DOI QR코드

DOI QR Code

Effect of Three-dimensional Warping on Stiffness Constants of Closed Section Composite Beams

  • Received : 2017.05.17
  • Accepted : 2017.07.31
  • Published : 2017.09.30

Abstract

This paper focuses on the investigation of three-dimensional (3D) warping effect on the stiffness constants of composite beams with closed section profiles. A finite element (FE) cross-sectional analysis is developed based on the Reissner's multifield variational principle. The 3D in-plane and out-of-plane warping displacements, and sectional stresses are approximated as linear functions of generalized sectional stress resultants at the global level and as FE shape functions at the local sectional level. The classical elastic couplings are taken into account which include transverse shear and Poisson deformation effects. A generalized Timoshenko level $6{\times}6$ stiffness matrix is computed for closed section composite beams with and without warping. The effect of neglecting the 3D warping on stiffness constants is shown to be significant indicating large errors as high as 93.3%.

Keywords

References

  1. Hodges, D. H., Nonlinear Composite Beam Theory, AIAA, Washington, DC, 2006. DOI:10.2514/4.866821
  2. Jung, S. N., Nagaraj, V. T. and Chopra, I., "Refined Structural Model for Thin- and Thick-Walled Composite Rotor Blades", AIAA Journal, Vol. 40, No. 1, 2002, pp. 105-106. DOI:10.2514/2.1619
  3. Chandra, R. and Chopra, I., "Structural Response of Composite Beams and Blades with Elastic Couplings", Composites Engineering, Vol. 2, Nos. 5-7, 1992, pp. 347-374. DOI: 10.1016/0961-9526(92)90032-2
  4. Berdichevsky, V., Armanios, E. and Badir, A., "Theory of Anisotropic Thin-Walled Closed-Cross-Section Beams", Composites Engineering, Vol. 2, Nos. 5-7, 1992, pp. 411-432. DOI:10.1016/0961-9526(92)90035-5
  5. Giavotto, V., Borri, M., Mantegazza, P., Ghiringhelli, G., Carmaschi, V., Maffioli, G. C. and Mussi, F., "Anisotropic Beam Theory and Applications", Computers and Structures, Vol. 16, Nos. 1-4, 1983, pp. 403-413. DOI:10.1016/0045- 7949(83)90179-7
  6. Cesnik, C. E. S. and Hodges, D. H., "VABS: a New Concept for Composite Rotor Blade Cross-Sectional Modeling", Journal of the American Helicopter Society, Vol. 42, No. 1, 1997, pp. 27-38. DOI:10.4050/JAHS.42.27
  7. Berdichevsky, V. L., "Variational-Asymptotic Method of Constructing a Theory of Shells", Journal of Applied Mathematics and Mechanics, Vol. 43, No. 4, 1979, pp. 711- 736. DOI:10.1016/0021-8928(79)90157-6
  8. Kim, H. S. and Kim, J. S., "A Rankine-Timoshenko-Vlasov Beam Theory for Anisotropic Beams via an Asymptotic Strain Energy Transformation", European Journal of Mechanics A/Solids, Vol. 40, 2013, pp. 131-138. DOI:10.1016/j.euromechsol.2013.01.004
  9. Dhadwal, M. K. and Jung, S. N., "Refined Sectional Analysis with Shear Center Prediction for Nonhomogeneous Anisotropic Beams with Nonuniform Warping", Meccanica, Vol. 51, No. 8, 2016, pp. 1839-1867. DOI:10.1007/s11012-015- 0338-2
  10. Reissner, E., "On Mixed Variational Formulations in Finite Elasticity", Acta Mechanica, Vol. 56, Nos. 3-4, 1985, pp. 117-125. DOI:10.1007/BF01177113
  11. Chen, H., Yu, W. and Capellaro, M., "A Critical Assessment of Computer Tools for Calculating Composite Wind Turbine Blade Properties", Wind Energy, Vol. 13, No. 6, 2010, pp. 497-516. DOI:10.1002/we.372