Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

On the optimal design of trusses under one loading condition


Author: Robert Levy
Journal: Quart. Appl. Math. 43 (1985), 129-134
MSC: Primary 73K40
DOI: https://doi.org/10.1090/qam/793520
MathSciNet review: 793520
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The optimal design of singly loaded trusses required to satisfy allowable stress criteria has the popular structural properties of a statically determinate configuration and fully stressed members. Linear programming and the duality theorem were used to attain these properties. This paper formulates the truss problem as a nonlinear programming problem, derives the optimality criteria via the Lagrangian and through proper physical interpretation of the Lagrange multipliers demonstrates the validity of the above results.


References [Enhancements On Off] (What's this?)

  • [1] F. H. Cilley, The exact design of statically indeterminant frameworks, An exposition of its possibility, But Futility, Transactions, ASCE, 43 (June 1900)
  • [2] A. G. M. Mitchell, The limits of economy of material in framed structures, Phil. Mag., 6 8 (1904)
  • [3] C. Y. Shen and L. A. Schmit, Minimum weight design of elastic redundant trusses under multiple static loading conditions, AIAA Journal, 10, 2 (Feb. 1972)
  • [4] W. S. Hemp, Optimum structures, Oxford University Press, 1973
  • [5] William R. Spillers, Iterative structural design, North-Holland Publishing Co., Amsterdam-Oxford; American Elsevier Publishing Co., Inc., New York, 1975. With a reprint of “Limits of economy of material in frame-structures” (Philos. Mag. 168 (1904), 589–597) by A. G. M. Michell and an appendix “Geometric optimization” by Lewis Friedland; North-Holland Monographs in Design Theory, No. 1. MR 0421265
  • [6] G. Hadley, Linear programming, Addison-Wesley Series in Industrial Management, Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1962. MR 0135622
  • [7] Mokhtar S. Bazaraa and C. M. Shetty, Nonlinear programming, John Wiley & Sons, New York-Chichester-Brisbane, 1979. Theory and algorithms. MR 533477
  • [8] D. G. Luenberger, Introduction to linear and nonlinear programming, Addison-Wesley, Reading, Mass., 1973
  • [9] W. R. Spillers, Automated structural analysis: An introduction, Pergamon Press, New York, 1972
  • [10] W. R. Spillers and Robert Levy, Truss design: Two loading conditions with prestress, Journal of Structural Engineering, ASCE, Volume 110, No. 4 (April 1984)

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 73K40

Retrieve articles in all journals with MSC: 73K40


Additional Information

DOI: https://doi.org/10.1090/qam/793520
Article copyright: © Copyright 1985 American Mathematical Society

American Mathematical Society