Abstract
A truss topology optimization problem under stress constraints is formulated as a Mixed Integer Programming (MIP) problem with variables indicating the existence of nodes and members. The local constraints on nodal stability and intersection of members are considered, and a moderately large lower bound is given for the cross-sectional area of an existing member. A lower-bound objective value is found by neglecting the compatibility conditions, where linear programming problems are successively solved based on a branch-and-bound method. An upper-bound solution is obtained as a solution of a Nonlinear Programming (NLP) problem for the topology satisfying the local constraints. It is shown in the examples that upper- and lower-bound solutions with a small gap in the objective value can be found by the branch-and-bound method, and the computational cost can be reduced by using the local constraints.
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References
arora87 Arora J, Tseng C (1987) Idesign User’s Manual, Ver. 3.5. Technical report, Optimal Design Laboratory, University of Iowa
cheng95 Cheng G (1995) Some aspects of truss topology optimization. Struct Optim 10:173–179
cheng97 Cheng G, Guo X (1997) ε-relaxed approach in structural topology optimization. Struct Optim 13:258–266
dobbs69 Dobbs W, Felton LP (1969) Optimization of truss geometry. Proc ASCE 95(ST10):2105–2119
dorn64 Dorn W, Gomory R, Greenberg H (1964) Automatic design of optimal structures. J Mecanique 3:25–52
gondzio95 Gondzio J (1995) Hopdm – a fast lp solver based on a primal-dual interior point method. Eur J Oper Res 85:221–225
guo00 Guo X, Cheng G (2000) An extrapolation approach for the solution of singular optima. Struct Optim 19:255–262
haug86 Haug EJ, Choi KK, Komkov V (1986) Design Sensitivity Analysis of Structural Systems. Academic, Amsterdam
kirsch89b Kirsch U (1989) Optimal topologies of truss structures. Appl Mech Rev 42:223–239
kirsch90 Kirsch U (1990) On singular topologies in optimum structural design. Struct Optim 2:133–142
kravanja98 Kravanja S, Kravanja Z, Bedenik BS (1998) The minlp optimization approach to structural optimization, part i: general view on simultaneous topology and parameter optimization. Int J Numer Methods Eng 43:263–292
nakamura92a Nakamura T, Ohsaki M (1992) A natural generator of optimum topology of plane trusses for specified fundamental frequency. Comput Methods Appl Mech Eng 94(1):113–129
ohsaki96b Ohsaki M, Nakamura T (1996) Minimum constraint perturbation method for topology optimization of systems. Eng Optim 26:171–186
ringertz85 Ringertz UT (1985) On topology optimization of trusses. Eng Optim 9:209–218
ringertz86 Ringertz UT (1986) A branch and bound algorithm for topology optimization of truss structures. Eng Optim 10:111–124
sheu72 Sheu CY, Schmit LA (1972) Minimum weight design of elastic redundant trusses under multiple static loading conditions. AIAA J 10(2):155–162
stolpe01 Stolpe M, Svanberg K (2001) On the trajectories of the epsilon-relaxation approach for stress-constrained truss topology optimization. Struct Optim 21:140–151
stolpe03 Stolpe M, Svanberg K (2003) A note on stress-constrained truss topology optimization. Struct Optim 25:62–64
sved68 Sved G, Ginos Z (1968) Structural optimization under multiple loading. Int J Mech Sci 10:803–805
imsl97 Visual Numerics (1997) IMSL Math/Library Ver. 4.01
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Ohsaki, M., Katoh, N. Topology optimization of trusses with stress and local constraints on nodal stability and member intersection. Struct Multidisc Optim 29, 190–197 (2005). https://doi.org/10.1007/s00158-004-0480-2
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DOI: https://doi.org/10.1007/s00158-004-0480-2