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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 91
PROCEEDINGS OF THE TWELFTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING
Edited by: B.H.V. Topping, L.F. Costa Neves and R.C. Barros
Paper 62

Heuristic Features of the Extended SIMP Algorithm in Topology Optimization

V. Pomezanski

Department of Structural Engineering, University of Pécs, Hungary

Full Bibliographic Reference for this paper
V. Pomezanski, "Heuristic Features of the Extended SIMP Algorithm in Topology Optimization", in B.H.V. Topping, L.F. Costa Neves, R.C. Barros, (Editors), "Proceedings of the Twelfth International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 62, 2009. doi:10.4203/ccp.91.62
Keywords: topology optimization, corner contacts, solid isotropic material with penalisation, extended optimality, exact solutions, tuning parameters, numerically calculated results.

Summary
The numerical results for finite element based optimal topologies of perforated plates in plane stress are one the most severe computational difficulties. The appearing checkerboard figures are based on square elements connected only through a corner node. Additional forms are the diagonal element chains or the isolated hinges [1]. It was shown [2,3] that both checkerboard patterns and diagonal chains may give an infinite compliance, if the latter is calculated by an exact analytical method. Thus using the exact analysis in compliance minimization will produce the worst possible solution.

Corner contacts may be suppressed by using a more accurate finite element analysis of ground elements in the optimization method for example using the extended Solid isotropic material with penalisation (SIMP) where four simple four-node finite elements are used per ground element and the total volume of the structure is minimized for a given compliance. If we know the exact analytical solution (containing an infinite number of cavities) then we can show that the numerical solution tends to the exact solution both in volume and in configuration.

The solutions of the applied extended-SIMP topology optimization method are strongly dependant on the choice of the so called tuning parameters e.g. compliance limit, number of elements, number of finite elements per ground element, position of the structure, etc. [4,5]. The main adjusting parameters are the element numbers; both for ground and for finite elements; and the compliance limit for displacement control. The paper presents the effects and opportunities of the increasing or changing of these main parameters with examples. The effect of many other listed tuning parameters is being studied and will be presented later.

The examples presented (e.g. Michell cantilever and Michell bicycle wheel) and the results affirm that the extended-SIMP method is able to present many optimal solutions for a given set. To determine which one is the real optimum additional adequate conditions are necessary.

References
1
V. Pomezanski, O.M. Querin, G.I.N. Rozvany, "CO-SIMP: extended SIMP algorithm with direct COrner COntact COntrol", Structural and Multidisciplinary Optimization, Springer, 30(2), 396-399, 2004. doi:10.1007/s00158-005-0514-4
2
G.I.N. Rozvany, O.M. Querin, Zs. Gáspár, V. Pomezanski, "Weight-increasing effect of topology simplification", Structural and Multidisciplinary Optimization, Springer, 25(5), 2003. doi:10.1007/s00158-003-0334-3
3
G.I.N. Rozvany, O.M. Querin, Zs. Gáspár, V. Pomezanski, "Extended optimality in topology design", G. Rozvany, (editor), Structural and Multidisciplinary Optimization, Springer, 24(3), 257-261, September 2002. doi:10.1007/s00158-002-0235-x
4
G.I.N. Rozvany, O.M. Querin, V. Pomezanski, Zs. Gáspár, J. Logo, "Some basic issues of topology optimization", IUTAM Symposium on Topological Design Optimization of Structures, Machines and Materials, Series of Solid Mechanics and Its Applications, M.P. Bendsoe, N. Olhoff, O. Sigmund, (editors), 137(2), 77-86, Springer, 2006. doi:10.1007/1-4020-4752-5_8
5
G.I.N. Rozvany, V. Pomezanski, Zs. Gáspár, O.M. Querin, "Some Pivotial Issues in Structural Optimization", 6th World Congress on Structural and Multidisciplinary Optimization (WCSMO6), Book of Abstracts and CD-ROM Proceedings, 147, Rio de Janeiro, 30 May-3 June 2005.

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