Kinematics of Thin Walled Beams

Part of the Solid Mechanics and Its Applications book series (SMIA, volume 131)


Composite Beam Rotor Blade Transverse Shear Strain Thin Wall Beam Twist Rate 
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  1. Allen, D. H. and Haisler, W. E. (1985) Introduction to Aerospace Structural Systems, John Wiley & Sons, New York, Chichester, Briscone.Google Scholar
  2. Argyris, J. H. and Dunne, P. C. (1947) “The General Theory of Cylindrical and Conical Tubes Under Torsion and Bending Loads,” Journal of Royal Aeronautical Society,Vol. 51, 199–269, 757–784, 884–930; Vol. 53 (1949) 461–483, 558–620.Google Scholar
  3. Ascione, L. and Grimaldi, A. (1983) “On the Stability and Postbuckling Behavior of Elastic Beams,” Thin-Walled Structures, (1), pp. 325–351.CrossRefGoogle Scholar
  4. Attard, M. M. (1986) “Non-Linear Theory of Non-Uniform Torsion of Thin-Walled Open Beams,” Thin-Walled Structures, (4), pp. 101–134.Google Scholar
  5. Badir, A. M., Berdichevsky, V. L. and Armanios, E. A. (1993) “Theory of Composite Thin-Walled Opened Cross Section Beams,” 34th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, AIAA/ASME Adaptive Structures Forum, La Jolla, CA, 19–22, April, pp. 2761–2770.Google Scholar
  6. Bauchau, O.A. (1985) “Theory for Anisotropic Materials,” Journal of Applied Mechanics, Trans. ASME, Vol. 52, pp. 416–422.zbMATHGoogle Scholar
  7. Bauchau, O. A., Coffenberry, B. S. and Rehfield, L.W. (1987) “Composite Box Beam Analysis: Theory and Experiments,” Journal of Reinforced Plastics and Composites, Vol. 6, pp. 25–35.Google Scholar
  8. Bauchau, O. A. and Hong, C. H. (1987a) “Finite Element Approach to Rotor Blade Modeling,” Journal of the American Helicopter Society, Vol. 32, No. 1, pp. 60–67.Google Scholar
  9. Bauchau, O. A. and Hong, C. H. (1987b) “Large Displacement Analysis of Naturally Curved and Twisted Composite Beams,” AIAA Journal, Vol. 25, No. 10, pp. 1469–1475.Google Scholar
  10. Bauchau, O.A. and Hong, C.H. (1988) “Nonlinear Composite Beam Theory,” Journal of Applied Mechanics, Trans. ASME, Vol. 55, No. 1, pp. 156–163.Google Scholar
  11. Benscoter, S. U. (1954) “A Theory of Torsion Bending for Multicell Beams,” Journal of Applied Mechanics, Vol. 20, pp. 25–34.Google Scholar
  12. Berdichevsky, V., Armanios, E., and Badir, A., (1992) “Theory of Anisotropic Thin-Walled Closed-Cross-Section Beams,” Composites Engineering, Vol. 2, Nos. 5–7, pp. 411–432.Google Scholar
  13. Bhaskar, K. and Librescu, L. (1995a) “A Geometrically Non-Linear Theory for Laminated Anisotropic Thin-Walled Beams,” International Journal of Engineering Science, Vol. 33, No. 9, pp. 1331–1344.CrossRefGoogle Scholar
  14. Bhaskar, K. and Librescu, L. (1995b) “Buckling under Axial Compression of Thin-Walled Composite Beams Exhibiting Extension Twist Coupling,” Composite Structures, Vol. 31, No. 3, pp. 203–242.CrossRefGoogle Scholar
  15. Borri, M. and Merlini, T. (1986) “A Large Displacement Formulation for Anisotropic Beam Analysis,” Meccanica, Vol. 21, pp. 30–37.CrossRefGoogle Scholar
  16. Capurso, M. (1964) “Sur calcolo delle travi di parete sotlite in presenta de forze e distorsions,” La Ricerca Scientifico, (34), Series (2), Section A, Vol. 6, pp. 213–286, Vol. 7, pp. 5–106.Google Scholar
  17. Chandra, R., Stemple, A. D. and Chopra, I. (1990) “Thin-Walled Composite Beams under Bending, Torsional and Extensional Loads,” Journal of Aircraft, Vol. 27, No. 7, pp. 619–626.Google Scholar
  18. Chandra, R. and Chopra, I. (1991) “Experimental and Theoretical Analysis of Composite I-Beams with Elastic Couplings,” AIAA Journal, Vol. 29, No. 12, pp. 2197–2206.Google Scholar
  19. Chandra, R. and Chopra, I. (1992a) “Experimental-Theoretical Investigation of the Vibration Characteristics of Rotating Composite Box Beams,” Journal of Aircraft, Vol. 29, No. 4, pp. 657–664.Google Scholar
  20. Chandra, R. and Chopra, I. (1992b) “Structural Response of Composite Beams and Blades with Elastic Couplings,” Composites Engineering, Vol. 2, Nos. 5–7, pp. 347–374.Google Scholar
  21. Chandiramani, N. K., Librescu, L. and Shete, C. D. (2001) “Free-Vibration of Rotating Composite Beams Incorporating Higher-Order Transverse Shear Effects,” International Mechanical Engineering Congress & Exposition, November 11–16, New York City, NY (on CD-ROM).Google Scholar
  22. Chandiramani, N. K., Librescu, L. and Shete, C. D. (2002) “On the Free-Vibration of Rotating Composite Beams Using a Higher-Order Shear Formulation,” Aerospace Science and Technology, Vol. 6, pp. 545–561.CrossRefGoogle Scholar
  23. De Lorenzis, L. and la Tegola, A. (2005) “Effect of the Actual Distribution of Applied Stresses on Global Buckling of Isotropic and Transversely Isotropic Thin-Walled Members: Theoretical Analysis,” Composite Structures, Vol. 68, pp. 339–348.Google Scholar
  24. Donaldson, B. K. (1993) Analysis of Aircraft Structures. An Introduction, McGraw-Hill Inc., New York, St. Louis.Google Scholar
  25. Dökmeci, M. C. (1972) “A General Theory of Elastic Beams,” International Journal of Solids and Structures, Vol. 8, pp. 1205–1222.zbMATHGoogle Scholar
  26. Fine, M. and Williams, D. (1945) “Effects of End Constraint on Thin-Walled Cylinders Subject to Torque,” Aeronautical Research Council, Rep. No. 2223.Google Scholar
  27. Fraternali, F. and Feo, L. (2000) “On a Moderate Rotation Theory of Thin-Walled Composite Beams,” Composites: Part B, Vol. 31, pp. 141–158.CrossRefGoogle Scholar
  28. Ghobarach, A. A. and Tso, W. K. (1971) “A Non-Linear Thin-Walled Beam Theory,” International Journal of Mechanical Sciences, Vol. 13,(12), pp. 1025–1038.Google Scholar
  29. Gjelsvik, A. (1981) The Theory of Thin Walled Beams, Wiley, New York, NY.Google Scholar
  30. Gol’denveiser, A. L. (1949) “The General Theory of Thin-Walled Beams” (in Russian), Prikladnaia Mathematika i Mechanika, Vol. 13, No. 6, pp. 561–596.Google Scholar
  31. Grimaldi, A. and Pignataro, M. (1979) “Postbuckling Behavior of Thin-Walled Open Cross-Section Compression Members,” Journal of Structural Mechanics, Vol. 7, No. 2, pp. 143–159.Google Scholar
  32. Hirashima, M. and Yoda, T. (1982) “Finite Displacement Theory of Curved and Twisted Thin-Walled Beams,” Memoirs of the School of Science & Engineering, Waseda University, No. 46, pp. 277–294.Google Scholar
  33. Hodges, D. H., Atilgan, A. R., Cesnik, C. E. S. and Fulton, M. V. (1992) “On a Simplified Strain Energy Function for Geometrically Nonlinear Behavior of Anisotropic Beams,” Composites Engineering, Vol. 2, Nos. 5–7, pp. 513–526.Google Scholar
  34. Hodges, D. H. and Dowell, E.H. (1974) “Nonlinear Equations of Motion for the Elastic Bending and Torsion of Twisted Nonuniform Rotor Blades,” NASA TN D-7818.Google Scholar
  35. Hong, C. H. and Chopra, I. (1986) “Aeroelastic Stability Analysis of a Composite Bearingless Rotor Blade,” Journal of American Helicopter Society, Vol. 31, pp. 29–35.Google Scholar
  36. Hughes, O. F. (1983) Ship Structural Design, John Wiley & Sons, New York.Google Scholar
  37. Jensen, J. J. (2001) Load and Global Response of Ships, Pergamon Press, Oxford.Google Scholar
  38. Jung, S. N., Nagaraj, V. T. and Chopra, I. (1999) “Assessment of Composite Rotor Blade: Modeling Techniques,” Journal of the American Helicopter Society, Vol. 44, No. 2, pp. 188–205.Google Scholar
  39. Kim, C. and White, S. R. (1996) “Analysis of Thick Hollow Composite Beams Under General Loadings,” Composite Structures, Vol. 34, pp. 263–277.CrossRefGoogle Scholar
  40. Kim, C., and White, S. R. (1997) “Thick-Walled Composite Beam Theory Including 3-D Elastic Effects and Torsional Warping,” International Journal of Solids and Structures, Vol. 34, Nos. 31–32, pp. 4237–4259.Google Scholar
  41. Kvaternik, R. G., White, S. F., Jr. and Kaza, K.R.V. (1978) “Nonlinear Flap-Lag-Axial Equations of a Rotational Beam with Arbitrary Precone Angle,” AIAA Journal, AIAA Paper No. 78-491.Google Scholar
  42. Iura, M. and Hirashima, M. (1985) “Geometrically Nonlinear Theory of Naturally Curved and Twisted Rods with Finite Rotations,” Proceedings of the JSCE, Structural Engineering/Earthquake Engineering, Vol. 2, No. 2, pp. 107–117.Google Scholar
  43. Lee, S. W. and Kim, Y. H. (1987) “Finite-Element Model for Composite Beams with Arbitrary Cross-Sectional Warping,” International Journal of Numerical Method Engineering, Vol. 24, No. 12, pp. 2327–2341.Google Scholar
  44. Librescu, L. (1975) Elasto-statics and Kinetics of Anisotropic and Heterogeneous Shell-Type Structures, Noordhoff International Publishers, Leyden, The Netherlands.Google Scholar
  45. Librescu, L., and Song, O. (1991) “Behavior of Thin-Walled Beams Made of Advanced Composite Materials and Incorporating Non-Classical Effects,” Applied Mechanics Reviews, Vol. 44, No. 11, Part 2, S174–S180.Google Scholar
  46. Librescu, L. and Song, O. (1992) “On the Static Aeroelastic Tailoring of Composite Aircraft Swept Wings Modelled as Thin-Walled Beam Structures,” Composites Engineering, Vol. 2, Nos. 5–7 (Special Issue: Use of Composites in Rotorcraft and Smart Structures) pp. 497–512.Google Scholar
  47. Librescu, L., Meirovitch, L. and Song, O. (1996) “Refined Structural Modeling for Enhancing Vibrations and Aeroelastic Characteristics of Composite Aircraft Wings,” La Recherche Aérospatiale, Vol. 1, pp. 23–35.Google Scholar
  48. Librescu, L. Meirovitch, L. and Na, S. S. (1997) “Control of Cantilever Vibration via Structural Tailoring and Adaptive Materials,” AIAA Journal, Vol. 35, No. 8, pp. 1309–1315.Google Scholar
  49. Librescu, L., Qin, Z. and Ambur, D. R. (2003) “Implications of Warping Restraint on Statics and Dynamics of Elastically Tailored Thin-Walled Composite Beams,” International Journal of Mechanical Sciences, Vol. 45, No. 8, pp. 1247–1267.CrossRefGoogle Scholar
  50. Loughlan, J. and Ata, M. (1995) “The Restrained Torsional Response of Open Section Carbon Fibre Composite Beams,” Composite Structures, Vol. 32, pp. 13–31.CrossRefGoogle Scholar
  51. Loughlan, J. and Ata, M. (1997) “The Behavior of Open and Closed Section Carbon Fibre Composite Beams Subjected to Constrained Torsion,” Composite Structures, Vol. 38, Nos. 1–4, pp. 631–647.Google Scholar
  52. Mansfield, E. H. and Sobey, A. J. (1979) “The Fibre Composite Helicopter Blade”, Part I: Stiffness Properties; Part 2: Prospects for Aeroelastic Tailoring, Aeronautical Quarterly, Vol. XXX, pp. 413–499.Google Scholar
  53. Megson, T. H. G. (1974) Linear Analysis of Thin-Walled Elastic Structures, John Wiley & Sons, New York.Google Scholar
  54. Megson, T. H. G. (1990) Aircraft Structures for Engineering Students, Second Edition, Halstedt Press.Google Scholar
  55. Meredith, D. and Witmer, E. A. (1981), “A Nonlinear Theory of General Thin-Walled Beams,” Computers & Structures, Vol. 13, pp. 3–9.CrossRefGoogle Scholar
  56. Minguet, P. and Dugundji, J. (1990a,b) “Experiments and Analysis for Composite Blades Under Large Deflections,” AIAA Journal, Part I, Vol. 28, pp. 1573–1579; Part II: Vol. 28, pp. 1580–588.MathSciNetGoogle Scholar
  57. Mollmann, H. (1982a, b) “Finite Displacements of Thin-Walled Beams,” Parts 1 and 2, Danish Center for Application Mathematics and Mechanics, Technical University of Denmark, Reports Nos. 252 and 253.Google Scholar
  58. Nayfeh, A. H. and Pai, P. F. (2004) Linear and Nonlinear Structural Mechanics, Wiley-Interscience.Google Scholar
  59. Nishino, F., Hasegawa, A. and Natori, E. (1977), “Thin-Walled Rectangular Beams with Shear Deformation and Cross Sectional Distortion,” Mechanics of Engineering, ASCE-EMD, University of Waterloo.Google Scholar
  60. Nishino, F., and Hasegawa, A. (1979) “Thin-Walled Elastic Members,” Journal of the Faculty of Engineering, The University of Tokyo CB, Vol. XXXV, No. 2, pp. 109–190.MathSciNetGoogle Scholar
  61. Oden, J. T. and Ripperger, E. A. (1981) Mechanics of Elastic Structures, Second Edition, Hemisphere Publication Corp., Washington.Google Scholar
  62. Pai, P. F. and Nayfeh, A.H. (1992) “A Nonlinear Composite Beam Thoery,” Nonlinear Dynamics, Vol. 3, pp. 273–303.CrossRefGoogle Scholar
  63. Pai, P. F. and Nayfeh, A. H. (1994) “A Fully Nonlinear Theory of Curved and Twisted Composite Rotor Blades Accounting for Warpings and Three-Dimensional Stress Effects,” International Journal of Solids and Structures, Vol. 3, pp. 1309–1340.Google Scholar
  64. Pedersen, P. T. (1991) “Beam Theories for Torsional-Bending Response of Ship Hulls,” Journal of Ship Research, Vol. 35, No. 3, pp. 254–265.Google Scholar
  65. Petre, A. (1984) The Analysis of Aeronautical Structures (in Romanian), Editura Technica, Bucharest.Google Scholar
  66. Polillo, V.R., Garcia, L. F.T. and Villaca, S. F. (1998) “Discussion about Geometrically Nonlinear Formulations for Combined Flexure and Torsion of Thin-Walled Open Bars,” Journal of the Brazilian Society of Mechanical Sciences, Vol. XX, No 1, pp. 103–115.Google Scholar
  67. Rehfield, L. W., Atilgan, A. R. and Hodges (1988) “Structural Modeling for Multicell Composite Rotor Blades,” Proceedings 28th AIAA/ASME/ASCE/AHS/ACS, Structures, Structural Dynamics and Materials Conference, AIAA Paper No. 88-2250.Google Scholar
  68. Rehfield, L.W., Atilgan, A. R. and Hodges, D. H. (1990) “Nonclassical Behavior of Thin-Walled Composite Beams with Closed Cross Sections,” Journal of the American Helicopter Society, Vol. 35, No. 2, pp. 42–51.Google Scholar
  69. Rehfield, L. W. (1985) “Design Analysis Methodology for Composite Rotor Blades,” 7th DoD/NASA Conference on Fibre Composites in Structural Design, Denver, CO, AFWALTR-85-3094, (Va-1)–(Va-15).Google Scholar
  70. Rivello, R. M. (1969) Theory and Analysis of Flight Structures, McGraw-Hill Book Company, New York, St. Louis.Google Scholar
  71. Roberts, T. M. and Azizian, Z. G. (1983) “Non Linear Analysis of Thin-Walled Bars of Open Cross Section,” International Journal of Mechanical Sciences, Vol. 25, No. 8, pp. 565–577.CrossRefGoogle Scholar
  72. Rosen, A. and Friedmann, P. P., (1979) “The Non-Linear Behavior of Elastic Slender Straight Beams Undergoing Small Strains and Moderate Rotations,” Journal of Applied Mechanics, Trans. ASME, Vol. 46, March, pp. 161–168.Google Scholar
  73. Smith, E. C. and Chopra, I. (1991) “Formulation and Evaluation of an Analytical Model for Composite Box-Beams,” Journal of the American Helicopter Society, Vol. 36, No. 3, pp. 23–35.Google Scholar
  74. Song, O. (1990) “Modeling and Response Analysis of Thin-Walled Beam Structures Constructed of Advanced Composite Materials,” Ph.D. Dissertation, Virginia Polytechnic Institute and State University.Google Scholar
  75. Song, O. and Librescu, L. (1993) “Free Vibration of Anisotropic Composite Thin-Walled Beams of Closed Cross-Section Contour,” Journal of Sound and Vibration, Vol. 167, No. 1, pp. 129–147.CrossRefGoogle Scholar
  76. Stemple, A.D. and Lee, S.W. (1988) “Finite-Element Model for Composite Beams with Arbitrary Cross-Sectional Warping,” AIAA Journal, Vol. 26, No. 12, pp. 1512–1520.Google Scholar
  77. Suhubi, E. S. (1968) “On the Foundations of the Theory of Rods,” International Journal of Engineering Science, Vol. 6, pp. 169–191.CrossRefzbMATHGoogle Scholar
  78. Suresh, J.K. and Nagaraj, V.T. (1996) “Higher-Order Shear Deformation Theory for Thin-Walled Composite Beams,” Journal of Aircraft, Vol. 33, No. 5, pp. 978–986.Google Scholar
  79. Tsay, H. S. and Kingsbury, H. B. (1988) “Vibrations of Rods with General Space Curvature,” Journal of Sound and Vibrations, Vol. 124, No. 2, pp. 539–554.Google Scholar
  80. Van Erp, G. M. (1987) “The Non-linear Flexural Torsional Behavior of Straight Slender Elastic Beams with Arbitrary Cross-Sections,” Eindhoven University of Technology, EVT Rept. WRW 87-050, Eindhoven, Netherlands.Google Scholar
  81. Vasiliev, G. V. (1986) Fundaments of the Analysis of Thin-Walled Aeronautical Structures (in Romanian), Vol. 1, Editura Academiei R. S. Romania.Google Scholar
  82. Vlasov, V. Z. (1961) Thin Walled Elastic Beams, National Science Foundation, Washington, DC, Israel Program for Scientific Translation, Jerusalem, Israel [First edition — Stroizdat (in Russian) Moscow, 1940].Google Scholar
  83. von Kármán, T. and Christensen, N. B. (1944) “Methods of Analysis for Torsion with Variable Twist,” Journal of Aeronautical Science, Vol. 11, pp. 110–124.Google Scholar
  84. Wallerstein, D. V. (2002) A Variational Approach to Structural Analysis, John Wiley & Sons, Inc.Google Scholar
  85. Wempner, G. (1981) Mechanics of Solids with Applications to Thin Bodies, Sijthoff & Noordhoff Alphen aan den Rijn, The Netherlands, Rockville, Maryland, USA.Google Scholar

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