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Structural Synthesis by Method of Centers in Force Formulation under Size and Stress Constraints

Published online by Cambridge University Press:  28 September 2011

B. Farshi  and
A. Alinia-ziazi
B. Farshi*
Affiliation:
Department of Mechanical Engineering, Iran University of Science and Technology, Narmak, Tehran 16846, Iran
A. Alinia-ziazi*
Affiliation:
Department of Mechanical Engineering, Iran University of Science and Technology, Narmak, Tehran 16846, Iran
*
* Associate Professor, corresponding author
** Graduate student
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Abstract

This paper studies a novel approach to optimize trusses and truss-like structures for minimum weight design. It is based on the force method of analysis which is incorporated inside the optimization routine. The design variables in force formulation are the member cross sectional areas and the redundant forces in each load condition. The optimization method used is the method of center points using the inscribed hyperspheres to the feasible-usable design space. By incorporating the analysis step as part of the optimization problem, a separate structural solution phase, which is necessary in all other methods, is avoided resulting in large computational savings. In this article the simplest form of structures i.e. trusses are treated to illustrate the efficacy of the method. Stress limits on the members as well as limitations on their sizes, and linking among them, under several load conditions have been considered. Combination of the method of center points and force formulation results in a viable routine for structural optimization. Comparison of the example results with those obtained by others clearly shows the effectiveness and novelty of the proposed method.

Keywords

Force methodCenter pointsTrussesMinimum weightOptimization
Type
Research Article
Information
Journal of Mechanics , Volume 26 , Issue 4 , December 2010 , pp. 513 - 524
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2010

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References

REFERENCES

1. Schmit, L., “Structural Design by Systematic Synthesis,” Proceedings, 2nd Conference on Electronic Computation,ASCE, pp. 105–122, New York (1960).Google Scholar
2. Schmit, L. A. and Farshi, B., “Some Approximation Concepts for Structural Synthesis,” American Institute of Aeronautics and Astronautics, 12, pp. 692–699 (1974).CrossRefGoogle Scholar
3. Schmit, L. and Miura, H., “Approximation Concepts for Efficient Structural Synthesis,” NASA-CR-2552, Washington DC: NASA (1976).Google Scholar
4. Vanderplaats, G. and Moses, F., “Structural Optimization by Methods of Feasible Directions,” Computers and Structures, 3, pp. 739–755 (1973).CrossRefGoogle Scholar
5. Harless, R., “ A Method for Synthesis of Optimal Weight,” Computers and Structures, 12, pp. 791–804 (1980).CrossRefGoogle Scholar
6. Arora, J and Haug, J., “Efficient Optimal Design of Structures by Generalized Steepest Descent Programming,” International Journal for Numerical Methods in Engineering, 10, pp. 747–766 (1976).CrossRefGoogle Scholar
7. Razani, R., “The Behaviour of the Fully Stressed Design of Structures and its Relationship to Minimum Weight Design,” AIAA Journal, 3, pp. 2262–2268 (1965).CrossRefGoogle Scholar
8. Venkayya, V., Khot, N. and Reddy, V., “Energy Distribution in an Optimum Structural Design,” Report No. AFFDL-TR-68-156, Air Force Flight Dynamics Laboratory, Wright-Patterson Air Force Base, Ohio. March (1969).Google Scholar
9. Venkayya, V., “Design of Optimum Structures,” Computers and Structures, 1, pp. 265–309 (1971).CrossRefGoogle Scholar
10. Allwood, R. and Chung, Y., “Minimum-Weight Design of Trusses by an Optimality Criteria Method,” International Journal for Numerical Methods in Engineering, 20, pp. 697–713 (1984).CrossRefGoogle Scholar
11. Patnaik, S. N., Guptill, J. and Berke, L., “Merits and Limitations of Optimality Criteria Method for Structural Optimization,” International Journal for Numerical Methods in Engineering, 38, pp. 3087–3120 (1995).CrossRefGoogle Scholar
12. Fleury, C., “A Unified Approach to Structural Weight Minimization,” Computers Methods Applied Mechanical Engineering, 20, pp. 17–38 (1979).CrossRefGoogle Scholar
13. Patnaik, S. N., Gendy, A., Berke, L. and Hopkins, D.,“Modified Fully Utilized Design (MFUD) Method for Stress and Displacement Constraints,” International Journal for Numerical Methods in Engineering, 41, pp. 1171–1194 (1998).3.0.CO;2-O>CrossRefGoogle Scholar
14. Makris, P. A. and Provatidis, C., “Weight Minimisation of Displacement-Constrained Truss Structures Using a Strain Energy Criterion,” Computers Methods Applied Mechanical Engineering, 191, pp. 2159–2177 (2002).CrossRefGoogle Scholar
15. Makris, P. A., Provatidis, C. G and Venetsanos, D. T., “Structural Optimization of Thin-Walled Tubular Trusses Using a Virtual Strain Energy Density Approach,” Thin-Walled Structures, 44, p. 235-246, ( 2006).Google Scholar
16. Lamberti, L. and Pappalettere, C., “Comparison of the Numerical Efficiency of Different Sequential Linear Programming Based Algorithms for Structural Optimization Problems,” Computers and Structures, 76, pp. 713–728 (2000).CrossRefGoogle Scholar
17. Lamberti, L. and Pappalettere, C., “Move Limits Definition in Structural Optimization with Sequential Linear Programming, Parts I and II,” Computers and Structures, 81, pp. 197–238 (2003).CrossRefGoogle Scholar
18. Lamberti, L. and Pappalettere, C., “Improved Sequential Linear Programming Formulation for Structural Weight Minimization,” Computers Methods Applied Mechanical Engineering, 193, pp. 3493–3521 (2004).CrossRefGoogle Scholar
19. Kirsch, U., “Optimal Design of Trusses by Approximate Compatibility,” Computers and Structures, 12, pp. 93–98 (1980).CrossRefGoogle Scholar
20. Reinschmidt, K. and Russell, A., “Applications of Linear Programming in Structural Layout and Optimization,” Computers and Structures, 4, pp. 853–869 (1974).CrossRefGoogle Scholar
21. Farshi, B. and Schmit, L., “Minimum Weight Design of Stress Limited Trusses,” Journal for Structures Division, ASCE, 100, pp. 97–107 (1974).CrossRefGoogle Scholar
22. Pearson, C., “Structural Design by High-Speed Computing Machines,” Proceedings of the First Conference on Electronic Compution,ASCE, pp. 417–436, New York (1958).Google Scholar
23. Przemieniecki, J., Theory of Matrix Structural Analysis, McGraw-Hill, New York (1968).Google Scholar
24. Sedaghati, R. and Esmailzadeh, E., “Optimum Design of Structures with Stress and Displacement Constraints Using the Force Method,” International Journal of Mechanical Sciences, 45, pp. 1369–1389 (2003).CrossRefGoogle Scholar
25. Sedaghati, R. “Benchmark Case Studies in Structural Design Optimization Using the Force Method,” International Journal of Solids and Structures, 42, pp. 5848–5871 (2005).CrossRefGoogle Scholar
26. Sedaghati, R., Suleman, A. and Tabarrok, B., “Structural Optimization with Frequency Constraints Using the Finite Element Force Method,” AIAA Journal, 40, pp. 382–388 (2002).CrossRefGoogle Scholar
27. Sedaghati, R., Suleman, A. and Tabarrok, B. “Optimum Design of Structures with Multiple Frequency Constraints Using the Finite Element Force Method,” Proceedings of the 42nd AIAA/ASME/ASCE/AHS/ASC Structures,Structural Dynamics, and Materials Conference,Seattle, WA, April 16.19 (2001).CrossRefGoogle Scholar
28. Kaveh, A. and Kalatjari, V., “Topology Optimization of Trusses Using Genetic Algorithm, Force Method and Graph Theory,” International Journal for Numerical Methods in Engineering, 58, pp. 771–791 (2003).CrossRefGoogle Scholar
29. Kaveh, A. and Kalatjari, V., “Size/Geometry Optimization of Trusses by the Force Method and Genetic Algorithm,” ZAMM Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 84, pp. 347–357 (2004).CrossRefGoogle Scholar
30. Kaveh, A. and Kalatjari, V., “Genetic Algorithm for Discrete-Sizing Optimal Design of Trusses Using the Force Method,” International Journal for Numerical Methods in Engineering, 55, pp. 55–72 (2002).CrossRefGoogle Scholar
31. Kaveh, A. and Rahami, H., “Analysis, Design and Optimization of Structures Using Force Method and Genetic Algorithm,” International Journal for Numerical Methods in Engineering, 65, pp. 1570–1584 (2006).CrossRefGoogle Scholar
32. Kaveh, A. and Rahami, H., “Nonlinear Analysis and Optimal Design of Structures Via Force Method and Genetic Algorithm,” Computers and Structures, 84, pp. 770–778 (2006).CrossRefGoogle Scholar
33. Rahami, H., Kaveh, A. and Gholipour, Y., “Sizing, Geometry and Topology Optimization of Trusses Via Force Method and Genetic Algorithm,” Engineering Structures, 30, pp. 2360–2369 (2008).CrossRefGoogle Scholar
34. Denke, P. H., “A General Digital Computer Analysis of Statically Indeterminate Structures,” NASA-TD-D-1666, (1962).Google Scholar
35. Robinson, J., “Automatic Selection of Redundancies in the Matrix Force Method: the Rank Technique,” Canadian Aeronautics and Space Journal, 11, pp. 9–12 (1965).Google Scholar
36. Kaneko, L., Lawo, M. and Thierauf, G., “On Computational Procedures for the Force Method,” International Journal for Numerical Methods in Engineering, 18, pp. 1469–1495 (1982).CrossRefGoogle Scholar
37. Patnaik, S., Berke, L. and Gallagher, R. H., “Compatibility Conditions of Structural Mechanics for Finite Element Analysis,” NASA Technical Memorandum 102413, (1990).Google Scholar
38. Kaveh, A., “Recent Developments in the Force Method of Structural Analysis,” Applied Mechanics Reviews, 45, pp. 401–418 (1992).CrossRefGoogle Scholar
39. Haftka, R. T., Gurdal, Z. and Kamat, M. P., “Elements of Structural Analysis,” 2nd Ed., Kulwer Academic Pub., (1990).Google Scholar