Abstract
A theory for laminated and sandwich beams is developed based on far-field stress and strain solutions called Fundamental State Solutions. Through-thickness stress and strain moments of the Fundamental Solutions are used to obtain homogenized axial, flexural and shear stiffness as well as a shear-strain moment correction. A sequence of beam models with similarity to the Timoshenko model are obtained. Excellent agreement is shown for all stress and strain components when compared to accurate two-dimensional finite element results.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Noor, A.K. and Burton, W.S., “Assessment of Shear Deformation Theories for Multilayer Composite Plates”, Applied Mechanics Reviews, Vol. 42,No. 1, 1989, pp. 1–13.
Kapania, R.K., “A Review on the Analysis of Laminated Shells”, ASME Journal of Pressure Vessel Technology, Vol. 111, May 1989, pp. 88–96.
Noor, A.K. and Burton, W.S., “Assessment of Computational Models for Multilayer Composite Shells”, Applied Mechanics Reviews, Vol. 43,No. 4, 1990, pp. 67–97.
Reddy, J.N., “A Review of Refined Theories of Laminated Composite Plates”, The Shock and Vibration Digest, Vol. 22,No. 7, 1990, pp. 3–17.
Timoshenko, S.P., “On the Correction for Shear of the Differential Equation for Transverse Vibrations of Prismatic Bars”, Philosophical Magazine, Vol. 21, 1921, pp. 744–746.
Timoshenko, S.P., “On the Transverse Vibrations of Bars of Uniform Cross-Section”, Philosophical Magazine, Vol. 43, 1922, pp. 125–131.
Reissner, E., “The Effect of Transverse Shear Deformation on the Bending of Elastic Plates”, Journal of Applied Mechanics, Vol. 12,No. 2, 1945, pp. 69–77.
Mindlin, R.D., “Influence of Rotary Inertia and Shear on The Effect of Transverse Shear Deformation on Flexural Motions of Isotropic, Elastic Plates”, Journal of Applied Mechanics, Vol. 18,No. 1, 1951, pp. 31–38.
Hansen, J.S. and Almeida, S.F.M., “A Theory for Laminated Composite Beams”, Final Report submitted April 2001, FAPES Grant No. 00/06183-0, Såo Paulo, Brasil, 157 pages.
Kennedy, G., “A Hierarchical Beam theory for Beams with Asymmetric Cross-Sections”, B.A.Sc. Thesis, Division of Engineering Science, Faculty of Engineering, University of Toronto, Dec. 2004.
Cowper, G.R., “The Shear Coefficient in Timoshenko’s Beam Theory”, Journal of Applied Mechanics, Vol. 33, June 1966, pp. 335–340.
Guiamatsia, I. and Hansen, J.S., “A Homogenization Based Laminated Plate Theory”, 2004 ASME International Mechanical Engineering Congress and RD & D EXPO, Anaheim, California, Nov. 13–19, 2004.
Hansen, J.S. and Almeida, S.F.M., “A Homogenization Based Laminated Beam Theory”, 21st International Congress of Theoretical and Applied Mechanics (ICTAM 2004), Warsaw, Poland, 16–20 August 2004.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer
About this paper
Cite this paper
Hansen, J.S., Kennedy, G., de Almeida, S.F. (2005). A Homogenization Based Theory for Laminated and Sandwich Beams. In: Thomsen, O., Bozhevolnaya, E., Lyckegaard, A. (eds) Sandwich Structures 7: Advancing with Sandwich Structures and Materials. Springer, Dordrecht. https://doi.org/10.1007/1-4020-3848-8_22
Download citation
DOI: https://doi.org/10.1007/1-4020-3848-8_22
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-3444-2
Online ISBN: 978-1-4020-3848-8
eBook Packages: EngineeringEngineering (R0)