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Abstrakty
This paper sets out to describe a multi-constrained approach to topology optimization of structures. In the optimization, a constant criterion surface algorithm and the multi-constraint procedure is used. The multi-constraint procedure consists of constraints normalization and equivalent design space assembling. The work is illustrated by an example of the L-shaped domain optimization with the horizontal line support and complex loads. The example takes into consideration stress, fatigue and compliance constraints. The separate and simultaneous application of constraints resulted in significant differences in structure topology layouts. The application of a fatigue constraint gave more conservative results when compared to static stress or compliance limitations. The multi-constrained approach allowed effectively lowering the mass of the structure while satisfying all constraints.
Rocznik
Tom
Strony
229--236
Opis fizyczny
Bibliogr. 33 poz., rys.
Twórcy
autor
- Institute of Rail Vehicles, Cracow University of Technology, 37 Jana Pawła II Ave., 31-864 Kraków, Poland, mrzyglod@mech.pk.edu.pl
Bibliografia
- [1] M. Zhou and G.I.N. Rozvany, “The COC algorithm. Part II: topological, geometrical and generalized shape optimization”, Comp. Meth. Appl. Eng. 89, 309–336 (1991).
- [2] Y.M. Xie and G.P. Steven, “A simple evolutionary procedure for structural optimization”, Comput. Struct. 49, 885–896 (1993).
- [3] M. Bendsoe and O. Sigmund, Topology Optimization. Theory, Methods, and Applications, Springer, New York, 2003.
- [4] B. Desmorat and R. Desmorat, “Topology optimization in damage governed low cycle fatigue”, Mecanique 336, 448–453 (2008).
- [5] M. Mrzyglod, “Multiaxial HCF and LCF constraints in topology optimization”, Proc 9-th Int Conf on Multiaxial Fatigue & Fracture 1, 803–810 (2010).
- [6] P. Honarmandi, J.W. Zu, and K. Behdinan, “Reliability-based design optimization of cantilever beams under fatigue constraint”, AIAA J. 45 (11), 2737–2746 (2007).
- [7] M. Bruggi and P. Venini, “A mixed FEM approach to stressconstrained topology optimization”, Int. J. Num. Meth. Eng. 73 (12), 1693–1714 (2008)
- [8] S. Min S. Nishiwaki, and N. Kikuchi, “Unified topology design of static and vibrating structures using multiobjective optimization”, Computers and Structures 75, 93–116 (2000).
- [9] D.-C. Lee, HS. Choi, and C.S. Han, “Design of automotive body structure using multicriteria optimization”, Struc. Multidisc. Optim. 32 (2), 161–167 (2006).
- [10] A. Ramani, “Multi-material topology optimization with strength constraints”, Struc. Multidisc. Optim. 43, 597–615 (2011).
- [11] C. Mattheck and S. Burkhardt, “A new method of structural shape optimisation based on biological growth”, Int. J. Fatigue 12 (3), 185–190 (1990)
- [12] Z. Wasiutyński, “On the congruency of the forming according to the minimum potential energy with that according to equal strength”, Bull. Pol. Ac.: Tech. 8 (6), 259–268 (1960)
- [13] Z. Mróz, “On a problem of minimum weight design”, Q. Appl. Math. 19, 127–135 (1961).
- [14] A.M. Brandt, Criteria and Methods of Structural Optimization, PWN, Warszawa, 1984.
- [15] K. Dems and Z. Mróz, “Multiparameter structural shape optimization by finite element method”, Int. J. Num. Meth. Eng. 13, 247–263 (1978).
- [16] O.M. Querin, G.P. Steven, and Y.M. Xie, “Evolutionary structural optimization (ESO) using bidirectional algorithm”, Eng. Comp. 15, 1031–104 (1998).
- [17] M. Mrzyglod, “Using layer expansion algorithm in topology optimization with stress constraints”, Proc. CMM-2009 – Computer Methods in Mechanics 1, 319–320 (2009).
- [18] S. Kirkpatrick, C.D. Gelatt, and M.P. Vecchi, “Optimization by simulated annealing”, Science 220, 671–680 (1983).
- [19] M. Nowak, “Structural optimization system based on trabecular bone surface adaptation”, Struc. Multidisc. Optim. 32 (3), 241–249 (2006).
- [20] A. Tovar, N.M. Patel, G.L. Niebur, M. Sen, and J.E. Renaud, “Topology optimization using a hybrid cellular automaton method with local control rules”, ASME J. Mechanical Design 128 (6), 1205–1216 (2006)
- [21] B. Bochenek and K. Tajs-Zielińska, “Novel local rules of cellular automata applied to topology and size optimization”, Eng. Optimization 44 (1), 23–25 (2012).
- [22] M. Mrzyglod, “Two-stage optimization method with fatigue constraints for thin-walled structures”, J. Theoretical and Applied Mechanics 48 (3), 567–578 (2010).
- [23] M. Matsuishi and T. Endo, “Fatigue of metals subjected to varying stress-fatigue lives under random loading”, Proc. Kyushu District Meeting, JSEM 1, 37–40 (1968).
- [24] G.I.N. Rozvany “Exact analytical solutions for some popular benchmark problems in topology optimization”, Struct. Optim. 15, 42–48 (1998).
- [25] T. Lewiński and G.I.N. Rozvany, “Exact analytical solutions for some popular benchmark problems in topology optimization III: L-shaped domains”, Struct. Multidisc. Optim. 35, 165–174 (2008).
- [26] T. Lewiński and G.I.N. Rozvany, “Analytical benchmarks for topology optimization IV: square-shaped line support”, Struct. Multidisc. Optim. 36, 143–158 (2008).
- [27] T. Sokół and T. Lewiński, “On the solution of the three forces problem and its application to optimal designing of a certain class of symmetric plane frameworks of least weight”, Struct. Multidisc. Optim. 42, 835–853 (2010).
- [28] H.A. Eschenauer and N. Olhoff, “Topology optimization of continuum structures: a review”, Applied Mechanics Reviews 54 (4), 331–389 (2001).
- [29] M. Bendsoe and O. Sigmund, Topology Optimization. Theory, Methods, and Applications, Springer, New York, 2003.
- [30] G. Chiandussi, “On the solution of a minimum compliance topology optimisation problem by optimality criteria without a priori volume constraint specification”, Comput. Mech. 38, 77–99 (2006).
- [31] A. Ramani, “Multi-material topology optimization with strength constraints”, Struct. Multidisc. Optim. 43, 597–615 (2011).
- [32] K. Dang Van, B. Griveau, and O. Message, “On a new multiaxial fatigue limit criterion: theory and application”, in Biaxial and Multiaxial Fatigue, pp. 479–496, Mechanical Engineering Publications, London, 1989.
- [33] M. Mrzyglod, “Multiaxial HCF and LCF constraints in topology optimization”, Proc. 9-th Int. Conf. on Multiaxial Fatigue & Fracture, ICMFF9 1, 803–809 (2010).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPG8-0078-0006