An efficient procedure to find shape functions and stiffness matrices of nonprismatic Euler-Bernoulli and Timoshenko beam elements

European Journal of Mechanics, A/Solids

Volumn 29, Issue 5, 2010, Pages 826-836

  Shooshtari, A ^a   Khajavi, R ^a  

^a FERDOWSI UNIVERSITY OF MASHHAD   (Iran)

Author keywords

Euler Bernoulli formulation; Nonprismatic beam element; Timoshenko formulation

Indexed keywords

BEAM ELEMENTS; BEAM MODELING; ENGINEERING STRUCTURES; EULER-BERNOULLI; GEOMETRICAL VARIATIONS; INTERPOLATING FUNCTIONS; LOW-ORDER POLYNOMIALS; NON-PRISMATIC; NUMERICAL EXAMPLE; RIGID-BODY MOTION; SHAPE FUNCTIONS; SIMPLE STRUCTURES; STIFFNESS MATRICES; STRAIN STATE; STRUCTURAL ENGINEERING; TAPERED BEAM; TIMOSHENKO BEAMS;

FUNCTION EVALUATION; INTERPOLATION; PARTICLE BEAMS; RIGID STRUCTURES; STIFFNESS; STIFFNESS MATRIX; STRAIN ENERGY;

VIBRATION MEASUREMENT;

EID: 77955467159     PISSN: 09977538     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.euromechsol.2010.04.003     Document Type: Article

References (46)

1. H.J. Al-Gahtani, and M.S. Khan Exact analysis of nonprismatic beams Journal of Engineering Mechanics ASCE 124 11 1998 1290 1293
2. S.Z. Al-Sadder Exact expressions for stability functions of a general non-prismatic beam-column member Journal of Constructional Steel Research 60 2004 1561 1584
3. N.M. Auciello, and A. Ercolano A general solution for dynamic response of axially loaded non-uniform Timoshenko beams International Journal of Solids and Structures 41 2004 4861 4874
4. C. Balkaya Behavior and modeling of nonprismatic members having T-sections Journal of Structural Engineering ASCE 127 8 2001 940 946
5. J.R. Banerjee, and F.W. Williams Exact Bernoulli-Euler static stiffness matrix for a range of tapered beam-columns International Journal for Numerical Methods in Engineering 23 1986 1615 1628
6. N. Bazeos, and D.L. Karabalis Efficient computation of buckling loads for plane steel frames with tapered members Engineering Structures 28 2006 771 775
7. B. Biondi, and S. Caddemi Euler-Bernoulli beams with multiple singularities in the flexural stiffness European Journal of Mechanics A-Solids 26 2007 789 809
8. M.A. Bradford, and P.E. Cuk Elastic buckling of tapered monosymmetric I-beams Journal of Structural Engineering ASCE 114 5 1988 977 996
9. C.J. Brown Approximate stiffness matrix for tapered beams Journal of Structural Engineering ASCE 110 12 1984 3050 3055
10. W.L. Cleghorn, and B. Tabarrok Finite element formulation of a tapered Timoshenko beam for free lateral vibration analysis Journal of Sound and Vibration 152 1992 461 470
11. J.O. Dow A Unified Approach to the Finite Element Method and Error Analysis Procedures 1999 Academic Press
12. G.P. Dube, and P.C. Dumir Tapered thin open section beams on elastic foundation - buckling analysis Computers and Structures 61 5 1996 845 857
13. M. Eisenberger, and Y. Reich Static, vibration and stability analysis of non-uniform beams Computers and Structures 31 1989 567 573
14. M. Eisenberger Explicit stiffness matrices for non-prismatic members Computers and Structures 20 4 1985 715 720
15. M. Eisenberger Exact solution for general variable cross-section members Computers and Structures 41 4 1991 765 772
16. N. El-Mezaini, C. Balkaya, and E. Citipitioglu Analysis of frames with nonprismatic beam elements Journal of Structural Engineering ASCE 117 6 1991 1573 1592
17. C.A. Felippa Customizing high performance elements by Fourier methods Trends in Computational Structural Mechanics 2001 CIMNE Barcelona, Spain
18. C. Franciosi, and M. Mecca Some finite elements for the static analysis of beams with varying cross section Computers and Structures 69 1998 191 196
19. Z. Frieman, and J.B. Kosmatka Exact stiffness matrix of a nonuniform beam - extension, torsion and bending of a Bernoulli-Euler beam Computers and Structures 42 5 1992 671 682
20. Z. Frieman, and J.B. Kosmatka Exact stiffness matrix of a nonuniform beam - bending of a Timoshenko beam Computers and Structures 49 3 1993 545 555
21. R.H. Gallagher, and C.H. Lee Matrix dynamic and instability analysis with non-uniform elements International Journal for Numerical Methods in Engineering 2 1970 265 275
22. J.M. Gere, and W.O. Carter Critical buckling loads for tapered columns Journal of the Structural Division ASCE 88 1 1962 1 11
23. D.H. Hodges, J.C. Ho, and W. Yu The effect of taper on section constants for in-plane deformation of an isotropic strip Journal of Mechanics of Materials and Structures 3 3 2008 425 440
24. D.J. Just Plane frameworks of tapering box and I-section Journal of the Structural Division ASCE 103 1 1977 71 86
25. D.L. Karabalis, and D.E. Beskos Static, dynamic and stability analysis of structures composed of tapered beams Computers and Structures 16 6 1983 731 748
26. Khajavi, R., 2004. Partitioning the stiffness matrix and the principal stiffness matrix of the finite element. M.Sc. Dissertation, Ferdowsi University of Mashhad, Iran (in Farsi).
27. B.L. Kruchoski, and J.W. Leonard Stability of nonprismatic Engineering Structures 3 1981 52 61
28. J. Li, and G. Li Buckling analysis of tapered lattice columns using a generalized finite element Communications in Numerical Methods in Engineering 20 2004 479 488
29. G.M. Lindberg Vibration of non-uniform beams Aeronautical Quarterly 14 1963 387 395
30. Y. Luo, F. Wu, and X. Xu Element stiffness matrix and modified coefficients for circular tube with tapered ends Journal of Constructional Steel Research 62 2006 856 862
31. Y.Z. Luo, X. Xu, and F. Wu Accurate stiffness matrix for nonprismatic members Journal of Structural Engineering ASCE 133 8 2007 1168 1175
32. Portland Cement Association (PCA), 1958. Handbook of frame constants: beam factors and moment coefficients for members of variable section. Skokie, III.
33. R.F. Rissoné, and J.J. Williams Vibrations of non-uniform cantilever beams The Engineer 220 1965 497 506
34. W.D. Rutledge, and B.E. Beskos Dynamic analysis of linearly tapered beams Journal of Sound and Vibration 79 3 1981 457 462
35. J. Saucha, and M. Antunac-Majcen General approach to the determination of critical buckling loads for tapered columns Transactions of Famena 26 2 2002 47 58
36. B.R. Somashekar A simple selectively integrated torsion-flexure coupled rapered beam element with transverse shear deformation Computers and Structures 17 3 1983 403 406
37. J. Stoer, and R. Bulirsch Introduction to Numerical Analysis second ed. 2002 Springer
38. H. Takabatake Cantilevered and linearly tapered thin-walled members Journal of Structural Engineering ASCE 116 4 1990 733 750
39. X. Tang Shape functions of tapered beam-column elements Computers and Structures 4 5 1993 943 953 (Pubitemid 23622492)
40. A. Tena-Colunga Stiffness formulation for nonprismatic beam elements Journal of Structural Engineering ASCE 122 12 1996 1484 1489
41. J. Thomas, and E. Dokumaci Improved finite elements for vibration analysis of tapered beams Aeronautical Quarterly 24 1973 39 46
42. C.W.S. To Higher order tapered beam finite elements for vibration analysis Journal of Sound and Vibration 63 1 1979 33 50
43. C.W.S. To A linearly tapered beam finite element incorporating shear deformation and rotary inertia for vibration analysis Journal of Sound and Vibration 78 1981 475 484
44. L. Vu-Quoc, and P. Léger Efficient evaluation of the flexibility of tapered I-beams accounting for shear deformations International Journal for Numerical Methods in Engineering 33 1992 553 566
45. H.C. Wang Generalized hypergeometric function solutions on the transverse vibration of a class of nonuniform beams Journal of Applied Mechanics 34 1967 702 708
46. Y. Yang, and H. Chiou Rigid body motion test for nonlinear analysis with beam elements Journal of Engineering Mechanics ASCE 113 9 1987 1404 1419