Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 974023, 23 pages
http://dx.doi.org/10.1155/2012/974023
Research Article

Static and Vibrational Analysis of Partially Composite Beams Using the Weak-Form Quadrature Element Method

Department of Civil Engineering, Tsinghua University, Beijing 100084, China

Received 29 August 2011; Revised 7 November 2011; Accepted 21 November 2011

Academic Editor: Trung Nguyen Thoi

Copyright © 2012 Zhiqiang Shen and Hongzhi Zhong. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. N. M. Newmark, C. D. Siess, and I. M. Viest, “Tests and analysis of composite beams with incomplete interaction,” Proceedings of the Society for Experimental Stress Analysis, vol. 9, pp. 75–92, 1951. View at Google Scholar
  2. U. A. Girhammar and D. H. Pan, “Exact static analysis of partially composite beams and beam-columns,” International Journal of Mechanical Sciences, vol. 49, no. 2, pp. 239–255, 2007. View at Publisher · View at Google Scholar · View at Scopus
  3. U. A. Girhammar, D. H. Pan, and A. Gustafsson, “Exact dynamic analysis of composite beams with partial interaction,” International Journal of Mechanical Sciences, vol. 51, no. 8, pp. 565–582, 2009. View at Publisher · View at Google Scholar · View at Scopus
  4. R. Xu and Y. Wu, “Static, dynamic, and buckling analysis of partial interaction composite members using Timoshenko's beam theory,” International Journal of Mechanical Sciences, vol. 49, no. 10, pp. 1139–1155, 2007. View at Publisher · View at Google Scholar · View at Scopus
  5. A. Kroflič, I. Planinc, M. Saje, G. Turk, and B. Čas, “Non-linear analysis of two-layer timber beams considering interlayer slip and uplift,” Engineering Structures, vol. 32, no. 6, pp. 1617–1630, 2010. View at Publisher · View at Google Scholar · View at Scopus
  6. J. M. Battini, Q. H. Nguyen, and M. Hjiaj, “Non-linear finite element analysis of composite beams with interlayer slips,” Computers and Structures, vol. 87, no. 13-14, pp. 904–912, 2009. View at Publisher · View at Google Scholar · View at Scopus
  7. J. B. M. Sousa, C. E. M. Oliveira, and A. R. da Silva, “Displacement-based nonlinear finite element analysis of composite beam-columns with partial interaction,” Journal of Constructional Steel Research, vol. 66, no. 6, pp. 772–779, 2010. View at Publisher · View at Google Scholar · View at Scopus
  8. G. Ranzi, “Locking problems in the partial interaction analysis of multi-layered composite beams,” Engineering Structures, vol. 30, no. 10, pp. 2900–2911, 2008. View at Publisher · View at Google Scholar · View at Scopus
  9. G. Ranzi, F. Gara, G. Leoni, and M. A. Bradford, “Analysis of composite beams with partial shear interaction using available modelling techniques: a comparative study,” Computers and Structures, vol. 84, no. 13-14, pp. 930–941, 2006. View at Publisher · View at Google Scholar · View at Scopus
  10. A. Dall'Asta and A. Zona, “Slip locking in finite elements for composite beams with deformable shear connection,” Finite Elements in Analysis and Design, vol. 40, no. 13-14, pp. 1907–1930, 2004. View at Publisher · View at Google Scholar · View at Scopus
  11. H. Zhong and T. Yu, “Flexural vibration analysis of an eccentric annular Mindlin plate,” Archive of Applied Mechanics, vol. 77, no. 4, pp. 185–195, 2007. View at Publisher · View at Google Scholar · View at Scopus
  12. H. Zhong and T. Yu, “A weak form quadrature element method for plane elasticity problems,” Applied Mathematical Modelling, vol. 33, no. 10, pp. 3801–3814, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. H. Zhong and Y. Wang, “Weak form quadrature element analysis of Bickford beams,” European Journal of Mechanics/Solids, vol. 29, no. 5, pp. 851–858, 2010. View at Publisher · View at Google Scholar · View at Scopus
  14. H. Zhong and M. Gao, “Quadrature element analysis of planar frameworks,” Archive of Applied Mechanics, vol. 80, no. 12, pp. 1391–1405, 2010. View at Publisher · View at Google Scholar · View at Scopus
  15. T. Rabczuk, G. Zi, S. Bordas, and H. Nguyen-Xuan, “A geometrically non-linear three-dimensional cohesive crack method for reinforced concrete structures,” Engineering Fracture Mechanics, vol. 75, no. 16, pp. 4740–4758, 2008. View at Publisher · View at Google Scholar · View at Scopus
  16. T. Rabczuk and T. Belytschko, “Application of particle methods to static fracture of reinforced concrete structures,” International Journal of Fracture, vol. 137, no. 1–4, pp. 19–49, 2006. View at Publisher · View at Google Scholar · View at Scopus
  17. T. Rabczuk, J. Akkermann, and J. Eibl, “A numerical model for reinforced concrete structures,” International Journal of Solids and Structures, vol. 42, no. 5-6, pp. 1327–1354, 2005. View at Publisher · View at Google Scholar · View at Scopus
  18. T. Rabczuk and T. Belytschko, “A three-dimensional large deformation meshfree method for arbitrary evolving cracks,” Computer Methods in Applied Mechanics and Engineering, vol. 196, no. 29-30, pp. 2777–2799, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  19. P. J. Davis and P. Rabinowitz, Methods of Numerical Integration, Computer Science and Applied Mathematics, Academic Press, Orlando, Fla, USA, 2nd edition, 1984.
  20. R. Bellman and J. Casti, “Differential quadrature and long-term integration,” Journal of Mathematical Analysis and Applications, vol. 34, pp. 235–238, 1971. View at Publisher · View at Google Scholar
  21. J. R. Quan and C. T. Chang, “New insights in solving distributed system equations by the quadrature method-I. Analysis,” Computers and Chemical Engineering, vol. 13, no. 7, pp. 779–788, 1989. View at Google Scholar · View at Scopus
  22. C. W. Bert and M. Malik, “Differential quadrature method in computational mechanics: a review,” Applied Mechanics Reviews, vol. 49, no. 1, pp. 1–27, 1996. View at Google Scholar · View at Scopus
  23. C. Shu, Differential Quadrature and Its Application in Engineering, Springer, London, UK, 2000.
  24. Y. F. Wu, R. Xu, and W. Chen, “Free vibrations of the partial-interaction composite members with axial force,” Journal of Sound and Vibration, vol. 299, no. 4-5, pp. 1074–1093, 2007. View at Publisher · View at Google Scholar · View at Scopus