Structural Engineering and Mechanics

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An efficient high-order warping theory for laminated plates

  • Deng, Zhongmin (School of Space Technology, Beijing University of Aeronautic and Astronautics (BUAA)) ;
  • Huang, Chuanyue (Chinese Helicopter Research and Design Institute)
  • Received : 2005.05.09
  • Accepted : 2005.11.11
  • Published : 2006.03.30
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Abstract

The theory with hierarchical warping functions had been used to analyze composite thin-walled structure, laminated beam and had good results. In the present paper, a series of hierarchical warping functions are developed to analyze the cylindrical bending problems of composite lamina. These warping functions which refine through-the-thickness variation of displacements were composed of basic and corrective functions by taking into account of anisotropic, material discontinues, and transverse shear and normal strain. Then the hierarchical finite element method was used to form a numerical algorithm. The distribution of the displacements, in-plane stresses, transverse shear stresses and transverse normal stress for composite laminate were analyzed with the present model. The results show that the present model has precise mechanical response compared with the first deformation transverse theory and the corrective order affects the accuracy of result.

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References

  1. Brank, B. (2003), 'On composite shell models with a piecewise linear warping function', Comp. Struct., 59, 163-171 https://doi.org/10.1016/S0263-8223(02)00240-4
  2. Deng, Z.M. and Zhu, D.C. (1999), 'High-order warping theory for twist analysis of composite thin-walled beams', Acta Aeronautic et Astronautical Sinica, 20, 458-461 (in Chinese)
  3. Huang, C.Y. (2002), 'A model of transverse distribution displacement functions for composite laminate', The Dissertation for Ph.D. of Beijing University of Aeronautic and Astronautic, Beijing, China (in Chinese)
  4. Kapuria, S. and Achary, G.G.S. (2004), 'An efficient higher order zigzag theory for laminated plates subjected to thermal loading', Int. J. Solids Struct., 41, 4461-4681
  5. Liu, M.L. (2003), 'Free vibration analysis of laminated composite shell structures using hybrid strain based layerwise finite elements', Finite Elements in Analysis and Design, 40, 83-120 https://doi.org/10.1016/S0168-874X(02)00193-2
  6. Matsunaga, H. (2002), 'Assessment of a global higher-order deformation theory for laminated composite and sandwich plates', Comp. Struct., 56, 279-291 https://doi.org/10.1016/S0263-8223(02)00013-2
  7. Mau, S.T. (1973), 'A refined laminated plate theory', J. Appl. Mech., 40, 606-607 https://doi.org/10.1115/1.3423032
  8. Noor, A.K. and Burton, W.S. (1989), 'Assessment of shear deformation theories for multilayered composite plates', Appl. Mech. Rev., 42, 1-12 https://doi.org/10.1115/1.3152418
  9. Pagano, N.J. (1970), 'Influence of shear coupling in cylindrical bending of anisotropic laminates', J. Compos. Mat., 4, 330-343 https://doi.org/10.1177/002199837000400305
  10. Reddy, J.N. (1997), Mechanics of Laminated Composite Plate: Theory and Analysis, CRC Press
  11. Reissner, E. and Stavsky, Y. (1961), 'Bending and stretching of certain types of heterogeneous aeolotropic elastic plates', J. Appl. Mech., 28, 402-408 https://doi.org/10.1115/1.3641719
  12. Rolfes, R., Noor, AX. and Sparr, H. (1998), 'Evaluation of transverse thermal stresses in composite plates based on first-order shear deformation theory', Comput. Methods Appl. Mech. Engrg., 167, 355-368 https://doi.org/10.1016/S0045-7825(98)00150-9
  13. Rolfes, R., Tebmer, J. and Rohwer, K. (2003), 'Models and tools for heat transfer, thermal stresses, and stability of composite aerospace structures', J. Thermal Stress, 26, 641-670 https://doi.org/10.1080/713855951
  14. Sciuna, M.Di. (1987), 'An improved shear-deformation theory for moderately thick mulitilayered anisotropic shells and plates', J. Appl. Mech., 54, 589-596 https://doi.org/10.1115/1.3173074
  15. Toledano, A. and Murakami, H. (1987), 'A high-order laminated plate theory with improved in-plane responses', Int. J. Solids Struct., 23, 111-131 https://doi.org/10.1016/0020-7683(87)90034-5
  16. Valisetty, R.R. and Rehfiedl, L.W. (1987), 'A theory for stress analysis of composite laminates', AIAA J., 23, 1111-1117 https://doi.org/10.2514/3.9045
  17. Wang, A. and Chou, P. (1972), 'Comparison of two laminated plate theories', J. Appl. Mech., 39, 611-613 https://doi.org/10.1115/1.3422734
  18. Whitney, J.M. (1972), 'Stress analysis of thick laminated composite and sandwich plates', J. Comp. Mater., 6, 426-440 https://doi.org/10.1177/002199837200600401
  19. Whitney, J.M. and Pagano, N.J. (1970), 'Shear deformation in heterogeneous anisotropic plates', J. Appl. Mech., 37, 1031-1036 https://doi.org/10.1115/1.3408654
  20. Zhu, D.C. (1957), 'An equilibrium theory of elastical thin-walled tubes', J. Beijing Institute of Aeronautic and Astronautics, 3, 39-60 (In Chinese)
  21. Zhu, D.C. (1986), 'Development of hierarchical finite element methods at BIAA', Proc. of Int. Conf. on Computation Mechanics, Tokyo, 1986, Springer-Verlag, 1, 123-128
  22. Zhu, D.C., Deng, Z.M. and Wang, X.W. (2001), 'Analysis for composite laminated helicopter rotor by hierarchical warping beam theory and finite method', Acta Mechanics Sinica, 17, 258-268 https://doi.org/10.1007/BF02486882