM; DEFORMATION PARAMETER; EIGENVALUES; FINITE-ELEMENT DISCRETIZATION; GENERALIZED EIGENVECTORS; NON-HOMOGENEOUS; PRISMATIC BEAM; RIGID-BODY MOTION; SAINT VENANT'S PRINCIPLE; SAINT-VENANT; SEMI-ANALYTICAL; VARIATIONAL FORMULATION;

ANISOTROPY; DEFORMATION; EIGENVALUES AND EIGENFUNCTIONS; ELASTICITY; EQUATIONS OF MOTION; ORDINARY DIFFERENTIAL EQUATIONS; WEAVING;

MECHANICAL PROPERTIES;

EID: 77949491654     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2010.01.017     Document Type: Article

References (36)

1. Berdichevsky V.L., and Staroselsky L.A. Bending, extension and torsion of naturally twisted rods. Journal of Applied Mathematics and Mechanics 49 6 (1985) 746-755
2. Borri M., Ghiringhelli G.L., and Merlini T. Linear analysis of naturally curved and twisted anisotropic beams. Composites Engineering 2 5-7 (1992) 433-456
3. Borri M., and Merlini T. A large displacement formulation for anisotropic beam analysis. Meccanica 21 1 (1986) 30-37
4. Bryson J.A.E., and Ho Y.-C. Applied Optimal Control: Optimization, Estimation, and Control (1975), Taylor & Francis
5. Cesnik, C.E.S., 1994. Cross-sectional analysis of initially twisted and curved composite beams. Ph.D. Thesis, Georgia Institute of Technology.
6. Cesnik C.E.S., and Hodges D.H. VABS: a new concept for composite rotor blade Cross-Sectional modeling. Journal of the American Helicopter Society 42 1 (1997) 27-38
7. Cesnik C.E.S., Hodges D.H., and Sutyrin V.G. Cross-sectional analysis of composite beams including large initial twist and curvature effects. AIAA Journal 34 9 (1996) 1913-1920
8. Cesnik, C.E.S., Sutyrin, V.G., Hodges, D.H., 1993. A refined composite beam theory based on the variational-asymptotical method. In: AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 34th and AIAA/ASME Adaptive Structures Forum, Technical Papers. Pt. 5. La Jolla, CA, pp. 2710-2720.
9. Druz A.N., Polyakov N.A., and Ustinov Y.A. Homogeneous solutions and Saint-Venant problems for a naturally twisted rod. Journal of Applied Mathematics and Mechanics 60 4 (1996) 657-664
10. Druz A.N., and Ustinov Y.A. Green's tensor for an elastic cylinder and its applications in the development of the Saint-Venant theory. Journal of Applied Mathematics and Mechanics 60 1 (1996) 97-104
11. Ghiringhelli G.L. On the thermal problem for composite beams using finite element semi-discretization. Composites Part B 6 5-6 (1997) 483-495
12. Ghiringhelli G.L., and Mantegazza P. Linear, straight and untwisted anisotropic beam section properties from solid finite elements. Composites Engineering 4 12 (1994) 1225-1239
13. Ghiringhelli G.L., Masarati P., and Mantegazza P. Characterization of anisotropic non-homogeneous beam section with embedded piezo-electric materials. Journal of Intelligent Material Systems and Structures 8 10 (1997) 842-858
14. Ghiringhelli G.L., Masarati P., Morandini M., and Muffo D. Integrated aeroservoelastic analysis of induced strain rotor blades. Mechanics of Advanced Materials and Structures 15 (2008) 291-306
15. Giavotto, V., 1986. Teoria elastica della trave anisotropa e non omogenea. In: Scritti per Lucio Lazzarino. Pacini Editore, Pisa, Italy, pp. 131-164 (in Italian).
16. Giavotto V., Borri M., Mantegazza P., Ghiringhelli G.L., Carmaschi V., Maffioli G.C., and Mussi F. Anisotropic beam theory and applications. Computers & Structures 16 (1983) 403-413
17. Golub G.H., and Wilkinson J.H. Ill-conditioned eigensystems and computation of the jordan canonical form. SIAM Review 18 4 (1976) 578-619
18. Hodges, D.H., 2006. Nonlinear composite beam theory. No. 213 in Progress in Astronautics and Aeronautics. American Institute of Aeronautics and Astronautics, 1801 Alexander Bell Drive, Suite 500, Reston, VA, pp. 20191-4344, USA.
19. Hodges D.H., Atilgan A.R., Cesnik C.E.S., and Fulton M.V. On a simplified strain energy function for geometrically nonlinear behaviour of anisotropic beams. Composites Engineering 2 5-7 (1992) 513-526
20. Hodges D.H., Atilgan A.R., Fulton M.V., and Rehfield L.W. Free vibration analysis of composite beams. Journal of the American Helicopter Society 36 3 (1991) 36-47
21. Horgan C.O. Recent developments concerning Saint-Venant's principle: an update. Applied Mechanics Reviews 42 11 (1989) 295-303 (November)
22. Horgan C.O. Recent developments concerning Saint-Venant's principle: a second update. Applied Mechanics Reviews 49 10 (1996) 101-111 (October)
23. Kirchgässner K. Wave-solutions of reversible systems and applications. Journal of Differential Eqs. 45 1 (1982) 113-127 (July)
24. Love, A.E.H., 1906. A Treatise on the Mathematical Theory of Elasticity, second edition. Cambridge University Press. Available from .
25. Mantegazza P. Analysis of semimonocoque beam sections by the displacement method. Aerotecnica Missili e Spazio 4 (1977) 179-182
26. Masarati, P., 2001. On the semi-analytical solution of beams subjected to distributed loads. In: XVI Congresso Nazionale AIDAA. Palermo, pp. 72.1-72.10, September 24-28.
27. Merlini T. On the development of static modes in slender elements under end loads. Aerotecnica - missili e spazio 67 1-4 (1988) 104-118
28. Mielke A. Saint-Venant's problem and semi-inverse solutions in nonlinear elasticity. Archive for Rational Mechanics and Analysis 102 3 (1988) 205-229
29. Mielke A. Normal hyperbolicity of center manifolds and Saint-Venant's principle. Archive for Rational Mechanics and Analysis 110 4 (1990) 353-372 (December)
30. Mielke A. Hamiltonian and Lagrangian Flows on Center Manifolds with Applications to Elliptic Variational Problems. Lecture Notes in Mathematics vol. 1489 (1991), Springer, Berlin/Heidelberg
31. Minguet P., and Dugundji J. Experiments and analysis for composite blades under large deflections. I - Static behavior. AIAA Journal 28 9 (1990) 1573-1579
32. Romanova N.M., and Ustinov Y.A. The Saint-Venant problem of the bending of a cylinder with helical anisotropy. Journal of Applied Mathematics and Mechanics 72 4 (2008) 481-488
33. Timoshenko S.P., and Goodier J.N. Theory of Elasticity. second edition (1951), McGraw Hill, New York
34. Toupin, R.A., 1965. Saint-Venant's principle. Archive for Rational Mechanics and Analysis 18 (2), 83-96. Available from .
35. Yu W., and Hodges D.H. Elasticity solutions versus asymptotic sectional analysis of homogeneous, isotropic, prismatic beams. Journal of Applied Mechanics 71 1 (2004) 15-23
36. Zubov L.M. The non-linear Saint-Venant problem of the torsion, stretching and bending of a naturally twisted rod. Journal of Applied Mathematics and Mechanics 70 2 (2006) 300-310