Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

A matrix displacement formulation for minimum weight design of frames

  • Orakdogen, Engin (Faculty of Civil Engineering, Technical University of Istanbul)
  • Published : 2002.10.25
⟨ Previous Next ⟩

Abstract

A static linear programming formulation for minimum weight design of frames that is based on a matrix displacement method is presented in this paper. According to elementary theory of plasticity, minimum weight design of frames can be carried out by using only the equilibrium equations, because the system is statically determinate when at an incipient collapse state. In the present formulation, a statically determinate released frame is defined by introducing hinges into the real frame and the bending moments in yield constraints are expressed in terms of unit hinge rotations and the external loads respectively, by utilizing the matrix displacement method. Conventional Simplex algorithm with some modifications is utilized for the solution of linear programming problem. As the formulation is based on matrix displacement method, it may be easily adopted to the weight optimization of frames with displacement and deformation limitations. Four illustrative examples are also given for comparing the results to those obtained in previous studies.

Keywords

References

  1. Foulkes, J.D. (1953), "Minimum weight design and the theory of plastic collapse", Q. Appl. Math., 10, 347-358. https://doi.org/10.1090/qam/99982
  2. Foulkes, J.D. (1954), "Minimum weight design of structural frames", Proc. Roy. Soc., A223, 482-494.
  3. Heyman, J. (1951), "Plastic design of beams and plane frames for minimum material consumption", Q. Appl. Math., 8, 373-381. https://doi.org/10.1090/qam/39533
  4. Heyman, J. (1959), "On the absolute minimum weight design of framed structures", Q. Appl. Math., 12, 314- 324. https://doi.org/10.1093/qjmam/12.3.314
  5. Heyman, J. (1960), "On the minimum-weight design of a simple portal frame", Int. J. Mech. Sci., 1, 121-134. https://doi.org/10.1016/0020-7403(60)90034-5
  6. Heyman, J. (1971), Plastic Design of Frames - Applications, Vol. II, Cambridge, pp. 196-198.
  7. Hodge, P.G. (1959), Plastic Analysis of Structures, McGraw Hill.
  8. Nguyen Dang Hung (1984), "CEPAO-An automatic program for rigid-plastic and elastic-plastic analysis and optimisation of frame structures", Eng. Struct., 6, 33-51. https://doi.org/10.1016/0141-0296(84)90060-9
  9. Jennings, A. and Tam, T.K.H. (1986), "Automatic plastic design of frames", Eng. Struct., 8, 139-147. https://doi.org/10.1016/0141-0296(86)90047-7
  10. Livesley, R.K. (1956), "The automatic design of structural frames", Q. J. Mech. Appl. Maths., 9, 257-278. https://doi.org/10.1093/qjmam/9.3.257
  11. Prager, W. and Shield, R.T. (1967), "A general theory of optimal plastic design", Trans. Am. Soc. Mech. Engrs., J. Appl. Mech., 34, 184-186. https://doi.org/10.1115/1.3607621
  12. Tam, T.K.H. and Jennings, A. (1992), "Computing alternative optimal collapse mechanisms", Int. J. Numer. Meth. Eng., 33, 1197-1216. https://doi.org/10.1002/nme.1620330607
  13. Toakley, A.R. (1968), "Some computational aspects of optimum rigid-plastic design", Int. J. Mech. Sci., 10, 531- 537. https://doi.org/10.1016/0020-7403(68)90033-7
  14. Watwood, V.B. (1979), "Mechanism generation for limit analysis of frames", J. Struct. Div., ASCE, 109, 1-15.