Structural Engineering and Mechanics

  • 제26권2호
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  • Pages.151-162
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  • 2007
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Analytical solutions for buckling of simply supported rectangular plates due to non-linearly distributed in-plane bending stresses

  • Jana, Prasun (Aerospace Engineering Department, IIT) ;
  • Bhaskar, K. (Aerospace Engineering Department, IIT)
  • 투고 : 2005.12.20
  • 심사 : 2006.11.10
  • 발행 : 2007.05.30
⟨ 이전 논문 다음 논문 ⟩

초록

Rigorous analytical solutions are obtained for the plane stress problem of a rectangular plate subjected to non-linearly distributed bending loads on two opposite edges. They are then used in a Galerkin type solution to obtain the corresponding convergent buckling loads. It is shown that the critical bending moment depends significantly on the actual edge load distribution and further the number of nodal lines of the buckled configuration can also be different from that corresponding to a linear antisymmetric distribution of the bending stresses. Results are tabulated for future use while judging approximate numerical solutions.

키워드

참고문헌

  1. Bedair, O.K. (1996), 'Buckling behaviour of plates partially restrained against rotation under stress gradient', Struct. Eng. Mech., 4, 383-396 https://doi.org/10.12989/sem.1996.4.4.383
  2. Benoy, M.B. (1969), 'An energy solution for the buckling of rectangular plates under non-unifonn in-plane loading', Aeronaut. J., 73, 974-977 https://doi.org/10.1017/S0001924000051423
  3. Bert, C.W. and Devarakonda, K.K. (2003), 'Buckling of rectangular plate subjected to nonlinearly distributed inplane loading', Int. J. Solids Struct., 40, 4097-4106 https://doi.org/10.1016/S0020-7683(03)00205-1
  4. Bulson, P.S. (1970), The Stability of Flat Plates, Chatto and Windus, London
  5. Chen, X.L. and Liew, K.M. (2004), 'Buckling of rectangular functionally graded material plates subjected to nonlinearly distributed in-plane edge loads', Smart Mater. Struct., 13, 1430-1437 https://doi.org/10.1088/0964-1726/13/6/014
  6. Hu, H., Badir, A. and Abatan, A. (2003), 'Buckling behavior of a graphite/epoxy composite plate under parabolic variation of axial loads', Int. J. Mech. Sci., 45, 1135-1147 https://doi.org/10.1016/j.ijmecsci.2003.08.003
  7. Jana, Prasun and Bhaskar, K. (2004), 'Buckling of rectangular plates under non-unifonn compression using rigorous plane stress solutions', Proc. of the Int. Conf. on Theoretical, Analytical, Computational and Experimental Mechanics, lIT, Kharagpur, December
  8. Jana, Prasun (2005), Analytical Solutions for Buckling of Rectangular Plates due to Non-linearly DistributedUniaxial and Biaxial Loads, Master's thesis, IIT, Madras
  9. Kang, J.H. and Liessa, A.W. (2005), 'Exact solutions for the buckling of rectangular plates having linearly varying in-plane loading on two opposite simply supported edges', Int. J. Solids Struct., 42, 4220-4238 https://doi.org/10.1016/j.ijsolstr.2004.12.011
  10. Liew, K.M. and Chen, X.L. (2004), 'Buckling of rectangular Mindlin plates subjected to partial in-plane edge loads using the radial point interpolation method', Int. J. Solids Struct., 41, 1677-1695 https://doi.org/10.1016/j.ijsolstr.2003.10.022
  11. Leissa, A.W. and Ayoub, E.F. (1988), 'Vibration and buckling of a simply supported rectangular plate subjected to a pair of in-plane concentrated forces', J. Sound Vib., 127, 155-171 https://doi.org/10.1016/0022-460X(88)90356-2
  12. Leissa, A.W. and Kang, J.H. (2002), 'Exact solutions for vibration and buckling of an SS-C-SS-C rectangular plate loaded by linearly varying in-plane stresses', Int. J. Mech. Sci., 44, 1925-1945 https://doi.org/10.1016/S0020-7403(02)00069-3
  13. Little, RW. (1973), Elasticity, Prentice Hall, Englewood Cliffs, NJ
  14. Srivastava, A.K.L., Datta, P.K. and Sheikh, A.H. (2003), 'Buckling and vibration of stiffened plates subjected to partial edge loading', Int. J. Mech. Sci., 45, 73-93 https://doi.org/10.1016/S0020-7403(03)00038-9
  15. Timoshenko, S.P. (1910), 'Stabilitat einer rechteckigen platte, die durch einzelne krafte gedrckt wird', ZAMP, 58, 357-360 https://doi.org/10.1007/s00033-006-0047-8
  16. Timoshenko, S.P. and Gere, J.M. (1961), Theory of Elastic Stability, McGraw-Hill, New York

피인용 문헌

  1. BUCKLING OF A PLATE ON A PASTERNAK FOUNDATION UNDER UNIFORM IN-PLANE BENDING LOADS vol.13, pp.03, 2013, https://doi.org/10.1142/S0219455412500708