Abstract
In this paper we present a displacement based method for maximum stiffness truss topology design. The ground structure approach is used, and the problem is formulated in terms of displacements and bar areas. This large, non—convex optimization problem can be solved by identifying an equivalent, unconstrained and convex problem in the displacement which can be solved by a non—smooth, steepest algorithm. In this method we circumvent the explicit solving of the equilibrium equations and the assembly of the global stiffness matrix. A large number of examples have been studied, showing the attractive features of topology design as well as exposing interesting features of optimal topologies.
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References
W. Achtziger, M.P. Bendsøe, A. Ben-Tal, J. Zowe (1991); “Equivalent Displacement Based Formulations for Maximum Strength Truss Topology Design”. Preprint, Universität Bayreuth (in preparation).
M.P. Bendsøe, N. Kikuchi (1988), “Generating Optimal Topologies in Structural Design using a Homogenization Method”. Comp. Meth. Appl. Mech. Engrg., 71, pp. 197–224.
M.P. Bendsøe, A. Ben-Tal, R.T. Haftka (1991), “New Displacement — Based Methods for Optimal Truss Topology Design”. Proc. AIAA/ASME/ASCE/AHS/ASC 32nd. Structures, Structural Dynamics and Materials Conference, Baltimore, MD, USA, April 8–10, 1991.
A. Ben-Tal, M.P. Bendsøe, (1991) “A New Method for Optimal Truss Topology Design”. MAT—Report No. 1991–8, Mathematical Institute, The Technical University of Denmark, DK-2800 Lyngby. 35 pp.
A. Diaz, B. Belding (1990), “On Optimum Truss Lay—out by a Homogenization Method”, ASME Transactions of Mechanical Design (to appear).
A. Diaz, M.P. Bendse (1991), “Shape Optimization of structures for multiple loading conditions using a homogenization method”, Structural Optimization (to appear).
W. Dorn, R. Gromory and M. Greenberg (1964), “Automatic Design of Optimal Structures”, J. de Mechanique, 3, pp. 25–52.
P. Fleron (1964), “The minimum weight of trusses”, Bygnings Statiske Meddelelser, 35, pp. 81–96.
R.T. Haftka, Z. Gürdal, M.P. Kamat (1990), Elements of Structural Optimization, 2nd edition, Kluwer Academic Publishers, Dordrecht, the Netherlands, p. 336.
W.S. Hemp (1973), Optimum Structures, Clarendon Press, Oxford, UK.
U. Kirsch (1989a), “Optimal Topologies of Structures”. Applied Mechanics Reviews, vol. 42, pp. 223–239.
U. Kirsch (1989b), “Optimal Topologies of Truss Structures”, Comp. Meth. Engrg., 72, pp. 15–28.
M. Kocvara (1991), “QP3 and CGO — Programs for Solving Truss Optimization Problems”, Internal Report, Math. Inst. Univ. of Bayreuth, FRG.
A.G.M. Michell (1904), “The Limits of Economy of Material in Frame Structures”, Philosophical Magazine, Series 6, Vol. 8, pp. 589–597.
P. Pederson (1970), “On the Minimum Mass Layout of Trusses”, AGARD Conf. Proc. No. 36, Symposium on Structural Optimization, AGARD—CP-36–70.
M.P. Rossow, J.E. Taylor (1973), “A finite element method for the optimal design of variable thichness sheets”, AIAA J. 11, 1566–1569.
G.I.N. Rozvany (1989), Structural Design via Optimality Criteria, Kluwer, Dordrecht.
G.I.N., Rozvany, M. Zhou (1991), “Applications of the COC Algorithm in Layout Optimization”. Proc. Int. Conf. Engrg. Optimization in Design Processes, Karlsruhe, 1990; Lecture Notes in Engineering vol 63, Springer Verlag, 59–70.
K. Suzuki and N. Kikuchi (1990), “A Homogenization Method for Shape and Topology Optimization,” Computer Methods in Applied Mechanics and Engineering (to appear).
J.E. Taylor (1969), “Maximum Strength Elastic Structural Design”, Proc. ASCE, 95, 653–663.
J.E. Taylor, M.P. Rossow (1977), “Optimal Truss Design Based on an Algorithm using Optimality Criteria”, Int. J. Solids Struct., 13, 913–923.
B.M.V. Topping (1983), “Shape Optimization of Skeletal Structures: A Review”, ACSE J. Struct. Engrg, 109, 1933–1951.
G.N. Vanderplaats (1984), “Numerical Methods for Shape Optimization: An Assessment of the State of the Art”, in New Directions in Optimum Structural Design ( E. Atrek et al., Eds.), Wiley, Chichester, UK.
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Bendsøe, M.P., Ben-Tal, A. (1993). Truss Topology Optimization by a Displacements Based Optimality Criterion Approach. In: Rozvany, G.I.N. (eds) Optimization of Large Structural Systems. NATO ASI Series, vol 231. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-9577-8_6
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DOI: https://doi.org/10.1007/978-94-010-9577-8_6
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