Skip to main content
SpringerLink
Log in

Reinforcement layout design for concrete structures based on continuum damage and truss topology optimization

  • Research Paper
  • Published:
Structural and Multidisciplinary Optimization Aims and scope Submit manuscript

Abstract

This article presents a new procedure for the layout design of reinforcement in concrete structures. Concrete is represented by a gradient-enhanced continuum damage model with strain-softening and reinforcement is modeled as elastic bars that are embedded into the concrete domain. Adjoint sensitivity analysis is derived in complete consistency with respect to path-dependency and the nonlocal model. Classical truss topology optimization based on the ground structure approach is applied to determine the optimal topology and cross-sections of the reinforcement bars. This approach facilitates a fully digital work flow that can be highly effective, especially for the design of complex structures. Several test cases involving two- and three-dimensional concrete structures illustrate the capabilities of the proposed procedure.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17

Similar content being viewed by others

References

  • Batoz JL, Dhatt G (1979) Incremental displacement algorithms for nonlinear problems. Int J Numer Methods Eng 14:1262–1267

    Article  MathSciNet  MATH  Google Scholar 

  • Bažant ZP, Belytschko TB, Chang T (1984) Continuum theory for strain-softening. ASCE J Eng Mech 110(12):1666–1692

    Article  Google Scholar 

  • Bendsøe MP (1989) Optimal shape design as a material distribution problem. Struct Optim 1:193–202

    Article  Google Scholar 

  • Bendsøe MP, Sigmund O (2003) Topology optimization—theory, methods and applications. Springer, Berlin

    Google Scholar 

  • Bogomolny M, Amir O (2012) Conceptual design of reinforced concrete structures using topology optimization with elasto-plastic material modeling. Int J Numer Methods Eng 90(13):1578–1597. doi:10.1002/nme.4253

    Article  MATH  Google Scholar 

  • Bruggi M (2009) Generating strut-and-tie patterns for reinforced concrete structures using topology optimization. Comput Struct 87(23–24):1483–1495

    Article  Google Scholar 

  • Červenka J, Papanikolaou VK (2008) Three dimensional combined fracture-plastic material model for concrete. Int J Plast 24(12):2192–2220

    Article  MATH  Google Scholar 

  • Chang T, Taniguchi H, Chen W (1987) Nonlinear finite element analysis of reinforced concrete panels. ASCE J Struct Eng 113:122–140

    Article  Google Scholar 

  • Dombernowsky P, Søndergaard A (2009) Three-dimensional topology optimisation in architectural and structural design of concrete structures. In: Proceedings of the International Association for Shell and Spatial Structures (IASS) symposium, Valencia, Spain

  • Drucker DC, Prager W (1952) Soil mechanics and plastic analysis or limit design. Q Appl Math 10(2):157–165

    MathSciNet  MATH  Google Scholar 

  • Feenstra PH, de Borst R (1996) A composite plasticity model for concrete. Int J Solids Struct 33:707–730

    Article  MATH  Google Scholar 

  • fib Task Group 44 (2008) Practitioners’ guide to finite element modelling of reinforced concrete structures. International Federation for Structural Concrete (fib), Lausanne, Switzerland

  • Kato J, Ramm E (2010) Optimization of fiber geometry for fiber reinforced composites considering damage. Finite Elem Anal Des 46(5):401–415

    Article  Google Scholar 

  • Kato J, Lipka A, Ramm E (2009) Multiphase material optimization for fiber reinforced composites with strain softening. Struct Multidisc Optim 39(1):63–81

    Article  Google Scholar 

  • Kwak HG, Noh SH (2006) Determination of strut-and-tie models using evolutionary structural optimization. Eng Struct 28(10):1440–1449

    Article  Google Scholar 

  • Lemaître J, Desmorat R (2005) Engineering damage mechanics. Springer, Berlin

    Google Scholar 

  • Liang Q, Xie Y, Steven G (2000) Topology optimization of strut-and-tie models in reinforced concrete structures using an evolutionary procedure. ACI Struct J 97(2):322–330

    Google Scholar 

  • Lubliner J, Oliver J, Oller S, Oñate E (1989) A plastic-damage model for concrete. Int J Solids Struct 25:299–326

    Article  Google Scholar 

  • Marti P (1985) Truss models in detailing. Concr Int 7:66–73

    Google Scholar 

  • Mazars J, Pijaudier-Cabot G (1989) Continuum damage theory—application to concrete. ASCE J Eng Mech 115(2):345–365

    Article  Google Scholar 

  • 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 37:2471–2499

    Article  MATH  Google Scholar 

  • Moen CD, Guest JK (2010) Reinforced concrete analysis and design with truss topology optimization. In: Proceedings of the 3rd fib international congress, Washington DC, USA

  • Peerlings RHJ, de Borst R, Brekelmans WAM, de Vree JHP (1996) Gradient enhanced damage for quasi-brittle materials. Int J Numer Methods Eng 39(19):3391–3403

    Article  MATH  Google Scholar 

  • Phillips D, Zienkiewicz O (1976) Finite element nonlinear analysis of concrete structures. ICE Proc 61(1):59–88

    Article  Google Scholar 

  • Schlaich J, Schafer K, Jennewein M (1987) Toward a consistent design of structural concrete. PCI J 32(3):74–150

    Google Scholar 

  • Sigmund O, Bendsøe MP (2004) Topology optimization: from airplanes to nano-optics. In: Stubkjær K, Kortenbach T (eds) Bridging from technology to society. Technical University of Denmark, Lyngby, Denmark

    Google Scholar 

  • Sigmund O, Torquato S (1997) Design of materials with extreme thermal expansion using a three-phase topology optimization method. J Mech Phys Solids 45(6):1037–1067

    Article  MathSciNet  Google Scholar 

  • Stromberg LL, Beghini A, Baker WF, Paulino GH (2011) Application of layout and topology optimization using pattern gradation for the conceptual design of buildings. Struct Multidisc Optim 43:165–180

    Article  Google Scholar 

  • Svanberg K (1987) The method of moving asymptotes—a new method for structural optimization. Int J Numer Methods Eng 24:359–373

    Article  MathSciNet  MATH  Google Scholar 

  • Victoria M, Querin OM, Martí P (2011) Generation of strut-and-tie models by topology optimization using different material properties in tension and compression. Struct Multidisc Optim 44:247–258

    Article  Google Scholar 

Download references

Acknowledgments

The work of the first author was funded by the Danish Council for Independent Research | Technology and Production Sciences. The work of the second author was funded by Villum Fonden via the NextTop project. These supports are gratefully acknowledged. We wish to thank Claus B.W. Pedersen for several fruitful discussions and for his important comments. We also thank Krister Svanberg for the FORTRAN MMA code.

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Technical University of Denmark, Lyngby, Denmark

    Oded Amir & Ole Sigmund

Authors
  1. Oded Amir
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ole Sigmund
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Oded Amir.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Amir, O., Sigmund, O. Reinforcement layout design for concrete structures based on continuum damage and truss topology optimization. Struct Multidisc Optim 47, 157–174 (2013). https://doi.org/10.1007/s00158-012-0817-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00158-012-0817-1

Keywords

Search

Navigation