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
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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.
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A. G. M. Mitchell, The limits of economy of material in framed structures, Phil. Mag., 6 8 (1904)
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)
W. S. Hemp, Optimum structures, Oxford University Press, 1973
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D. G. Luenberger, Introduction to linear and nonlinear programming, Addison-Wesley, Reading, Mass., 1973
W. R. Spillers, Automated structural analysis: An introduction, Pergamon Press, New York, 1972
W. R. Spillers and Robert Levy, Truss design: Two loading conditions with prestress, Journal of Structural Engineering, ASCE, Volume 110, No. 4 (April 1984)
F. H. Cilley, The exact design of statically indeterminant frameworks, An exposition of its possibility, But Futility, Transactions, ASCE, 43 (June 1900)
A. G. M. Mitchell, The limits of economy of material in framed structures, Phil. Mag., 6 8 (1904)
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)
W. S. Hemp, Optimum structures, Oxford University Press, 1973
W. R. Spillers, Iterative structural design, North Holland, Amsterdam, 1976
G. Hadley, Linear programming, Addison Wesley, Reading, Mass., 1962
M. S. Bazaara and C. M. Shetty, Nonlinear programming, John Wiley, New York, 1979
D. G. Luenberger, Introduction to linear and nonlinear programming, Addison-Wesley, Reading, Mass., 1973
W. R. Spillers, Automated structural analysis: An introduction, Pergamon Press, New York, 1972
W. R. Spillers and Robert Levy, Truss design: Two loading conditions with prestress, Journal of Structural Engineering, ASCE, Volume 110, No. 4 (April 1984)
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Article copyright:
© Copyright 1985
American Mathematical Society
