The focus of this paper is on consistent and accurate adjoint sensitivity analyses for structural topology optimization with anisotropic plastic materials under plane strain conditions. In order to avoid the locking issue, the Enhanced Assumed Strain (EAS) elements are adopted in the finite element discretization, and the anisotropic Hoffman plasticity model, which can simulate the strength differences in tension and compression, is incorporated within the framework of density-based topology optimization. The path-dependent sensitivity analysis is presented wherein the enhanced element parameters are consistently incorporated in the constraints. The objective of topology optimization is to maximize the plastic work. Several numerical examples are presented to show the effectiveness of the proposed framework. The results illustrate that the optimized topologies are highly dependent on the plastic anisotropic material properties.
Bitte loggen Sie sich ein, um Zugang zu diesem Inhalt zu erhalten
Sie möchten Zugang zu diesem Inhalt erhalten? Dann informieren Sie sich jetzt über unsere Produkte:
Springer Professional "Wirtschaft+Technik"
Online-Abonnement
Mit dem Kombi-Abo erhalten Sie vollen Zugriff auf über 1,8 Mio. Dokumente aus mehr als 61.000 Fachbüchern und rund 500 Fachzeitschriften aus folgenden Fachgebieten:
Mit dem Technik-Abo erhalten Sie Zugriff auf über 1 Mio. Dokumente aus mehr als 40.000 Fachbüchern und 300 Fachzeitschriften aus folgenden Fachgebieten:
Allaire G, Jouve F, Toader A-M (2004) Structural optimization using sensitivity analysis and a level-set method. J Comput Phys 194(1):363–393
MathSciNetCrossRefMATH
Armero F (2000) On the locking and stability of finite elements in finite deformation plane strain problems. Comput Struct 75(3):261–290. doi:
10.1016/S0045-7949(99)00136-4CrossRef
Banabic D (2010) Plastic Behaviour of Sheet Metal. In: Sheet Metal Forming Processes: Constitutive Modelling and Numerical Simulation. Springer Berlin Heidelberg, Berlin, Heidelberg, pp 27–140. doi: 10.1007/978-3-540-88113-1_2
Barlat F, Lian K (1989) Plastic behavior and stretchability of sheet metals. Part I: a yield function for orthotropic sheets under plane stress conditions. Int J Plast 5(1):51–66. doi:
10.1016/0749-6419(89)90019-3CrossRef
Bazeley G, Cheung YK, Irons BM, Zienkiewicz O Triangular elements in plate bending—conforming and nonconforming solutions. In: Proceedings of the Conference on Matrix Methods in Structural Mechanics, 1965. Wright Patterson AF Base, Ohio, pp 547–576
Bendsøe MP (1989) Optimal shape design as a material distribution problem. Struct Optim 1(4):193–202
CrossRef
Bendsøe MP, Kikuchi N (1988) Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Eng 71(2):197–224
MathSciNetCrossRefMATH
Bendsøe MP, Sigmund O (1999) Material interpolation schemes in topology optimization. Arch Appl Mech 69(9–10):635–654
MATH
Bendsøe MP, Sigmund O (2003) Topology optimization: theory, methods and applications, 2nd edn. Springer, Berlin
MATH
Bogomolny M, Amir O (2012) Conceptual design of reinforced concrete structures using topology optimization with elastoplastic material modeling. Int J Numer Methods Eng 90(13):1578–1597
CrossRefMATH
Bruggi M (2016a) A numerical method to generate optimal load paths in plain and reinforced concrete structures. Comput Struct 170:26–36
Bruggi M (2016b) Topology optimization with mixed finite elements on regular grids. Comput Methods Appl Mech Eng 305:133–153
Bruggi M, Cinquini C (2009) An alternative truly-mixed formulation to solve pressure load problems in topology optimization. Comput Methods Appl Mech Eng 198(17–20):1500–1512. doi:
10.1016/j.cma.2008.12.009CrossRefMATH
Bruggi M, Duysinx P (2012) Topology optimization for minimum weight with compliance and stress constraints. Struct Multidiscip Optim 46(3):369–384
MathSciNetCrossRefMATH
Bruggi M, Duysinx P (2013) A stress–based approach to the optimal design of structures with unilateral behavior of material or supports. Struct Multidiscip Optim 48(2):311–326
MathSciNetCrossRef
Bruggi M, Venini P (2008) A mixed FEM approach to stress-constrained topology optimization. Int J Numer Methods Eng 73(12):1693–1714. doi:
10.1002/nme.2138MathSciNetCrossRefMATH
Buhl T, Pedersen CB, Sigmund O (2000) Stiffness design of geometrically nonlinear structures using topology optimization. Struct Multidiscip Optim 19(2):93–104
CrossRef
Christensen PW, Klarbring A (2008) An introduction to structural optimization, vol 153. Springer Science & Business Media
Crisfield M (1997) Non-linear finite element analysis of solids and structures: Volume 1 Essentials. John Wiley & Sons
De Borst R, Feenstra PH (1990) Studies in anisotropic plasticity with reference to the Hill criterion. Int J Numer Methods Eng 29(2):315–336
CrossRefMATH
de Souza Neto EA, Peric D, Owen DRJ (2011) Computational methods for plasticity: theory and applications. John Wiley & Sons
Deaton JD, Grandhi RV (2014) A survey of structural and multidisciplinary continuum topology optimization: post 2000. Struct Multidiscip Optim 49(1):1–38
MathSciNetCrossRef
Eschenauer HA, Olhoff N (2001) Topology optimization of continuum structures: a review*. Appl Mech Rev 54(4):331–390
CrossRef
Glaser S, Armero F (1997) On the formulation of enhanced strain finite elements in finite deformations. Eng Comput 14(7):759–791. doi:
10.1108/02644409710188664CrossRefMATH
Hashagen F, de Borst R (2001) Enhancement of the Hoffman yield criterion with an anisotropic hardening model. Comput Struct 79(6):637–651. doi:
10.1016/S0045-7949(00)00164-4CrossRef
Jang G-W, Kim YY (2009) Topology optimization with displacement-based nonconforming finite elements for incompressible materials. J Mech Sci Technol 23(2):442–451. doi:
10.1007/s12206-008-1114-1CrossRef
Jones RM (1998) Mechanics of composite materials. CRC press
Kasper EP, Taylor RL (1997) A Mixed Enhanced Strain Method: Linear Problems Department of Civil and Environmental Engineering, University of California at Berkeley; Report No.: UCB/SEMM-97/02, Berkeley
Kasper EP, Taylor RL (2000) A mixed-enhanced strain method: part I: geometrically linear problems. Comput Struct 75(3):237–250. doi:
10.1016/S0045-7949(99)00134-0CrossRef
Kato J, Hoshiba H, Takase S, Terada K, Kyoya T (2015) Analytical sensitivity in topology optimization for elastoplastic composites. Struct Multidiscip Optim 52(3):507–526
MathSciNetCrossRef
Kiran R, Li L, Khandelwal K (2015) Performance of cubic convergent methods for implementing nonlinear constitutive models. Comput Struct 156:83–100. doi:
10.1016/j.compstruc.2015.04.011CrossRef
Klarbring A, Strömberg N (2013) Topology optimization of hyperelastic bodies including non-zero prescribed displacements. Struct Multidiscip Optim 47(1):37–48
MathSciNetCrossRefMATH
Koh CG, Owen DRJ, Perić D (1995) Explicit dynamic analysis of elasto-plastic laminated composite shells: implementation of non-iterative stress update schemes for the Hoffman yield criterion. Comput Mech 16(5):307–314. doi:
10.1007/bf00350720CrossRefMATH
Korelc J, Wriggers P (1996) An efficient 3D enhanced strain element with Taylor expansion of the shape functions. Comput Mech 19(2):30–40. doi:
10.1007/bf02757781CrossRefMATH
Li L, Khandelwal K (2014) Two-point gradient-based MMA (TGMMA) algorithm for topology optimization. Comput Struct 131:34–45
CrossRef
Li L, Khandelwal K (2015a) Topology optimization of structures with length-scale effects using elasticity with microstructure theory. Comput Struct 157:165–177
Li L, Khandelwal K (2015b) Volume preserving projection filters and continuation methods in topology optimization. Eng Struct 85:144–161
Li X, Duxbury PG, Lyons P (1994) Considerations for the application and numerical implementation of strain hardening with the hoffman yield criterion. Comput Struct 52(4):633-644. doi:
10.1016/0045-7949(94)90345-X
Lindgaard E, Dahl J (2013) On compliance and buckling objective functions in topology optimization of snap-through problems. Struct Multidiscip Optim 47(3):409–421
MathSciNetCrossRefMATH
Luo Y, Kang Z (2012) Topology optimization of continuum structures with Drucker–Prager yield stress constraints. Comput Struct 90:65–75
CrossRef
Maute K, Schwarz S, Ramm E (1998) Adaptive topology optimization of elastoplastic structures. Struct Optim 15(2):81–91
CrossRef
Michaleris P, Tortorelli DA, Vidal CA (1994) Tangent operators and design sensitivity formulations for transient non‐linear coupled problems with applications to elastoplasticity. Int J Numer Methods Eng 37(14):2471–2499
CrossRefMATH
Nakshatrala P, Tortorelli D (2015) Topology optimization for effective energy propagation in rate-independent elastoplastic material systems. Comput Methods Appl Mech Eng 295:305–326
MathSciNetCrossRef
Rozvany G, Zhou M (1991) Applications of the COC algorithm in layout optimization. In: Engineering optimization in design processes. Springer, pp 59–70
Schellekens JCJ, de Borst R (1990) The use of the Hoffman yield criterion in finite element analysis of anisotropic composites. Comput Struct 37(6):1087–1096. doi:
10.1016/0045-7949(90)90020-3CrossRef
Schwarz S, Ramm E (2001) Sensitivity analysis and optimization for non-linear structural response. Eng Comput 18(3/4):610–641
CrossRefMATH
Schwarz S, Maute K, Ramm E (2001) Topology and shape optimization for elastoplastic structural response. Comput Methods Appl Mech Eng 190(15):2135–2155
CrossRefMATH
Sigmund O, Clausen PM (2007) Topology optimization using a mixed formulation: an alternative way to solve pressure load problems. Comput Methods Appl Mech Eng 196(13–16):1874–1889. doi:
10.1016/j.cma.2006.09.021MathSciNetCrossRefMATH
Sigmund O, Maute K (2013) Topology optimization approaches. Struct Multidiscip Optim 48(6):1031–1055
MathSciNetCrossRef
Sigmund O, Petersson J (1998) Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Struct Optim 16(1):68–75
CrossRef
Simo JC, Armero F (1992) Geometrically non-linear enhanced strain mixed methods and the method of incompatible modes. Int J Numer Methods Eng 33(7):1413–1449. doi:
10.1002/nme.1620330705CrossRefMATH
Simo JC, Rifai MS (1990) A class of mixed assumed strain methods and the method of incompatible modes. Int J Numer Methods Eng 29(8):1595–1638. doi:
10.1002/nme.1620290802MathSciNetCrossRefMATH
Simo JC, Armero F, Taylor RL (1993) Improved versions of assumed enhanced strain tri-linear elements for 3D finite deformation problems. Comput Methods Appl Mech Eng 110(3):359–386. doi:
10.1016/0045-7825(93)90215-JCrossRefMATH
Svanberg K (1987) The method of moving asymptotes- a new method for structural optimization. Int J Numer Methods Eng 24(2):359–373
MathSciNetCrossRefMATH
Wallin M, Jönsson V, Wingren E (2016) Topology optimization based on finite strain plasticity. Structural and Multidisciplinary Optimization: 1–11
Wang MY, Wang X, Guo D (2003) A level set method for structural topology optimization. Comput Methods Appl Mech Eng 192(1):227–246
MathSciNetCrossRefMATH
Wilson E, Taylor R, Doherty W, Ghaboussi J (1973) Incompatible displacement models. In: Fenves S, Perrone N, Robinson A, Schnobrich W (eds) Numerical and computer methods in structural mechanics. Academic, New York, pp 43–57
Xie Y, Steven GP (1993) A simple evolutionary procedure for structural optimization. Comput Struct 49(5):885–896
CrossRef
Über diesen Artikel
Titel
Topology optimization of structures with anisotropic plastic materials using enhanced assumed strain elements
Die B2B-Firmensuche für Industrie und Wirtschaft: Kostenfrei in Firmenprofilen nach Lieferanten, Herstellern, Dienstleistern und Händlern recherchieren.
Lesen Sie in diesem ausgewählten Buchkapitel alles über den 3D-Druck im Hinblick auf Begriffe, Funktionsweise, Anwendungsbereiche sowie Nutzen und Grenzen additiver Fertigungsverfahren. Eigenschaften eines schlanken Produktionssystems sowie der Aspekt der „Schlankheit“ werden ebenso beleuchtet wie die Prinzipien und Methoden der Lean Production. Jetzt gratis downloaden!
Marktübersichten
Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.
