Static and dynamic analysis of flexible beams: A consistent updated Lagrangian formulation

Transactions of the Canadian Society for Mechanical Engineering

Volumn 21, Issue 2, 1997, Pages 141-177

  Behdinan, K ^a   Stylianou, M C ^b   Tabarrok, B ^a  

^a UNIVERSITY OF VICTORIA   (Canada)

^b MARC Analysis Research Corp   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DEFLECTION (STRUCTURES); DEFORMATION; FLEXIBLE STRUCTURES; LAGRANGE MULTIPLIERS; STRAIN; STRUCTURAL ANALYSIS;

DYNAMIC ANALYSIS; EULER BERNOULLI HYPOTHESIS; FLEXIBLE BEAMS; STATIC ANALYSIS;

BEAMS AND GIRDERS;

EID: 0030715127     PISSN: 03158977     EISSN: None     Source Type: Journal    
DOI: 10.1139/tcsme-1997-0010     Document Type: Article

References (43)

1. Frisch-Fay, R., 1962, Flexible Bars, ButterWorths, London.
2. Holden, J.T., 1972, "On the Finite Deflections of Thin Beams", Int. J. Solids Structures, 8, pp. 1051-1055.
3. Lau, J.H., 1982, "Large Deflections of Beams with Combined Loads", Proceedings of the American Society of Civil Engineering ASCE, 108, EM1, pp. 180-185.
4. Schmidt, R., and DaDeppo, D.A., 1971, "A Survey of Literature on Large Deflections of Nonshallow Arches. Bibliography of Finite Deflections of Straight and Curved Beams, Rings, and Shallow Arches.", J. of the Industrial Mathematics Society, 21, pp. 91-114.
5. Mattiasson, K., 1981, "Numerical Results from Large Deflection Beam and Frame Problems Analysed by Means of Elliptic Integrals", Int. J. Numer. Meth. Engng., 17, pp. 145-153.
6. Stoker, J.J., 1968, Nonlinear Elasticity, Gordon and Breach, New York.
7. Spillers, W.R., 1990, "Geometric Stiffness Matrix for Space Frames", Computers & Structures, 36, 1, pp. 29-37.
8. Crisfield, M.A., 1990, "A Consistent Co-rotational Formulation for Nonlinear, Three-Dimensional, Beam-Elements", Comput. Meth. Appl. Mech. Engng, 81, pp. 131-150.
9. Bathe, K.J., and Bolourchi, S., 1979, "Large Displacement Analysis of Three-Dimensional Beam Structures", Int. J. Numer. Meth. Engng, 14, pp. 961-986.
10. Rankin, C.C., and Brogan, F.A., 1986, "An Element Independent Co-rotational Procedure for the Treatment of Large Rotations", J. of Pressure Vessel Technology, 108, pp. 165-174.
11. Crisfield, M.A., Moita, G.F., 1996, "A Unified Co-rotational Framework for Solids, Shells and Beams", Int. J. Solids Structures, 33, 20, pp. 2969-2992.
12. Simo, J.C., 1985, "A Finite Strain Beam Formulation. The Three Dimensional Dynamic Problem. Part I", Comput. Meth. Appl. Mech. Engng, 49, pp. 55-70.
13. Simo, J.C., Vu-Quoc, L., 1986, "A Three-Dimensional Finite-Strain Rod Model. Part II: Computational Aspects", Comput. Meth. Appl. Mech. Engng, 58, pp. 79-116.
14. Yang, Y.B., Leu, L.J., 1994, "Nonlinear Stiffnesses in Analysis of Planar Frames", Comput. Meth. Appl. Mech. Engng, 117, pp. 233-247.
15. Surana, K.S., and Sorem, R.M., 1989, "Geometrically Non-linear Formulation for Three Dimensional Curved Beam Elements with Large Rotations", Int. J. Numer. Meth. Engng, 28, pp. 43-73.
16. Chen, Z.Q., and Agar, T.J.A., 1993, "Geometric Nonlinear Analysis of Flexible Spatial Beam Structures", Computers & Structures, 49, 6, pp. 1083-1094.
17. Argyris, J., and Mlejnek, H.P., 1991, Texts on Computational Mechanics, V, Dynamics of Structures, Elsevier Science, North-Holland.
18. Crisfield, M.A., and Shi, J., 1994, "A Co-rotational Element Time-Integration Strategy for Nonlinear Dynamics", Int. J. Numer. Meth. Engng, 37, pp. 1897-1913.
19. Hughes, T.J.R., Liu, W.K., and Caughy, 1978, "Transient Finite Element Formulations that Preserve Energy", ASME J. Appl. Mech., 45, pp. 366-370.
20. Simo, J.C., and Wong, K.K., 1991, "Unconditionally Stable Algorithms for Rigid Body Dynamics that Exactly Preserve Energy and Momentum", Int. J. Numer. Meth. Engng, 31, pp. 19-52.
21. Simo, J.C., Rifai, M.S., and Fox, D.D., 1992, "On a Stress Resultant Geometrically Exact Shell Model. Part VI: Conserving Algorithms for Nonlinear Dynamics", Int. J. Numer. Meth. Engng, 34, pp. 117-164.
22. Simo, J.C., and Tarnow, N., 1992, "The Discrete Energy-Momentum Method. Conserving Algorithms for Nonlinear Elastodynamics", Z Angew Math. Phys., 43, pp. 757-792.
23. Hilber, H.M., Hughes, T.J.R., and Taylor, R.L., 1977, "Improved Numerical Dissipation for Time Integration Algorithms in Structural Dynamics", Earthquake Engineering and Structural Dynamics, 5, pp. 283-292.
24. Zienkiewicz, O.C., Wood, W.L., and Taylor, R.L., 1980, "An Alternative Single-Step Algorithm for Dynamic Problems", Earthquake Engineering and Structural Dynamics, 8, pp. 31-40.
25. Bathe, K.J., Ramm, E., and Wilson, E.L., 1975, "Finite Element Formulations for Large Deformation Dynamic Analysis", Int. J. Numer. Meth. Engng, 9, pp. 353-386.
26. Geradin, M., and Cardona, A., 1989, "Kinematics and Dynamics of Rigid and Flexible Mechanisms Using Finite Element and Quarternion Algebra", Comput. Mech., pp. 115-136.
27. Kane, T.R., and Levinson, D.A., 1981, "Simulation of Large Motions of Nonuniform Beams in Orbit: Part II-The Unrestrained Beam", The J. of the Astronautical Science, 29, 3, pp. 245-276.
28. Levinson, D.A., and Kane, T.R., 1981, "Simulation of Large Motions of Nonuniform Beams in Orbit: Part I-The Cantilever Beam", The J. of the Astronautical Science, 29, 3, pp. 213-244.
29. Simo, J.C., Vu-Quoc, L., 1986, "On the Dynamics of Flexible Beams Under Large Overall Motions-The Plane Case: Part I", ASME J. Appl. Mech., 53, 4, pp. 849-854.
30. Simo, J.C., Vu-Quoc, L., 1988, "On the Dynamics in Space of Rods Undergoing Large Motions-A Geometrically Exact Approach", Comput. Meth. Appl. Mech. Engng, 66, pp. 125-161.
31. Belytschko, T., and Hseih, B.J., 1973, "Nonlinear Transient Finite Element Analysis with Convected Coordinates", Int. J. Numer. Meth. Engng, 7, pp. 255-271.
32. Belytschko, T., and Glaum, L.W., 1979, "Application of Higher Order Co-rotational Stretch Theories to Nonlinear Finite Element Analysis", Computers & Structures, 10, pp. 175-182.
33. Hsiao, K.M., and Jang, J., 1991, "Dynamic Analysis of Planar Flexible Mechanisms by Co-rotational Formulation", Comput. Meth. Appl. Mech. Engng, 24, pp. 359-381.
34. Elkaranshawy, H.A., Dokainish, M.A., 1995, "Co-rotational Finite Element Analysis of Planar Flexible Multibody Systems", Computers & Structures, 54, 5, pp. 881-890.
35. Iura, M., and Atluri, S.N., 1995, "Dynamic Analysis of Planar Flexible Beams with Finite Rotations by Using Inertial and Rotating Frames", Computers & Structures, 55, 3, pp. 453-462.
36. Behdinan, K., 1996, Dynamics of Geometrically Nonlinear Sliding Beams, Ph.D. Thesis, Dept. of Mech. Engng, University of Victoria, Canada
37. Behdinan, K., Stylianou, M.C., and Tabarrok, B., 1996, "Co-rotational Dynamic Analysis of Flexible Beams", Submitted to Comput. Meth. Appl. Mech. Engng.
38. Cook, R.D., 1981, Concepts and Applications of Finite Element Analysis, John Wiley & Sons, Inc., U.S.A.
39. Bathe, K.J., 1982, Finite Element Procedures in Engineering Analysis, Prentice-Hall, Inc., Toronto.
40. Leong, L.K., 1992, Dynamic Stability of Suddenly Loaded Structures, M.Sc. Thesis, Dept. of Aeronautics, Imperial College, London.
41. Bathe, K.J., 1986, Finite Element Procedures for Solid and Structures-Nonlinear Analysis, MIT Centre for Advanced Engineering Studies.
42. Stylianou, M.C., 1993, Dynamics of Flexible Extendible Beam, Ph.D. Thesis, Dept. of Mech. Engng, University of Victoria, Canada.
43. Rice, D.L., and Ting, E.C., 1993, "Large Displacement Transient Analysis of Flexible Structures", Int. J. Numer. Meth. Engng, 36, pp. 1541-1562.