Skip to main content
SpringerLink
Log in

Kinematics of Thin Walled Beams

  • Chapter
Book cover Thin-Walled Composite Beams

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

  • 1794 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Allen, D. H. and Haisler, W. E. (1985) Introduction to Aerospace Structural Systems, John Wiley & Sons, New York, Chichester, Briscone.

    Google Scholar 

  • 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 

  • Ascione, L. and Grimaldi, A. (1983) “On the Stability and Postbuckling Behavior of Elastic Beams,” Thin-Walled Structures, (1), pp. 325–351.

    Article  Google Scholar 

  • 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 

  • 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 

  • Bauchau, O.A. (1985) “Theory for Anisotropic Materials,” Journal of Applied Mechanics, Trans. ASME, Vol. 52, pp. 416–422.

    MATH  Google Scholar 

  • 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 

  • 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 

  • 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 

  • 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 

  • Benscoter, S. U. (1954) “A Theory of Torsion Bending for Multicell Beams,” Journal of Applied Mechanics, Vol. 20, pp. 25–34.

    Google Scholar 

  • 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 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Borri, M. and Merlini, T. (1986) “A Large Displacement Formulation for Anisotropic Beam Analysis,” Meccanica, Vol. 21, pp. 30–37.

    Article  Google Scholar 

  • 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 

  • 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 

  • 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 

  • 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 

  • 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 

  • 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 

  • 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.

    Article  Google Scholar 

  • 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 

  • Donaldson, B. K. (1993) Analysis of Aircraft Structures. An Introduction, McGraw-Hill Inc., New York, St. Louis.

    Google Scholar 

  • Dökmeci, M. C. (1972) “A General Theory of Elastic Beams,” International Journal of Solids and Structures, Vol. 8, pp. 1205–1222.

    MATH  Google Scholar 

  • 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 

  • Fraternali, F. and Feo, L. (2000) “On a Moderate Rotation Theory of Thin-Walled Composite Beams,” Composites: Part B, Vol. 31, pp. 141–158.

    Article  Google Scholar 

  • 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 

  • Gjelsvik, A. (1981) The Theory of Thin Walled Beams, Wiley, New York, NY.

    Google Scholar 

  • 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 

  • 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 

  • 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 

  • 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 

  • 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 

  • 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 

  • Hughes, O. F. (1983) Ship Structural Design, John Wiley & Sons, New York.

    Google Scholar 

  • Jensen, J. J. (2001) Load and Global Response of Ships, Pergamon Press, Oxford.

    Google Scholar 

  • 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 

  • Kim, C. and White, S. R. (1996) “Analysis of Thick Hollow Composite Beams Under General Loadings,” Composite Structures, Vol. 34, pp. 263–277.

    Article  Google Scholar 

  • 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 

  • 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 

  • 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 

  • 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 

  • Librescu, L. (1975) Elasto-statics and Kinetics of Anisotropic and Heterogeneous Shell-Type Structures, Noordhoff International Publishers, Leyden, The Netherlands.

    Google Scholar 

  • 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 

  • 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 

  • 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 

  • 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 

  • 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.

    Article  Google Scholar 

  • Loughlan, J. and Ata, M. (1995) “The Restrained Torsional Response of Open Section Carbon Fibre Composite Beams,” Composite Structures, Vol. 32, pp. 13–31.

    Article  Google Scholar 

  • 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 

  • 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 

  • Megson, T. H. G. (1974) Linear Analysis of Thin-Walled Elastic Structures, John Wiley & Sons, New York.

    Google Scholar 

  • Megson, T. H. G. (1990) Aircraft Structures for Engineering Students, Second Edition, Halstedt Press.

    Google Scholar 

  • Meredith, D. and Witmer, E. A. (1981), “A Nonlinear Theory of General Thin-Walled Beams,” Computers & Structures, Vol. 13, pp. 3–9.

    Article  Google Scholar 

  • 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.

    MathSciNet  Google Scholar 

  • 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 

  • Nayfeh, A. H. and Pai, P. F. (2004) Linear and Nonlinear Structural Mechanics, Wiley-Interscience.

    Google Scholar 

  • 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 

  • 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.

    MathSciNet  Google Scholar 

  • Oden, J. T. and Ripperger, E. A. (1981) Mechanics of Elastic Structures, Second Edition, Hemisphere Publication Corp., Washington.

    Google Scholar 

  • Pai, P. F. and Nayfeh, A.H. (1992) “A Nonlinear Composite Beam Thoery,” Nonlinear Dynamics, Vol. 3, pp. 273–303.

    Article  Google Scholar 

  • 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 

  • 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 

  • Petre, A. (1984) The Analysis of Aeronautical Structures (in Romanian), Editura Technica, Bucharest.

    Google Scholar 

  • 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 

  • 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 

  • 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 

  • 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 

  • Rivello, R. M. (1969) Theory and Analysis of Flight Structures, McGraw-Hill Book Company, New York, St. Louis.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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 

  • 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 

  • 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 

  • 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.

    Article  Google Scholar 

  • 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 

  • Suhubi, E. S. (1968) “On the Foundations of the Theory of Rods,” International Journal of Engineering Science, Vol. 6, pp. 169–191.

    Article  MATH  Google Scholar 

  • 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 

  • 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 

  • 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 

  • Vasiliev, G. V. (1986) Fundaments of the Analysis of Thin-Walled Aeronautical Structures (in Romanian), Vol. 1, Editura Academiei R. S. Romania.

    Google Scholar 

  • 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 

  • 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 

  • Wallerstein, D. V. (2002) A Variational Approach to Structural Analysis, John Wiley & Sons, Inc.

    Google Scholar 

  • Wempner, G. (1981) Mechanics of Solids with Applications to Thin Bodies, Sijthoff & Noordhoff Alphen aan den Rijn, The Netherlands, Rockville, Maryland, USA.

    Google Scholar 

Download references

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer

About this chapter

Cite this chapter

(2006). Kinematics of Thin Walled Beams. In: Thin-Walled Composite Beams. Solid Mechanics and Its Applications, vol 131. Springer, Dordrecht. https://doi.org/10.1007/1-4020-4203-5_2

Download citation

  • DOI: https://doi.org/10.1007/1-4020-4203-5_2

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-3457-2

  • Online ISBN: 978-1-4020-4203-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation