Skip to main content
Top
Published in: Acta Mechanica Sinica 6/2018

06-07-2018 | Research Paper

A modified stiffness spreading method for layout optimization of truss structures

Authors: Mingjie Cao, Haitao Ma, Peng Wei

Published in: Acta Mechanica Sinica | Issue 6/2018

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

The stiffness spreading method (SSM) was initially proposed for layout optimization of truss structures, in which an artificial elastic material of low modulus is uniformly distributed in the design domain to create connections between discrete members. In this paper, a modified stiffness spreading method is proposed by replacing the artificial elastic material with auxiliary bars to connect real members of the truss structure. Since the background continuum mesh for the elastic material is no longer required, the computational cost is significantly reduced. Like SSM, the new method is advantageous in that an initial design may consist of disconnected bars allocated in the design domain, and mathematical programming methods can be applied for the efficient solution of the formulated optimization problem. A number of solution strategies are also developed to achieve more practical designs with lower computational cost. Numerical examples of both 2-D and 3-D truss structures are presented to demonstrate the feasibility, robustness and effectiveness of the proposed method.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference Michell, A.G.M.: The limits of economy of material in frame-structures. Philos. Mag. 8, 589–597 (1904)CrossRef Michell, A.G.M.: The limits of economy of material in frame-structures. Philos. Mag. 8, 589–597 (1904)CrossRef
2.
go back to reference Dorn, W.S., Gomory, R.E., Greenberg, H.J.: Automatic design of optimal structures. J. de Meca. 3, 25–52 (1964) Dorn, W.S., Gomory, R.E., Greenberg, H.J.: Automatic design of optimal structures. J. de Meca. 3, 25–52 (1964)
3.
go back to reference Rozvany, G., Bendsoe, M.P., Kirsch, U.: Layout optimization of structures. Appl. Mech. Rev. 48, 41–119 (1995)CrossRef Rozvany, G., Bendsoe, M.P., Kirsch, U.: Layout optimization of structures. Appl. Mech. Rev. 48, 41–119 (1995)CrossRef
4.
go back to reference Zhou, K., Li, X.: Topology optimization for minimum compliance under multiple loads based on continuous distribution of members. Struct. Multidisc. Optim. 37, 49–56 (2008)CrossRef Zhou, K., Li, X.: Topology optimization for minimum compliance under multiple loads based on continuous distribution of members. Struct. Multidisc. Optim. 37, 49–56 (2008)CrossRef
5.
go back to reference Zegard, T., Paulino, G.H.: GRAND—Ground structure based topology optimization for arbitrary 2D domains using MATLAB. Struct. Multidisc. Optim. 50, 861–882 (2014)MathSciNetCrossRef Zegard, T., Paulino, G.H.: GRAND—Ground structure based topology optimization for arbitrary 2D domains using MATLAB. Struct. Multidisc. Optim. 50, 861–882 (2014)MathSciNetCrossRef
6.
go back to reference Zegard, T., Paulino, G.H.: GRAND3-Ground structure based topology optimization for arbitrary 3D domains using MATLAB. Struct. Multidisc. Optim. 52, 1161–1184 (2015)CrossRef Zegard, T., Paulino, G.H.: GRAND3-Ground structure based topology optimization for arbitrary 3D domains using MATLAB. Struct. Multidisc. Optim. 52, 1161–1184 (2015)CrossRef
7.
go back to reference Gao, G., Liu, Z., Li, Y., et al.: A new method to generate the ground structure in truss topology optimization. Eng. Optimiz. 49, 235–251 (2017)MathSciNetCrossRef Gao, G., Liu, Z., Li, Y., et al.: A new method to generate the ground structure in truss topology optimization. Eng. Optimiz. 49, 235–251 (2017)MathSciNetCrossRef
8.
go back to reference Achtziger, W.: On simultaneous optimization of truss geometry and topology. Struct. Multidisc. Optim. 33, 285–304 (2007)MathSciNetCrossRef Achtziger, W.: On simultaneous optimization of truss geometry and topology. Struct. Multidisc. Optim. 33, 285–304 (2007)MathSciNetCrossRef
9.
go back to reference Pedersen, P.: Optimal joint positions for space trusses. J. Struct. Div. 99, 2459–2476 (1973) Pedersen, P.: Optimal joint positions for space trusses. J. Struct. Div. 99, 2459–2476 (1973)
10.
go back to reference Vanderplaat, G.N., Moses, F.: Automated design of trusses for optimal geometry. J. Struct. Div. 98, 671–690 (1972) Vanderplaat, G.N., Moses, F.: Automated design of trusses for optimal geometry. J. Struct. Div. 98, 671–690 (1972)
11.
go back to reference Rule, W.K.: Automatic truss design by optimized growth. J. Struct. Eng. 120, 3063–3070 (1994)CrossRef Rule, W.K.: Automatic truss design by optimized growth. J. Struct. Eng. 120, 3063–3070 (1994)CrossRef
12.
go back to reference McKeown, J.J.: Growing optimal pin-jointed frames. Struct. Optim. 15, 92–100 (1998)CrossRef McKeown, J.J.: Growing optimal pin-jointed frames. Struct. Optim. 15, 92–100 (1998)CrossRef
13.
go back to reference Bojczuk, D., Mróz, Z.: On optimal design of supports in beam and frame structures. Struct. Optim. 16, 47–57 (1998)CrossRef Bojczuk, D., Mróz, Z.: On optimal design of supports in beam and frame structures. Struct. Optim. 16, 47–57 (1998)CrossRef
14.
go back to reference Martínez, P., Martí, P., Querin, O.M.: Growth method for size, topology, and geometry optimization of truss structures. Struct. Multidisc. Optim. 33, 13–26 (2007)CrossRef Martínez, P., Martí, P., Querin, O.M.: Growth method for size, topology, and geometry optimization of truss structures. Struct. Multidisc. Optim. 33, 13–26 (2007)CrossRef
15.
go back to reference Bendsoe, M.P., Sigmund, O.: Topology Optimization: Theory, Methods, and Applications. Springer, Berlin (2002)MATH Bendsoe, M.P., Sigmund, O.: Topology Optimization: Theory, Methods, and Applications. Springer, Berlin (2002)MATH
16.
go back to reference Ohsaki, M.: Optimization of Finite Dimensional Structures. CRC Press, Boca Raton (2011)MATH Ohsaki, M.: Optimization of Finite Dimensional Structures. CRC Press, Boca Raton (2011)MATH
17.
go back to reference Stolpe, M.: Truss optimization with discrete design variables: a critical review. Struct. Multidisc. Optim. 53, 349–374 (2016)MathSciNetCrossRef Stolpe, M.: Truss optimization with discrete design variables: a critical review. Struct. Multidisc. Optim. 53, 349–374 (2016)MathSciNetCrossRef
18.
go back to reference Wei, P., Ma, H., Wang, M.Y.: The stiffness spreading method for layout optimization of truss structures. In: The 6th China-Japan-Korea Joint Symposium on Optimization of Structural and Mechanical Systems. Kyoto, Japan (2010) Wei, P., Ma, H., Wang, M.Y.: The stiffness spreading method for layout optimization of truss structures. In: The 6th China-Japan-Korea Joint Symposium on Optimization of Structural and Mechanical Systems. Kyoto, Japan (2010)
19.
go back to reference Wei, P., Ma, H., Wang, M.Y.: The stiffness spreading method for layout optimization of truss structures. Struct. Multidisc. Optim. 49, 667–682 (2014)MathSciNetCrossRef Wei, P., Ma, H., Wang, M.Y.: The stiffness spreading method for layout optimization of truss structures. Struct. Multidisc. Optim. 49, 667–682 (2014)MathSciNetCrossRef
20.
go back to reference Wei, P., Shi, J., Ma, H.: Integrated layout optimization design of multi-component systems based on the stiffness spreading method. In: Proceedings of the 7th China–Japan–Korea Joint Symposium on Optimization of Structural and Mechanical Systems, Huangshan, China (2012) Wei, P., Shi, J., Ma, H.: Integrated layout optimization design of multi-component systems based on the stiffness spreading method. In: Proceedings of the 7th China–Japan–Korea Joint Symposium on Optimization of Structural and Mechanical Systems, Huangshan, China (2012)
21.
go back to reference Li, Y., Wei, P., Ma, H.: Integrated optimization of heat- transfer systems consisting of discrete thermal conductors and solid material. Int. J. Heat Mass Trans. 113, 1059–1069 (2017)CrossRef Li, Y., Wei, P., Ma, H.: Integrated optimization of heat- transfer systems consisting of discrete thermal conductors and solid material. Int. J. Heat Mass Trans. 113, 1059–1069 (2017)CrossRef
22.
go back to reference Wei, P., Shi, J., Ma, H.: The stiffness spreading method in integrated layout optimization design for multi-component structural systems. In: The 10th World Congress on Structural and Multidisciplinary Optimization May 19-24, Orlando, Florida, USA (2013) Wei, P., Shi, J., Ma, H.: The stiffness spreading method in integrated layout optimization design for multi-component structural systems. In: The 10th World Congress on Structural and Multidisciplinary Optimization May 19-24, Orlando, Florida, USA (2013)
23.
go back to reference Zegard, T., Paulino, G.H.: Truss layout optimization within a continuum. Struct. Multidisc. Optim. 48, 1–16 (2013)CrossRef Zegard, T., Paulino, G.H.: Truss layout optimization within a continuum. Struct. Multidisc. Optim. 48, 1–16 (2013)CrossRef
24.
go back to reference Guo, X., Zhang, W., Zhong, W.: Doing topology optimization explicitly and geometrically—a new moving morphable components based framework. J. Appl. Mech. 81, 081009 (2014)CrossRef Guo, X., Zhang, W., Zhong, W.: Doing topology optimization explicitly and geometrically—a new moving morphable components based framework. J. Appl. Mech. 81, 081009 (2014)CrossRef
25.
go back to reference Zhang, W., Zhang, J., Guo, X.: Lagrangian description based topology optimization—a revival of shape optimization. J. Appl. Mech. 83, 041010 (2016)CrossRef Zhang, W., Zhang, J., Guo, X.: Lagrangian description based topology optimization—a revival of shape optimization. J. Appl. Mech. 83, 041010 (2016)CrossRef
26.
go back to reference Zhang, W., Yuan, J., Zhang, J., et al.: A new topology optimization approach based on moving morphable components (MMC) and the ersatz material model. Struct. Multidisc. Optim. 53, 1243–1260 (2016)MathSciNetCrossRef Zhang, W., Yuan, J., Zhang, J., et al.: A new topology optimization approach based on moving morphable components (MMC) and the ersatz material model. Struct. Multidisc. Optim. 53, 1243–1260 (2016)MathSciNetCrossRef
27.
go back to reference Zhang, W., Chen, J., Zhu, X., et al.: Explicit three dimensional topology optimization via moving morphable void (MMV) approach. Comput. Methods Appl. Mech. Engrg. 322, 590–614 (2017)MathSciNetCrossRef Zhang, W., Chen, J., Zhu, X., et al.: Explicit three dimensional topology optimization via moving morphable void (MMV) approach. Comput. Methods Appl. Mech. Engrg. 322, 590–614 (2017)MathSciNetCrossRef
28.
go back to reference Zhang, J., Zhang, W.H., Zhu, J.H., et al.: Integrated layout design of multi-component systems using XFEM and analytical sensitivity analysis. Comput. Methods Appl. Mech. Engrg. 245–246, 75–89 (2012)MathSciNetCrossRef Zhang, J., Zhang, W.H., Zhu, J.H., et al.: Integrated layout design of multi-component systems using XFEM and analytical sensitivity analysis. Comput. Methods Appl. Mech. Engrg. 245–246, 75–89 (2012)MathSciNetCrossRef
29.
go back to reference Zhou, Y., Zhang, W., Zhu, J., et al.: Feature-driven topology optimization method with signed distance function. Comp. Methods Appl. Mech. Engrg. 310, 1–32 (2016)MathSciNetCrossRef Zhou, Y., Zhang, W., Zhu, J., et al.: Feature-driven topology optimization method with signed distance function. Comp. Methods Appl. Mech. Engrg. 310, 1–32 (2016)MathSciNetCrossRef
30.
go back to reference Cao, M., Ma, H., Wei, P.: Modified stiffness spreading method for layout optimization of truss structures. In: The 7th China-Japan-Korea Joint Symposium on Optimization of Structural and Mechanical Systems, Huangshan, China (2012) Cao, M., Ma, H., Wei, P.: Modified stiffness spreading method for layout optimization of truss structures. In: The 7th China-Japan-Korea Joint Symposium on Optimization of Structural and Mechanical Systems, Huangshan, China (2012)
31.
go back to reference Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM J. Optimiz. 12, 555–573 (2002)MathSciNetCrossRef Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM J. Optimiz. 12, 555–573 (2002)MathSciNetCrossRef
Metadata
Title
A modified stiffness spreading method for layout optimization of truss structures
Authors
Mingjie Cao
Haitao Ma
Peng Wei
Publication date
06-07-2018
Publisher
The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences
Published in
Acta Mechanica Sinica / Issue 6/2018
Print ISSN: 0567-7718
Electronic ISSN: 1614-3116
DOI
https://doi.org/10.1007/s10409-018-0776-x

Other articles of this Issue 6/2018

Acta Mechanica Sinica 6/2018 Go to the issue

Premium Partners