Multi-constrained topology optimization using constant criterion surface algorithm

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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.

[1] M. Zhou and G.I.N. Rozvany, “The COC algorithm. Part II: topological, geometrical and generalized shape optimization”, Comp. Meth. Appl. Eng.

[2] Y.M. Xie and G.P. Steven, “A simple evolutionary procedure for structural optimization”, (1993).

[3] M. Bendsoe and O. Sigmund, Topology Optimization. Theory,Methods, and Applications

[4] B. Desmorat and R. Desmorat, “Topology optimization in damage governed low cycle fatigue”, (2008).

[5] M. Mrzyglod, “Multiaxial HCF and LCF constraints in topology optimization”, Fracture

[6] P. Honarmandi, J.W. Zu, and K. Behdinan, “Reliability-based design optimization of cantilever beams under fatigue constraint”, AIAA J.

[7] M. Bruggi and P. Venini, “A mixed FEM approach to stressconstrained topology optimization”, (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

[9] D.-C. Lee, HS. Choi, and C.S. Han, “Design of automotive body structure using multicriteria optimization”, Optim.

[10] A. Ramani, “Multi-material topology optimization with strength constraints”, (2011).

[11] C. Mattheck and S. Burkhardt, “A new method of structural shape optimisation based on biological growth”, 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”,

[13] Z. Mroz, “On a problem of minimum weight design”, Q. Appl.Math.

[14] A.M. Brandt, Criteria and Methods of Structural Optimization, PWN, Warszawa, 1984.

[15] K. Dems and Z. Mroz, “Multiparameter structural shape optimization by finite element method”, 13, 247-263 (1978).

[16] O.M. Querin, G.P. Steven, and Y.M. Xie, “Evolutionary structural optimization (ESO) using bidirectional algorithm”, Comp.

[17] M. Mrzyglod, “Using layer expansion algorithm in topology optimization with stress constraints”, Methods in Mechanics

[18] S. Kirkpatrick, C.D. Gelatt, and M.P. Vecchi, “Optimization by simulated annealing”,

[19] M. Nowak, “Structural optimization system based on trabecular bone surface adaptation”, 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”, Design

[21] B. Bochenek and K. Tajs-Zielińska, “Novel local rules of cellular automata applied to topology and size optimization”, Optimization

[22] M. Mrzyglod, “Two-stage optimization method with fatigue constraints for thin-walled structures”, Mechanics

[23] M. Matsuishi and T. Endo, “Fatigue of metals subjected to varying stress-fatigue lives under random loading”, Kyushu District Meeting, JSEM

[24] G.I.N. Rozvany “Exact analytical solutions for some popular benchmark problems in topology optimization”, 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”, (2008).

[26] T. Lewiński and G.I.N. Rozvany, “Analytical benchmarks for topology optimization IV: square-shaped line support”, Multidisc. Optim.

[27] T. Sokoł 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”, Multidisc. Optim.

[28] H.A. Eschenauer and N. Olhoff, “Topology optimization of continuum structures: a review”, 54 (4), 331-389 (2001).

[29] M. Bendsoe and O. Sigmund, Topology Optimization. Theory,Methods, and Applications

[30] G. Chiandussi, “On the solution of a minimum compliance topology optimisation problem by optimality criteria without a priori volume constraint specification”, 77-99 (2006).

[31] A. Ramani, “Multi-material topology optimization with strength constraints”, (2011).

[32] K. Dang Van, B. Griveau, and O. Message, “On a new multiaxial fatigue limit criterion: theory and application”, in and Multiaxial Fatigue, Publications, London, 1989.

[33] M. Mrzyglod, “Multiaxial HCF and LCF constraints in topology optimization”, & Fracture, ICMFF9

Bulletin of the Polish Academy of Sciences Technical Sciences

The Journal of Polish Academy of Sciences

Journal Information

IMPACT FACTOR 2016: 1.156
5-year IMPACT FACTOR: 1.238

CiteScore 2016: 1.50

SCImago Journal Rank (SJR) 2016: 0.457
Source Normalized Impact per Paper (SNIP) 2016: 1.239


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