DOI QR코드

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A discussion on simple third-order theories and elasticity approaches for flexure of laminated plates

  • Singh, Gajbir (Structural Design and Analysis Division, Structural Engineering Group, Vikram Sarabhai Space Centre) ;
  • Rao, G. Venkateswara (Structural Design and Analysis Division, Structural Engineering Group, Vikram Sarabhai Space Centre) ;
  • Iyengar, N.G.R. (Department of Aerospace Engineering, Indian Institute of Technology)
  • 발행 : 1995.03.25

초록

It is well known that two-dimensional simplified third-order theories satisfy the layer interface continuity of transverse shear strains, thus these theories violate the continuity of transverse shear stresses when two consecutive layers differ either in fibre orientation or material. The third-order theories considered herein involve four/or five dependent unknowns in the displacement field and satisfy the condition of vanishing of transverse shear stresses at the bounding planes of the plate. The objective of this investigation is to examine (i) the flexural response prediction accuracy of these third-order theories compared to exact elasticity solution (ii) the effect of layer interface continuity conditions on the flexural response. To investigate the effect of layer interface continuity conditions, three-dimensional elasticity solutions are developed by enforcing the continuity of different combinations of transverse stresses and/or strains at the layer interfaces. Three dimensional twenty node solid finite element (having three translational displacements as degrees of freedom) without the imposition of any of the conditions on the transverse stresses and strains is also employed for the flexural analysis of the laminated plates for the purposes of comparison with the above theories. These shear deformation theories and elasticity approaches in terms of accuracy, adequacy and applicability are examined through extensive numerical examples.

키워드

참고문헌

  1. Bhimaraddi, A. and Stevens, L.K. (1984), "A higher order theory for vibration of orthotropic homogeneous and laminated rectangular plates", J. Appl. Mech., 51, pp. 107-113. https://doi.org/10.1115/1.3167552
  2. Bogner, F. K., Fox, R. L. and Schmit, L. A. (1966), "The generation of interelement compatible stiffness and mass matrices by the use of interpolation formulas", Proc. Conf. Matrix Methods in Structural Mech. AFFDL-TR-66-80. Wright-Patterson A.F.B., Ohio (October, 1966).
  3. Kant, T. and Pandya, B. N. (1988), "A simple finite element formulation of a higher order theory for unsymmetrically laminated plates", Composite Structures, 9, pp. 215-246. https://doi.org/10.1016/0263-8223(88)90015-3
  4. Librescu, L. and Khdeir, A. A. (1988), "Analysis of symmetric cross-ply laminated elastic plates using a higher order theory-Part I", 7, pp. 189-213.
  5. Lim, S. P., Lee, K. H., Chow, S. T. and Santhilnathan, N. R. (1988), "Linear and nonlinear bending of shear deformable plates", Computers and Structures, 30, pp. 945-952. https://doi.org/10.1016/0045-7949(88)90132-0
  6. Lo, K. H., Chirstensen, R. M. and Wu, E. M. (1977a), "A higher order theory of plate deformation, Part I: Homogeneous plates", J. Appl. Mech., 44, pp. 663-668. https://doi.org/10.1115/1.3424154
  7. Lo, K. H., Chirstensen, R. M. and Wu, E. M. (1977b), "A higher order theory of plate deformation, Part II: Laminated plates", J. Appl. Mech., 44, pp. 669-676. https://doi.org/10.1115/1.3424155
  8. Mindlin, R. D. (1951), "Influence of rotatory inertia and shear on the flexural motion of isotropic, elastic plates", J. Appl. Mech., 18 (TRANS ASME 73), A31.
  9. Noor, A. K. and Burton, W. S. (1989), "Assessment of shear deformation theories for multilayered composite plates", Appl. Mech. Rev., 42(1), pp. 1-12. https://doi.org/10.1115/1.3152418
  10. Pagano, N. J. (1970), "Exact solutions for rectangular bidirectional composites and sandwich plates", J Composite Materials, 4, pp. 20-34. https://doi.org/10.1177/002199837000400102
  11. Pagano, N. J. and Hatifield, S. J. (1972), "Elastic behavior of multilayered bidirectional composites", AIAA Journal. 10(7), pp. 931-933. https://doi.org/10.2514/3.50249
  12. Putcha, N. S. and Reddy, J. N. (1986), "A refined mixed shear flexible finite element for the nonlinear analysis of laminated plates", Computers and Structures, 22, pp. 529-538. https://doi.org/10.1016/0045-7949(86)90002-7
  13. Reddy, J. N. (1984), "Refined higher-order theory for laminated composite plates", J. Appl. Mech., 51, pp. 745-752. https://doi.org/10.1115/1.3167719
  14. Reddy, J. N. (1990), "A general non-linear third order theory of plates with moderate thickness", Int. J. Nonlinear Mech., 25, pp. 677-686. https://doi.org/10.1016/0020-7462(90)90006-U
  15. Reddy, J. N. and Phan, N. D. (1985), "Stability and Vibration of isotropic, orthotropic and laminated plates according to a higher-order shear deformation theory", J. Sound and Vibration, 98, pp. 157-170. https://doi.org/10.1016/0022-460X(85)90383-9
  16. Reissner, E. (1985), "Reflection on the theory of elastic plates", Appl. Mech. Rev., 38(4), pp. 1453-1464. https://doi.org/10.1115/1.3143699
  17. Srinivas, S. and Rao, A. K. (1970), "Bending vibration and buckling of simply-supported thick orthotropic rectangular plates", Int. J Solids and Structures, 6, pp. 1463-1481. https://doi.org/10.1016/0020-7683(70)90076-4

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