Abstract: The algorithm of optimization of trusses is presented in the paper, where for topology optimization the bars exchange method is used. In the first case, the problem aimed at cost minimization with a constraint set on global stiffness is formulated. In the second case, the problem of minimizing the cost function subjected to stress and cross-sectional area constraints is discussed and here the multiple-load case is taken into consideration. The conditions for introduction of topology modification and its acceptance are specified. The paper is illustrated with three examples.
B I B L I O G R A F I A[1] U. Kirsch, "Integration of reduction and expansion processes in layout optimization", Struct. Optim. 11, 13-18 (1996).
[2] W.S. Dorn, R.E. Gomory, and H.J. Greenberg, "Automatic design of optimal structures", J. de Mecanique 3, 25-52 (1964).
[3] U. Kirsch, "Optimal topologies of truss structures", Appl. Mech. Rev. 42, 223-239 (1989).
[4] G.I.N. Rozvany, "Topology optimization in structural mechanics", in CISM Courses and Lectures 374, Springer, Wien, 1967.
[5] W. Achtziger, "On simultaneous optimization of truss geometry and topology", Struct. Multidisc. Optim. 33, 285-304 (2007).
[6] D. Bojczuk and Z. Mróz, "Optimal design of trusses with account for topology variation", Mech. Struct. &Mach. 26, 21-40 (1998).
[7] J.J. McKeown, "Growing optimal pin-jointed frames", Struct. Optim. 15, 92-100 (1998).
[8] T. Hagishita and M. Ohsaki, "Topology optimization of trusses by growing ground structure method", Struct. Multidisc. Optim. 37, 377-393 (2009).
[9] D. Bojczuk, Sensitivity Analysis and Optimization of Bar Structures, Publishing House of Kielce University of Technology, Kielce, 1999, (in Polish).
[10] Z. Mróz and D. Bojczuk, "Finite topology variations in optimal design of structures", Struct. Multidisc. Optim. 25, 153-173 (2003).
[11] G. Leugerging and J. Sokolowski, "Topological sensitivity analysis for elliptic problems on graphs", Control and Cybernetics 37 (4), 971-997 (2008).
[12] G.I.N. Rozvany, "On symmetry and non-uniqueness in exact topology optimization", Struct. Multidisc. Optim. 43, 297-317 (2011).
[13] D. Bojczuk, "Sensitivity analysis of elastic bar and beam structures", Eng. Transactions 35, 171-204 (1987), (in Polish).
[14] Z.P. Bazant and L. Cedolin, Stability of Structures, Oxford University Press, Oxford, 1991. 
Pełny tekst 
DOI 
Web of Science 
YADDA/CEON