Skip to main content
SpringerLink
Log in

High resolution topology optimization using graphics processing units (GPUs)

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

Abstract

We present a Graphics Processing Unit (GPU) implementation of the level set method for topology optimization. The solution of three-dimensional topology optimization problems with millions of elements becomes computationally tractable with this GPU implementation and NVIDIA supercomputer-grade GPUs. We demonstrate this by solving the inverse homogenization problem for the design of isotropic materials with maximized bulk modulus. We trace the maximum bulk modulus optimization results to very high porosities to demonstrate the detail achievable with a high computational resolution. By utilizing a parallel GPU implementation rather than a sequential CPU implementation, similar increases in tractable computational resolution would be expected for other topology optimization problems.

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

Similar content being viewed by others

Notes

  1. Here we obtain 3D, macroscopically isotropic analogues of the structures first considered by Vigdergauz (1989).

References

  • Allaire G, Jouve F, Toader AM (2004) Structural optimization using sensitivity analysis and a level-set method. J Comput Phys 194:363–393

    Article  MATH  MathSciNet  Google Scholar 

  • Bendsøe MP, Sigmund O (2004) Topology optimization: theory methods and applications, 2nd edn. Springer, Berlin

    Book  Google Scholar 

  • Bensoussan A, Lions J, Papanicolaou G (1978) Asymptotic analysis for periodic structures. North-Holland, Amsterdam

    MATH  Google Scholar 

  • Cao TT, Tang K, Mohamed A, Tan TS (2010) Parallel banding algorithm to compute exact distance transform with the GPU. In: Proceedings of the 2010 ACM SIGGRAPH symposium on interactive 3d graphics and games, pp 83–90

  • Challis VJ (2010) A discrete level-set topology optimization code written in Matlab. Struc Multidisc Optim 41(3):453–464

    Article  MATH  MathSciNet  Google Scholar 

  • Challis VJ, Roberts AP, Wilkins AH (2008) Design of three dimensional isotropic microstructures for maximized stiffness and conductivity. Int J Solids Struct 45:4130–4146

    Article  MATH  Google Scholar 

  • Challis VJ, Roberts AP, Grotowski JF, Zhang LC, Sercombe TB (2010) Prototypes for bone implant scaffolds designed via topology optimization and manufactured by solid freeform fabrication. Adv Eng Mater 12(11):1106–1110

    Article  Google Scholar 

  • Challis VJ, Guest JK, Grotowski JF, Roberts AP (2012) Prototypes for bone implant scaffolds designed via topology optimization and manufactured by solid freeform fabrication. Int J Solids Struct 49:3397–3408

    Article  Google Scholar 

  • Chen Y, Zhou S, Li Q (2010) Multiobjective topology optimization for finite periodic structures. Comput Struct 88:806–811

    Article  Google Scholar 

  • Chen Y, Zhou S, Li Q (2011) Microstructure design of biodegradable scaffold and its effect on tissue regeneration. Biomaterials 32:5003–5014

    Article  Google Scholar 

  • Garboczi EJ (1998) Finite element and finite difference programs for computing the linear electric and elastic properties of digital images of random materials. Tech rep, NISTIR 6269. http://ciks.cbt.nist.gov/garbocz/manual/man.html

  • Guest JK, Prévost JH (2006) Optimizing multifunctional materials: design of microstructures for maximized stiffness and fluid permeability. Int J Solids Struct 43:7028–7047

    Article  MATH  Google Scholar 

  • Guest JK, Prévost JH, Belytschko T (2004) Achieving minimum length scale in topology optimization using nodal design variables and projection functions. Int J Numer Meth Engng 61(2):238–254

    Article  MATH  Google Scholar 

  • Hashin Z, Shtrikman S (1963) A variational approach to the theory of the elastic behaviour of multiphase materials. J Mech Phys Solids 11:127–140

    Article  MATH  MathSciNet  Google Scholar 

  • Hollister SJ (2005) Porous scaffold design for tissue engineering. Nat Mater 4:518–524

    Article  Google Scholar 

  • Huang X, Zhou S, Xie Y, Li Q (2013) Topology optimization of microstructures of cellular materials and composites for macrostructures. Comput Mater Sci 67(0):397–407

    Article  Google Scholar 

  • Kirk DB, Hwu WW (2013) Programming massively parallel processors: a hands-on approach, 2nd edn. Elsevier, Amsterdam

    Google Scholar 

  • Lin CY, Kikuchi N, Hollister SJ (2004) A novel method for biomaterial scaffold internal architecture design to match bone elastic properties with desired porosity. J Biomech 37(5):623–636

    Article  Google Scholar 

  • Lin CY, Wirtz T, LaMarca F, Hollister SJ (2007) Structural and mechanical evaluations of a topology optimized titanium interbody fusion cage fabricated by selective laser melting process. J Biomed Mater Res A 83A(2):272–279

    Article  Google Scholar 

  • NVIDIA (2011) Compute command line profiler user guide

  • NVIDIA (2012a) CUDA C programming guide version 4.2

  • NVIDIA (2012b) CUDA toolkit 4.2 thrust quick start guide

  • Sanchez-Palencia E (1980) Non-homogeneous media and vibration theory, lecture notes in physics, vol 127. Springer, Berlin

    Google Scholar 

  • Sethian JA (1999) Level set methods and fast marching methods: evolving interfaces in computational geometry, fluid mechanics, computer vision and materials science, 2nd edn.Cambridge University Press, Cambridge

  • Sigmund O (1999) On the optimality of bone microstructure. In: Bendsøe MP, Pedersen P (eds) IUTAM symposium on synthesis in bio solid mechanics. Kluwer, New York, pp 221–234

    Google Scholar 

  • Sigmund O (2000) A new class of extremal composites. J Mech Phys Solids 48:397–428

    Article  MATH  MathSciNet  Google Scholar 

  • Swan CC, Rahmatalla SF (2006) Strategies for computational efficiency in continuum structural topology optimization. In: Pandey M, Xie WC, Xu L (eds) Advances in engineering structures, mechanics & construction, solid mechanics and its applications, vol 140. Springer, pp 673–683

  • Vigdergauz S (1989) Regular structures with extremal elastic properties. Mech Solids 24(3):57–63

    Google Scholar 

  • Wadbro E, Berggren M (2009) Megapixel topology optimization on a graphics processing unit. SIAM Rev 51(4):707–721

    Article  MATH  MathSciNet  Google Scholar 

  • Wang MY, Wang X, Guo D (2003) A level set method for structural topology optimization. Comput Methods Appl Mech Engrg 192:227–246

    Article  MATH  MathSciNet  Google Scholar 

  • Wang SY, Wang MY (2006) A moving superimposed finite element method for structural topology optimization. Int J Numer Methods Eng 65:1892–1922

    Article  MATH  Google Scholar 

  • Weaire D, Fortes MA (1994) Stress and strain in liquid and solid foams. Adv Phys 43(6):685–738

    Article  Google Scholar 

  • Zhu HX, Knott JF, Mills NJ (1997) Analysis of the elastic properties of open-cell foams with tetrakaidecahedral cells. J Mech Phys Solids 45:319–343

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics & Physics, The University of Queensland, Brisbane, QLD 4072, Australia

    Vivien J. Challis, Anthony P. Roberts & Joseph F. Grotowski

Authors
  1. Vivien J. Challis
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Anthony P. Roberts
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Joseph F. Grotowski
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vivien J. Challis.

Additional information

This research was supported under the Australian Research Council’s Discovery Projects funding scheme (project number DP110101653). The computational resources used in this work were funded by a Major Equipment and Infrastructure Grant from The University of Queensland. The authors are grateful to C. J. Foster for assistance with the C++ programming and to B. A. Burton for helpful discussions regarding the presentation of timing data.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Challis, V.J., Roberts, A.P. & Grotowski, J.F. High resolution topology optimization using graphics processing units (GPUs). Struct Multidisc Optim 49, 315–325 (2014). https://doi.org/10.1007/s00158-013-0980-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00158-013-0980-z

Keywords

Search

Navigation