Structural Engineering and Mechanics

  • 제4권5호
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  • Pages.541-552
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  • 1996
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Rayleigh-Ritz optimal design of orthotropic plates for buckling

  • Levy, Robert (Faculty of Civil Engineering, Technion-Israel Institute of Technology)
  • 발행 : 1996.09.25
⟨ 이전 논문 다음 논문 ⟩

초록

This paper is concerned with the structural optimization problem of maximizing the compressive buckling load of orthotropic rectangular plates for a given volume of material. The optimality condition is first derived via variational calculus. It states that the thickness distribution is proportional to the strain energy density contrary to popular claims of constant strain energy density at the optimum. An engineers physical meaning of the optimality condition would be to make the average strain energy density with respect to the depth a constant. A double cosine thickness varying plate and a double sine thickness varying plate are then fine tuned in a one parameter optimization using the Rayleigh-Ritz method of analysis. Results for simply supported square plates indicate an increase of 89% in capacity for an orthotropic plate having 100% of its fibers in $0^{\circ}$ direction.

키워드

참고문헌

  1. Banichuk, N.V. (1983), Problems and Methods of Optimal Design, Plenum Press, New York, NY.
  2. Haug, E.J. (1981), "A review of distributed structural optimization literature", Optimization of Distributed Parameter Structures, E.J. Haug and J. Cea., Sijthhoff & Noordhoff, Alpen aan den Rijn, Netherlands. 3-68.
  3. Keller, J.B. (1960), "The shape of the strongest column", Arch. Rat. Mech. Analysis, 5, 275-285. https://doi.org/10.1007/BF00252909
  4. Levy, R. and Spillers, W.R. (1989), "Optimal design of axisymmetric cylindrical shell buckling", J. Engr. Mech., ASCE, 115(8), 1683-1690. https://doi.org/10.1061/(ASCE)0733-9399(1989)115:8(1683)
  5. Levy, R. (1990), "Buckling optimization of beams and plates on elastic foundation", J. Engr. Mech., ASCE, 116(1), 18-34. https://doi.org/10.1061/(ASCE)0733-9399(1990)116:1(18)
  6. Masur, E.F. (1970), "Optimum stiffness and strength of elastic structures", J. Engr. Mech., ASCE, 96(5), 621-640.
  7. Spillers, W.R. and Levy, R. (1990), "Optimal design for plate buckling", J. Struct. Engr., ASCE, 116(3), 850-858. https://doi.org/10.1061/(ASCE)0733-9445(1990)116:3(850)
  8. Tadjbakhsh, I. and Keller, J.B. (1962), "Strongest columns and isoperimetric inequalities for eigenvalues", J. Appl. Mech., ASCE, 29, 159-164. https://doi.org/10.1115/1.3636448
  9. Timoshenko, S.P. and Krieger, S.W. (1959), Theory of Plates and Shells, 2nd. Ed., McGraw Hill Book Company, New York, NY.

피인용 문헌

  1. Exact solutions for buckling and vibration of stepped rectangular Mindlin plates vol.41, pp.1, 2004, https://doi.org/10.1016/j.ijsolstr.2003.09.007
  2. Buckling analysis of laminated plates using the extended Kantorovich method and a system of first-order differential equations vol.30, pp.5, 2016, https://doi.org/10.1007/s12206-016-0419-8
  3. EXACT BUCKLING AND VIBRATION SOLUTIONS FOR STEPPED RECTANGULAR PLATES vol.250, pp.3, 2002, https://doi.org/10.1006/jsvi.2001.3922
  4. An evolutionary method for optimization of plate buckling resistance vol.29, pp.3-4, 1998, https://doi.org/10.1016/S0168-874X(98)00012-2
  5. BUCKLING AND VIBRATION OF STEPPED, SYMMETRIC CROSS-PLY LAMINATED RECTANGULAR PLATES vol.01, pp.03, 2001, https://doi.org/10.1142/S0219455401000275
  6. Dynamic response of functionally graded annular/circular plate in contact with bounded fluid under harmonic load vol.65, pp.5, 2018, https://doi.org/10.12989/sem.2018.65.5.523
  7. A level set topology optimization method for the buckling of shell structures vol.60, pp.5, 1996, https://doi.org/10.1007/s00158-019-02374-9