Effect of Compatibility and Prestressing on Optimized Trusses
Publication: Journal of Structural Engineering
Volume 115, Issue 3
Abstract
Assuming force method analysis formulation, the effect of compatibility conditions on optimal design of trusses is studied. Neglecting the latter conditions, a linear programming (LP) formulation is obtained. The possibility of applying prestressing forces by “lack of fit” to maintain compatibility at the LP optimum is demonstrated. It has been shown that for structures subjected to a single loading condition, the LP lower‐bound solution is the final optimum. Prestressing might be required to maintain compatibility in cases where the optimal solution represents a statically indeterminate structure. The various possible solutions for structures subjected to multiple loading conditions are discussed. It is shown that under certain circumstances, compatibility conditions can be satisfied at the LP optimum only by applying different sets of prestressing forces for the various loadings. For certain geometries, the LP solution represents multiple optimal topologies, part of them being statically determinate structures. In such cases, the LP lower‐bound solution is the final optimum, and no prestressing is required to maintain compatibility. In cases where compatibility conditions considerably affect the solution, prestressing by lack of fit might significantly improve the final optimum.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Dorn, W. C., Gomory, R. E., and Greenberg, H. J. (1964). “Automatic design of optimal structures.” J. Mech., 3(1), 25–52.
2.
Farshi, B., and Schmit, L. A. (1974). “Minimum weight of stress limited trusses.” J. Struct. Div., ASCE, 100(1), 97–107.
3.
Kirsch, U. (1976). “Synthesis of elastic structures with controlled forces.” Comput. Struct., 6, 111–116.
4.
Kirsch, U., and Moses, F. (1976). “The relationship between plastic and prestressed elastic optimal design.” Proc., First ASCE Conf. on Mechanics in Engineering, Waterloo, Ontario, Canada, 207–221.
5.
Kirsch, U., and Moses, F. (1977). “Optimization of structures with control forces and displacements.” Engrg. Optim., 3(1), 37–44.
6.
Kirsch, U. (1980). “Optimal design of trusses by approximate compatibility.” Comput. Struct., 12, 93–98.
7.
Kirsch, U., and Benardout, D. (1980). “Optimal design of elastic trusses by approximate equilibrium.” Comput. Methods Appl. Mech. Eng., 22, 347–359.
8.
Kirsch, U., and Taye, S. (1986). “On optimal topology of grillage structures.” Eng. with Comput., 1, 229–243.
9.
Kirsch, U. (1986). “Optimal topologies of flexural systems.” Proc., NATO Advanced Study Institute on Computer Aided Optimal Design, Troia, Portugal,
also inEngrg. Opt. (1987), 11, 141–149.
10.
Kirsch, U. (1987). “The effect of compatibility conditions on optimal design of flexural structures.” Int. J. Numer. Methods Engrg., 24, 1173–1185.
11.
Kirsch, U., and Taye, S. (1987). “High quality approximations of forces for optimum structural design.” Proc., CIVIL‐COMP 87, Third Int. Conf. on Civil and Structural Engineering Computing, London, U.K., also in Comput. Struct. (1988), 30(3), 519–527.
12.
Kirsch, U. (1989). “Optimal topologies of truss structures.” Comput. Struct., (in press).
13.
Levy, R. (1985). “Linear programming in prestressed trusses.” Proc., CTVIL‐COMP 85, Second Int. Conf. on Civil and Structural Engineering Computing, London, U.K.
14.
Reinschmidt, K. F., and Russel, A. D. (1974). “Application of linear programming in structural layout and optimization.” Comput. Struct., 4, 855–869.
15.
Reinschmidt, K. F., and Norabhoompipat, J. (1975). “Structural optimization by equilibrium linear programming.” J. Struct. Div., ASCE101(4), 921–938.
16.
Somekh, E., and Kirsch, U. (1981). “Interactive optimal design of truss structures.” CAD J., 13(5), 253–259.
17.
Spillers, W. R., and Levy, R. (1984). “Truss design: two loading conditions with prestress.” J. Struct. Engrg., ASCE, 110(4), 677–687.
Information & Authors
Information
Published In
Copyright
Copyright © 1989 ASCE.
History
Published online: Mar 1, 1989
Published in print: Mar 1989
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.