Approximate discrete variable optimization of plate structures using dual methods

  • Published : 1995.07.25


This study presents an efficient method for optimum design of plate and shell structures, when the design variables are continuous or discrete. Both sizing and shape design variables are considered. First the structural responses such as element forces are approximated in terms of some intermediate variables. By substituting these approximate relations into the original design problem, an explicit nonlinear approximate design task with high quality approximation is achieved. This problem with continuous variables, can be solved by means of numerical optimization techniques very efficiently, the results of which are then used for discrete variable optimization. Now, the approximate problem is converted into a sequence of second level approximation problems of separable form and each of which is solved by a dual strategy with discrete design variables. The approach is efficient in terms of the number of required structural analyses, as well as the overall computational cost of optimization. Examples are offered and compared with other methods to demonstrate the features of the proposed method.


  1. Schmit, L.A. and Fleury, C. (1980), "Discrete-continuous variables structural synthesis using dual methods, AIAA J., 18, 1515-1524.
  2. Vanderplaats, G.N. (1984), Numerical optimization techniques for engineering design: with applications, McGraw-Hill, Inc., New York.
  3. Vanderplaats, G.N. and Salajegheh, E. (1988), "An efficient approximation technique for frequency constraints in frame optimization", Int. J. Num. Mech. Engng., 26,1057-1069.
  4. Vanderplaats, G.N. and Salajegheh, E. (1989), "A new approximation method for stress constraints in structural synthesis", AIAA J., 27, 352-358.
  5. Vanderplaats, G.N. and Thomas, H.L. (1993), "An improved approximation for stress constraints in plate structures", Struct. Optim., 6(4), 1-7.
  6. Vanderplaats, G.N. and Salajegheh, E. (1994), "An approximation method for structural synthesis with discrete sizing and shape variables, using duality theory", AIAA J., to appear.
  7. Salajegheh, E. (1994a), "Approximate discrete variable optimization of frame structures with dual methods", Proc. 17th Energy-Sources Technology Conference & Exhibition (ETCE), held at the University of Texas, U.S.A., ASME 1994, PD, 61, Tribology Symposium, 81-89.
  8. Salajegheh, E. (1994b), "A two level approximation technique for structural optimization", In press in the Journal of Engineering, Islamic Republic of Iran.
  9. Salajegheh, E. (1994c), "Optimum design of plate and shell structures with discrete design variables", Proc. of the Second International Conference on computational Structures Technology, Topping, B.H.V. and Papadrakakis, M. (Editors), Advances in Structural Optimization, Civil-Comp Ltd., Edinburgh. Scotland, 113-117.
  10. Schmit, L.A. and Miura, H. (1976), "Approximation concepts for efficient structural synthesis", NASA CR-2552.
  11. Salajegheh, E. (1993b), "Structural optimization technique involving discrete design variables", Proc. 2nd Asian-Pacific Conference on computational Mechanics, held at the Univ. of New South Wales, Australia, Valliappan, S., Pulmano, V.A. and Tin-Loi, F. (Editors), Balkema, Rotterdam, 975-980.
  12. Salajegheh, E. (1993a), "Efficient optimum design of structures", Proc. 4th Int. Conference on Space Structures, held at the Univ. of Surrey, England, Parke, G.A.P. and Howard, C.M. (Editors), Thomas Telford Services Ltd., London, 1735-1745.
  13. Salajegheh, E. (1984), "Optimum design of double layer grids, Proc. 3rd Int. Conference of Space Structures, held at the Univ. of Surrey, England, Nooshing, H. (Editor), Elsevier Applied Publishers, London, 661-668.
  14. Salajegheh, E. and Vanderplaats, G.N. (1986, 1987), "An efficient approximation method for structural synthesis with reference to space structures", Int. J. of Space Structures, 2, 165-175.
  15. Salajegheh, E. and Vanderplaats, G.N. (1993a), "Efficient optimum design of structures with discrete design variables", Int. J. Space Structures, 8(3), 199-208.
  16. Salajegheh, E. and Vanderplaats, G.N. (1993b), "Optimum design of trusses with discrete sizing and shape variables", Struct. Optim., 6(2), 79-85.
  17. Arora, J.S., Huang, M.W. and Hsieh, C.C. (1994), "Methods for optimization of nonlinear problems with discrete variables; A review", Struct. Optim., 8(2/3), 69-85.
  18. DOT Users Manual (1992), VMA Engineering, Goleta, CA.
  19. Fleury, C. and Braibant, V. (1986), "Structural optimization: A new dual method using mixed variables", Int. J. Num. Meth. Engng. 23(3), 409-429.
  20. Moore, G.J. and Vanderplaats, G.N. (1990), "Improved approximations for static stress constraints in shape optimal design of shell structures", Proc. AIAA/ASME/ASCE/ASC 31st Structures, Structural Dynamics and Materials Conf., (held in Long beach, CA), Washington, D.C.: AIAA., 161-170.
  21. Zienkiewicz, O.C. and Taylor, R.L. (1989), The finite element method, 4th Edn, McGraw-Hill Book Company, UK.

Cited by

  1. Structural optimization using response approximation and optimality criteria methods vol.19, pp.7, 1997,
  2. Optimum design of plate structures using three-point approximation vol.13, pp.2-3, 1997,