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Erschienen in: Structural and Multidisciplinary Optimization 4/2014

01.04.2014 | RESEARCH PAPER

Topology optimization of fail-safe structures using a simplified local damage model

verfasst von: Miche Jansen, Geert Lombaert, Mattias Schevenels, Ole Sigmund

Erschienen in: Structural and Multidisciplinary Optimization | Ausgabe 4/2014

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Abstract

Topology optimization of mechanical structures often leads to efficient designs which resemble statically determinate structures. These economical structures are especially vulnerable to local loss of stiffness due to material failure. This paper therefore addresses local failure of continuum structures in topology optimization in order to design fail-safe structures which remain operable in a damaged state.
A simplified model for local failure in continuum structures is adopted in the robust approach. The complex phenomenon of local failure is modeled by removal of material stiffness in patches with a fixed shape. The damage scenarios are taken into account by means of a minimax formulation of the optimization problem which minimizes the worst case performance.
The detrimental influence of local failure on the nominal design is demonstrated in two representative examples: a cantilever beam optimized for minimum compliance and a compliant mechanism. The robust approach is applied successfully in the design of fail-safe alternatives for the structures in these examples.

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Literatur
Zurück zum Zitat Achtziger W (1999) Optimal topology design of discrete structures resisting degradation effects. Struct Multidiscip Optim 17:74–78CrossRef Achtziger W (1999) Optimal topology design of discrete structures resisting degradation effects. Struct Multidiscip Optim 17:74–78CrossRef
Zurück zum Zitat Akgün M, Garcelon J, Haftka R (2001) Fast exact linear and non-linear structural reanalysis and the Sherman-Morrison-Woodbury formulas. Int J Numer Methods Eng 50(7):1587–1606MATHCrossRef Akgün M, Garcelon J, Haftka R (2001) Fast exact linear and non-linear structural reanalysis and the Sherman-Morrison-Woodbury formulas. Int J Numer Methods Eng 50(7):1587–1606MATHCrossRef
Zurück zum Zitat Amir O, Sigmund O (2011) On reducing computational effort in topology optimization: how far can we go? Struct Multidiscip Optim 44:25–29MATHCrossRef Amir O, Sigmund O (2011) On reducing computational effort in topology optimization: how far can we go? Struct Multidiscip Optim 44:25–29MATHCrossRef
Zurück zum Zitat Amir O, Stolpe M, Sigmund O (2010) Efficient use of iterative solvers in nested topology optimization. Struct Multidiscip Optim 42:55–72MATHCrossRef Amir O, Stolpe M, Sigmund O (2010) Efficient use of iterative solvers in nested topology optimization. Struct Multidiscip Optim 42:55–72MATHCrossRef
Zurück zum Zitat Amir O, Sigmund O, Lazarov BS, Schevenels M (2012) Efficient reanalysis techniques for robust topology optimization. Comput Methods Appl Mech Eng 245–246(0):217–231MathSciNetCrossRef Amir O, Sigmund O, Lazarov BS, Schevenels M (2012) Efficient reanalysis techniques for robust topology optimization. Comput Methods Appl Mech Eng 245–246(0):217–231MathSciNetCrossRef
Zurück zum Zitat Arnout S, Firl M, Bletzinger KU (2012) Parameter free shape and thickness optimisation considering stress response. Struct Multidiscip Optim 45:801–814MATHCrossRef Arnout S, Firl M, Bletzinger KU (2012) Parameter free shape and thickness optimisation considering stress response. Struct Multidiscip Optim 45:801–814MATHCrossRef
Zurück zum Zitat Arora J, Govil A, Haskell D (1980) Optimal design of large structures for damage tolerance. AIAA Journal 18:563–570CrossRef Arora J, Govil A, Haskell D (1980) Optimal design of large structures for damage tolerance. AIAA Journal 18:563–570CrossRef
Zurück zum Zitat Ben-Tal A, El Ghaoui L, Nemirovski A (2009) Robust optimization. Princeton Series in Applied Mathematics, Princeton University, Princeton Ben-Tal A, El Ghaoui L, Nemirovski A (2009) Robust optimization. Princeton Series in Applied Mathematics, Princeton University, Princeton
Zurück zum Zitat Bendsøe M (1989) Optimal shape design as a material distribution problem. Struct Multidiscip Optim 1:193–202CrossRef Bendsøe M (1989) Optimal shape design as a material distribution problem. Struct Multidiscip Optim 1:193–202CrossRef
Zurück zum Zitat Bendsøe M, Díaz A (1998) A method for treating damage related criteria in optimal topology design of continuum structures. Struct Multidiscip Optim 16:108–115CrossRef Bendsøe M, Díaz A (1998) A method for treating damage related criteria in optimal topology design of continuum structures. Struct Multidiscip Optim 16:108–115CrossRef
Zurück zum Zitat Bendsøe M, Sigmund O (2004) Topology optimization: theory, Methods and Applications, 2nd. Springer, Berlin Bendsøe M, Sigmund O (2004) Topology optimization: theory, Methods and Applications, 2nd. Springer, Berlin
Zurück zum Zitat Beyer H, Sendhoff B (2007) Robust optimization–A comprehensive survey. Comput Methods Appl Mech Eng 196(33–34):3190–3218MATHMathSciNetCrossRef Beyer H, Sendhoff B (2007) Robust optimization–A comprehensive survey. Comput Methods Appl Mech Eng 196(33–34):3190–3218MATHMathSciNetCrossRef
Zurück zum Zitat Bruns T, Tortorelli D (2001) Topology optimization of non-linear elastic structures and compliant mechanisms. Comput Methods Appl Mech Eng 190(26–27):3443–3459MATHCrossRef Bruns T, Tortorelli D (2001) Topology optimization of non-linear elastic structures and compliant mechanisms. Comput Methods Appl Mech Eng 190(26–27):3443–3459MATHCrossRef
Zurück zum Zitat Diehl M, Bock H, Kostina E (2006) An approximation technique for robust nonlinear optimization. Math Program 107(1):213–230MATHMathSciNetCrossRef Diehl M, Bock H, Kostina E (2006) An approximation technique for robust nonlinear optimization. Math Program 107(1):213–230MATHMathSciNetCrossRef
Zurück zum Zitat Feng Y (1988) The theory of structural redundancy and its effect on structural design. Comput Struct 28(1):15–24CrossRef Feng Y (1988) The theory of structural redundancy and its effect on structural design. Comput Struct 28(1):15–24CrossRef
Zurück zum Zitat Feng Y, Moses F (1986) Optimum design, redundancy and reliability of structural systems. Comput Struct 24(2):239–251CrossRef Feng Y, Moses F (1986) Optimum design, redundancy and reliability of structural systems. Comput Struct 24(2):239–251CrossRef
Zurück zum Zitat Frangopol D, Curley J (1987) Effects of damage and redundancy on structural reliability. J Struct Eng 113(7):1533–1549CrossRef Frangopol D, Curley J (1987) Effects of damage and redundancy on structural reliability. J Struct Eng 113(7):1533–1549CrossRef
Zurück zum Zitat Guest J, Prevost J, Belytschko T (2004) Achieving minimum length scale in topology optimization using nodal design variables and projection functions. Int J Numer Methods Eng 61(2):238–254MATHMathSciNetCrossRef Guest J, Prevost J, Belytschko T (2004) Achieving minimum length scale in topology optimization using nodal design variables and projection functions. Int J Numer Methods Eng 61(2):238–254MATHMathSciNetCrossRef
Zurück zum Zitat Kanno Y, Ben-Haim Y (2011) Redundancy and robustness, or when is redundancy redundant? J Struct Eng 137(9):935–945CrossRef Kanno Y, Ben-Haim Y (2011) Redundancy and robustness, or when is redundancy redundant? J Struct Eng 137(9):935–945CrossRef
Zurück zum Zitat Kim T, Kim J, Jeong J, Kim Y (2004) Filtering technique to control member size in topology design optimization. J MechSci Technol 18:253–261 Kim T, Kim J, Jeong J, Kim Y (2004) Filtering technique to control member size in topology design optimization. J MechSci Technol 18:253–261
Zurück zum Zitat Kreisselmeier G, Steinhauser R (1983) Application of vector performance optimization to a robust control loop design for a fighter aircraft. Int J Control 37(2):251–284MATHCrossRef Kreisselmeier G, Steinhauser R (1983) Application of vector performance optimization to a robust control loop design for a fighter aircraft. Int J Control 37(2):251–284MATHCrossRef
Zurück zum Zitat Lazarov B, Schevenels M, Sigmund O (2012) Topology optimization with geometric uncertainties by perturbation techniques. Int Journal Numer Methods Eng 90(11):1321–1336MATHCrossRef Lazarov B, Schevenels M, Sigmund O (2012) Topology optimization with geometric uncertainties by perturbation techniques. Int Journal Numer Methods Eng 90(11):1321–1336MATHCrossRef
Zurück zum Zitat Ma D, Braatz R (2001) Worst-case analysis of finite-time control policies. Control Syst Technol IEEE Trans on 9(5):766–774CrossRef Ma D, Braatz R (2001) Worst-case analysis of finite-time control policies. Control Syst Technol IEEE Trans on 9(5):766–774CrossRef
Zurück zum Zitat Marhadi K, Venkataraman S (2009) Surrogate measures to optimize structures for robust and predictable progressive failure. Struct Multidiscip Optim 39:245–261CrossRef Marhadi K, Venkataraman S (2009) Surrogate measures to optimize structures for robust and predictable progressive failure. Struct Multidiscip Optim 39:245–261CrossRef
Zurück zum Zitat Marhadi K, Venkataraman S, Wong S (2011) Load redistribution mechanism in damage tolerant and redundant truss structure. Struct Multidiscip Optim 44:213–233CrossRef Marhadi K, Venkataraman S, Wong S (2011) Load redistribution mechanism in damage tolerant and redundant truss structure. Struct Multidiscip Optim 44:213–233CrossRef
Zurück zum Zitat Martins J, Poon N (2005) On structural optimization using constraint aggregation In: 6th World Congress on Structural and Multidisciplinary Optimization. Rio de Janeiro, Brazil Martins J, Poon N (2005) On structural optimization using constraint aggregation In: 6th World Congress on Structural and Multidisciplinary Optimization. Rio de Janeiro, Brazil
Zurück zum Zitat Poulsen T (2003) A new scheme for imposing a minimum length scale in topology optimization. Int J Numer Methods Eng 57(6):741–760MATHMathSciNetCrossRef Poulsen T (2003) A new scheme for imposing a minimum length scale in topology optimization. Int J Numer Methods Eng 57(6):741–760MATHMathSciNetCrossRef
Zurück zum Zitat Rozvany G (2009) A critical review of established methods of structural topology optimization. Struct Multidiscip Optim 37:217–237MATHMathSciNetCrossRef Rozvany G (2009) A critical review of established methods of structural topology optimization. Struct Multidiscip Optim 37:217–237MATHMathSciNetCrossRef
Zurück zum Zitat Schevenels M, Lazarov B, Sigmund O (2011) Robust topology optimization accounting for spatially varying manufacturing errors. Comput Methods Appl Mech Eng 200(49-52):3613–3627MATHCrossRef Schevenels M, Lazarov B, Sigmund O (2011) Robust topology optimization accounting for spatially varying manufacturing errors. Comput Methods Appl Mech Eng 200(49-52):3613–3627MATHCrossRef
Zurück zum Zitat Sebastian W (2004) Collapse considerations and electrical analogies for statically indeterminate structures. J Struct Eng 130(10):1445–1453CrossRef Sebastian W (2004) Collapse considerations and electrical analogies for statically indeterminate structures. J Struct Eng 130(10):1445–1453CrossRef
Zurück zum Zitat Sigmund O (1997) On the design of compliant mechanisms using topology optimization. Mech Struct Mach 25(4):493–524CrossRef Sigmund O (1997) On the design of compliant mechanisms using topology optimization. Mech Struct Mach 25(4):493–524CrossRef
Zurück zum Zitat Sigmund O (2007) Morphology-based black and white filters for topology optimization. Struct Multidiscip Optim 33(4–5):401–424CrossRef Sigmund O (2007) Morphology-based black and white filters for topology optimization. Struct Multidiscip Optim 33(4–5):401–424CrossRef
Zurück zum Zitat Sørensen J, Rizzuto E, Narasimhan H, Faber M (2012) Robustness: theoretical framework. Struct Eng Int 22(1):66–72CrossRef Sørensen J, Rizzuto E, Narasimhan H, Faber M (2012) Robustness: theoretical framework. Struct Eng Int 22(1):66–72CrossRef
Zurück zum Zitat Svanberg K (1987) The method of moving asymptotes – A new method for structural optimization. Int J Numer Methods Eng 24:359–373MATHMathSciNetCrossRef Svanberg K (1987) The method of moving asymptotes – A new method for structural optimization. Int J Numer Methods Eng 24:359–373MATHMathSciNetCrossRef
Zurück zum Zitat Tempo R, Calafiore G, Dabbene F (2013) Randomized Algorithms for Analysis and Control of Uncertain Systems Communications and Control Engineering, 2nd. Springer-Verlag Tempo R, Calafiore G, Dabbene F (2013) Randomized Algorithms for Analysis and Control of Uncertain Systems Communications and Control Engineering, 2nd. Springer-Verlag
Zurück zum Zitat Vrouwenvelder T, Leira B, Sykora M (2012) Modelling of hazards. Struct Eng Int 22(1):73–78CrossRef Vrouwenvelder T, Leira B, Sykora M (2012) Modelling of hazards. Struct Eng Int 22(1):73–78CrossRef
Zurück zum Zitat Wang F, Lazarov B, Sigmund O (2011) On projection methods, convergence and robust formulations in topology optimization. Struct Multidiscip Optim 43:767–784MATHCrossRef Wang F, Lazarov B, Sigmund O (2011) On projection methods, convergence and robust formulations in topology optimization. Struct Multidiscip Optim 43:767–784MATHCrossRef
Zurück zum Zitat Zhou M, Rozvany G (1991) The COC algorithm, part II: Topological, geometrical and generalized shape optimizations. Comput Methods Appl Mech Eng 89(1-3):309–336CrossRef Zhou M, Rozvany G (1991) The COC algorithm, part II: Topological, geometrical and generalized shape optimizations. Comput Methods Appl Mech Eng 89(1-3):309–336CrossRef
Metadaten
Titel
Topology optimization of fail-safe structures using a simplified local damage model
verfasst von
Miche Jansen
Geert Lombaert
Mattias Schevenels
Ole Sigmund
Publikationsdatum
01.04.2014
Verlag
Springer Berlin Heidelberg
Erschienen in
Structural and Multidisciplinary Optimization / Ausgabe 4/2014
Print ISSN: 1615-147X
Elektronische ISSN: 1615-1488
DOI
https://doi.org/10.1007/s00158-013-1001-y

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