Design of Trusses Under Uncertain Loads Using Convex Models
Publication: Journal of Structural Engineering
Volume 124, Issue 3
Abstract
The optimal design of trusses subjected to loads considered to be uncertain in both magnitude and direction is investigated. A non-probabilistic ellipsoidal convex model is established for considering the uncertainties using three different criteria. The convex model is described as a set of constraints on the upper and lower limits of the load magnitudes and directions. The optimal design of the trusses is performed using two different optimization objectives. The first objective function to be minimized is the structural volume; constraints are imposed on the stresses and buckling loads of the members and on the joint displacements. Another objective function to be minimized is a selected displacement; constraints are implemented on the stresses and buckling loads of the members and on the structural volume. The presented method yields optimal designs that violate stress, displacement, and buckling constraints with less frequency than the assumed worst load condition. This method offers an alternative to formal probabilistic methods.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Al-Harthy, A. S., and Frangopol, D. M.(1994a). “Reliability assessment of prestressed concrete beams.”J. Struct. Engrg., ASCE, 120(1), 180–199.
2.
Al-Harthy, A. S., and Frangopol, D. M.(1994b). “Reliability-based design of prestressed concrete beams.”J. Struct. Engrg., ASCE, 120(11), 3156–3177.
3.
Ben-Haim, Y.(1993). “Failure of an axial compressed beam with uncertain initial deflection of bounded strain energy.”Int. J. Engrg. Sci., 31(7), 989–1001.
4.
Ben-Haim, Y.(1994). “A non-probabilistic concept of reliability.”Structural Safety, 14, 227–295.
5.
Ben-Haim, Y.(1995a). “A note on convex models of uncertainty for small initial imperfections of non linear structures.”Zeitschrift für Angewandte Mathematik und Mechanik, 75, 901–908.
6.
Ben-Haim, Y.(1995b). “A non-probabilistic measure of reliability of linear systems based on expansion of convex models.”Structural Safety, 17, 91–109.
7.
Ben-Haim, Y. (1996a). “Robust reliability of structures.”Adv. in Appl. Mech., 33.
8.
Ben-Haim, Y. (1996b). Robust reliability in the mechanical sciences. Springer-Verlag, Berlin, Germany.
9.
Ben-Haim, Y., and Elishakoff, I. (1990). Convex models of uncertainty in applied mechanics. Elsevier, New York, N.Y.
10.
Ben-Haim, Y., Chen, G., and Soong, T. T.(1996). “Maximum structural response using convex models.”J. Engrg. Mech., ASCE, 122(4), 325–333.
11.
Elishakoff, I.(1995a). “Essay on uncertainties in elastic and viscoelastic structures: From A. M. Fraudenthal's criticism to modern convex modeling.”Computers and Structures, 56(6), 871–895.
12.
Elishakoff, I.(1995b). “An idea on the uncertainty triangle.”Editors Rattle Space: The Shock and Vibration Digest, 22(10), 1.
13.
Elishakoff, I., Cai, G. Q., and Starnes, J. H.(1994a). “Non-linear buckling of a column with initial imperfection via stochastic and non-stochastic convex models.”Int. J. Non-linear Mech., 29, 71–82.
14.
Elishakoff, I., Haftka, R. T., and Fang, J.(1994b). “Structural design under bounded uncertainty optimization with anti-optimization.”Computers and Structures, 53, 1401–1405.
15.
Frangopol, D. M. (1986). “Structural optimization under conditions of uncertainty with reference to serviceability and ultimate limit states.”Proc., ASCE Structures Cong. 86, F. Y. Cheng, ed., ASCE, Reston, Va., 54–71.
16.
Gellatly, R. A., and Gallagher, R. H.(1966). “A procedure for automated minimum weight structural design.”Aeronautical Quarterly, 17(3), 216–230.
17.
Greene, W. H., and Haftka, R. T.(1991). “Computational aspects of sensitivity calculations in linear transient analysis.”Struct. Optimization, 3, 176–201.
18.
Hasofer, A. M., and Lind, N. C.(1974). “An exact and invariant first-order reliability format.”J. Engrg. Mech. Div., ASCE, 100(1), 111–121.
19.
Haug, E. I., and Arora, J. S. (1979). Applied optimal design. John Wiley & Sons, Inc., New York, N.Y.
20.
Hsieh, C. C., and Arora, J. S.(1984). “Design sensitivity analysis and optimization of dynamic response.”Comp. Meth. in Appl. Mech. and Engrg., 43, 195–219.
21.
Kirsch, U. (1981). Optimum structural design. McGraw-Hill Inc., New York, N.Y.
22.
Koskisto, O. J., and Ellingwood, B. R.(1997). “Reliability-based optimization of plant precast concrete structures.”J. Struct. Engrg., ASCE, 123(3), 298–304.
23.
Lindberg, H. E.(1992a). “An evaluation of convex modeling for multimode dynamic buckling.”J. Appl. Mech., 59, 929–936.
24.
Lindberg, H. E.(1992b). “Convex models for uncertain imperfection control in multimode dynamic buckling.”J. Appl. Mech., 59, 937–945.
25.
Liu, Z. S., Chen, S. H., and Han, W. Z.(1994). “Solving the extremum of static response for structural systems with unknown but bounded parameters.”Computers and Struct., 50, 557–561.
26.
Natke, H. G., and Soong, T. T. (1993). “Topological structural optimization under dynamic loads.”Optimization of structural system and applications, S. Hernandez and C. A. Brebbia, eds., Computational Mechanics and Publications, Southampton, U.K., 67–78.
27.
Pantelides, C. P.(1996a). “Buckling and postbuckling of stiffened elements with uncertainty.”Thin walled structures, Elsevier Science Ltd., Great Britain, 26(1), 1–17.
28.
Pantelides, C. P.(1996b). “Stability of elastic bars on uncertain foundations using a convex model.”Int. J. Solids Struct., 33(9), 1257–1269.
29.
Vanderplaats, G. N.(1984). “An efficient feasible directions algorithm for design synthesis.”AIAA J., 22(11), 1633–1640.
30.
Vanderplaats Research and Development, Inc. (VR&D). (1995). DOT users manual. Version 4.20, Colorado Springs, Col.
31.
Wang, C.-K. (1986). Structural analysis on microcomputers. Macmillan, New York, N.Y.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 124 • Issue 3 • March 1998
Pages: 318 - 329
Copyright
Copyright © 1998 American Society of Civil Engineers.
History
Published online: Mar 1, 1998
Published in print: Mar 1998
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.