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Structural topology optimization: Extensibility and attainability

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  • Special Topic: Computational Mechanics
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Abstract

Extensibility and attainability of topology optimization are discussed by investigating a variety of simultaneous topology opti-mization methods extended from the standard formulation. First, the state of the art is highlighted through systematic classification of developed methods, such as simultaneous topology optimizations of microstructure and macrostructure, structure and supports, structure and design-dependent loads, structure and locations of involved components. Second, some recent results about simultaneous topology optimization of structure and applied loads are presented. It is shown that the simultaneous topology optimization is an integrated methodology that extends the concept of standard topology optimization in the sense of systematic design. The presence of more than one kind of design variable of different nature makes the optimization problem complex but enlarges the design space to attain the optimization.

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References

  1. Rozvany G I N. Aims, scope, methods, history and unified terminology of computer-aided topology optimization in structural mechanics. Struct Multidiscip O, 2001, 21: 90–108

    Article  Google Scholar 

  2. Bendsoe M P, Kikuchi N. Generating optimal topologies in structural design using a homogenization method. Comput Method Appl M, 1988, 71: 197–224

    Article  MathSciNet  Google Scholar 

  3. Zhang W H, Sun S P. Scale-related topology optimization of cellular materials and structures (in Chinese). Int J Numer Meth Eng, 2006, 68: 993–1011

    Article  MATH  Google Scholar 

  4. Yan J, Cheng G D, Liu L, et al. Concurrent material and structural optimization of hollow plate with truss-like material. Struct Multidiscip O, 2008, 35: 153–163

    Article  Google Scholar 

  5. Stegmann J, Lund E. Discrete material optimization of general composite shell structures. Int J Numer Meth Eng, 2005, 62: 2009–2027

    Article  MATH  Google Scholar 

  6. Stegmann J, Lund E. Nonlinear topology optimization of layered shell structures. Struct Multidiscip O, 2005, 29: 349–360

    Article  Google Scholar 

  7. Lund E. Buckling topology optimization of laminated multi-material composite shell structures. Compos Struct, 2009, 91: 158–167

    Article  Google Scholar 

  8. Bruyneel M. SFP—A new parameterization based on shape functions for optimal material selection: Application to conventional composite plies. Struct Multidiscip O, 2011, 43: 17–27

    Article  Google Scholar 

  9. Bruyneel M, Duysinx P, Fleury C, et al. Extensions of the shape functions with penalization parameterization for composite-ply optimization. AIAA J, 2011, 49: 2325–2329

    Article  Google Scholar 

  10. Gao T, Zhang W H, Duysinx P. A bi-value coding parameterization scheme for the discrete optimal orientation design of the composite laminate. Int J Numer Meth Eng, 2012, 91: 98–114

    Article  MATH  Google Scholar 

  11. Gao T, Zhang W H, Duysinx P. Simultaneous design of structural layout and discrete fiber orientation using bi-value coding parameterization and volume constraint. Struct Multidiscip O, 2013, 45: 1–14

    Google Scholar 

  12. Chickermane H, Gea H C. Design of multi-component structural systems for optimal layout topology and joint locations. Eng Comput Germany, 1997, 13: 235–243

    Article  Google Scholar 

  13. Zhang W H, Zhang Q. Finite-circle method for component approximation and packing design optimization. Eng Optimiz, 2009, 41: 971–987

    Article  Google Scholar 

  14. Xia L, Zhu J H, Zhang W H, et al. An implicit model for the integrated optimization of component layout and structure topology. Comput Method Appl M, 2013, 257: 87–102

    Article  MATH  MathSciNet  Google Scholar 

  15. Zhang J, Zhang W H, Zhu J H, et al. Integrated layout design of multi-component systems using XFEM and analytical sensitivity analysis. Comput Method Appl M, 2012, 245–246: 75–89

    Article  Google Scholar 

  16. Zhu J H, Zhang W H, Beckers P. Integrated layout design of multi-component system. Int J Numer Meth Eng, 2009, 78: 631–651

    Article  MATH  Google Scholar 

  17. Zhu J, Beckers P, Zhang W. On the multi-component layout design with inertial force. J Comput Appl Math, 2010, 234: 2222–2230

    Article  MATH  Google Scholar 

  18. Mroz Z, Rozvany G I N. Optimal design of structures with variable support conditions. J Optimiz Theory App, 1975, 15: 85–101

    Article  MATH  MathSciNet  Google Scholar 

  19. Prager W, Rozvany G I N. Plastic design of beams-optimal locations of supports and steps in yield moment. Int J Mech Sci, 1975, 17: 627–631

    Article  MATH  Google Scholar 

  20. Rozvany G I N. Optimization of unspecified generalized forces in structural design. J Appl Mech, 1974, 41: 1143–1145

    Article  Google Scholar 

  21. Szelag D, Mroz Z. Optimal design of vibrating beams with unspecified support reactions. Comput Method Appl M, 1979, 19: 333–349

    Article  MATH  MathSciNet  Google Scholar 

  22. Zhu J H, Zhang W H. Maximization of structural natural frequency with optimal support layout. Struct Multidiscip O, 2006, 31: 462–469

    Article  Google Scholar 

  23. Bojczuk D, Mroz Z. On optimal design of supports in beam and frame structures. Struct Optimization, 1998, 16: 47–57

    Article  Google Scholar 

  24. Buhl T. Simultaneous topology optimization of structure and supports. Struct Multidiscip O, 2002, 23: 336–346

    Article  Google Scholar 

  25. Pedersen P. Topology Optimization of Three-Dimensional Trusses. Topology Design of Structures: Springer Netherlands, 1993. 19–30

    Chapter  Google Scholar 

  26. Zhu J H, Zhang W H. Integrated layout design of supports and structures. Comput Method Appl M, 2010, 199: 557–569

    Article  MATH  Google Scholar 

  27. Gao T, Zhang W H, Zhu J H, et al. Topology optimization of heat conduction problem involving design-dependent heat load effect. Finite Elem Anal Des, 2008, 44: 805–813

    Article  Google Scholar 

  28. Gao T, Zhang W H. Structural topology optimization under inertial loads (in Chinese). Chin J Theor App Mech, 2009, 41: 530–541

    Google Scholar 

  29. Gao T, Zhang W H. Topology optimization of multiphase material structures under design dependent pressure loads. Int J Siimu Mult Desig Optimiz, 2009, 3: 297–306

    Article  Google Scholar 

  30. Allaire G, Jouve F, Toader A M. Structural optimization using sensitivity analysis and a level-set method. J Comput Phys, 2004, 194: 363–393

    Article  MATH  MathSciNet  Google Scholar 

  31. Bendsoe M. Methods for Optimization of Structural Topology, Shape and Material. New York: Springer Verlag, 1995

    Book  Google Scholar 

  32. Chen B C, Kikuchi N. Topology optimization with design-dependent loads. Finite Elem Anal Des, 2001, 37: 57–70

    Article  MATH  Google Scholar 

  33. Du J, Olhoff N. Topological optimization of continuum structures with design-dependent surface loading—Part II: algorithm and examples for 3D problems. Struct Multidiscip O, 2004, 27: 166–177

    Article  MATH  MathSciNet  Google Scholar 

  34. Fuchs M B, Shemesh N N Y. Density-based topological design of structures subjected to water pressure using a parametric loading surface. Struct Multidiscip O, 2004, 28: 11–19

    Article  Google Scholar 

  35. Hammer V B, Olhoff N. Topology optimization of continuum structures subjected to pressure loading. Struct Multidiscip O, 2000, 19: 85–92

    Article  Google Scholar 

  36. Liu Z, Korvink J G, Huang R. Structure topology optimization: fully coupled level set method via FEMLAB. Struct Multidiscip O, 2005, 29: 407–417

    Article  MATH  MathSciNet  Google Scholar 

  37. Sigmund O, Clausen P M. Topology optimization using a mixed formulation: An alternative way to solve pressure load problems. Comput Method Appl M, 2007, 196: 1874–1889

    Article  MATH  MathSciNet  Google Scholar 

  38. Gao T, Zhang W H. Topology optimization involving thermo-elastic stress loads. Struct Multidiscip O, 2010, 42: 725–738

    Article  MATH  Google Scholar 

  39. Ansola R, Canales J, Tarrago J A. An efficient sensitivity computation strategy for the evolutionary structural optimization (ESO) of continuum structures subjected to self-weight loads. Finite Elem Anal Des, 2006, 42: 1220–1230

    Article  Google Scholar 

  40. Cho S H, Choi J Y. Efficient topology optimization of thermo-elasticity problems using coupled field adjoint sensitivity analysis method. Finite Elem Anal Des, 2005, 41: 1481–1495

    Article  MathSciNet  Google Scholar 

  41. Li Q, Steven G P, Xie Y M. Displacement minimization of thermoelastic structures by evolutionary thickness design. Comput Method Appl M, 1999, 179: 361–378

    Article  MATH  Google Scholar 

  42. Rodrigues H, Fernandes P. A material based model for topology optimization of thermoelastic structures. Int J Numer Meth Eng, 1995, 38: 1951–1965

    Article  MATH  MathSciNet  Google Scholar 

  43. Zuo K, Qian Q, Zhao Y, et al. Research on the topology optimization about thermo-structural coupling field. Acta Mech Solida Sin, 2005, 26: 447–452

    Google Scholar 

  44. Zheng B, Chang C J, Gea H C. Design of piezoelectric actuator with in-plane motion using topology optimization. In: ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2007. 1343–1350

    Google Scholar 

  45. Kang Z, Wang R, Tong L. Combined optimization of Bi-material structural layout and voltage distribution for in-plane piezoelectric actuation. Comput Method Appl Mech Eng, 2011, 200: 1467–1478

    Article  MATH  MathSciNet  Google Scholar 

  46. Rozvany G I N, Prager W. A new class of structural optimization problems: optimal archgrids. Comput Method Appl Mech Eng, 1979, 19: 127–150

    Article  MATH  MathSciNet  Google Scholar 

  47. Rozvany G I N, Wang C M. On plane prager-structures-1. Int J Mech Sci, 1983, 25: 519–527

    Article  MATH  Google Scholar 

  48. Fuchs M B, Moses E. Optimal structural topologies with transmissible loads. Struct Multidiscip O, 2000, 19: 263–273

    Article  Google Scholar 

  49. Chiandussi G, Codegone M, Ferrero S. Topology optimization with optimality criteria and transmissible loads. Comput Math Appl, 2009, 57: 772–788

    Article  MATH  MathSciNet  Google Scholar 

  50. Svanberg K. A globally convergent version of MMA without linesearch. In: First World Congress of Structural and Multidisciplinary Optimization. New York, 1995. 9–16

    Google Scholar 

  51. Sigmund O. A 99 line topology optimization code written in Matlab. Struct Multidiscip O, 2001, 21: 120–127

    Article  Google Scholar 

  52. Rozvany G I N. Exact analytical solutions for some popular benchmark problems in topology optimisation. Struct Optimization, 1998, 15: 42–48

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Engineering Simulation and Aerospace Computing (ESAC), School of Mechanical Engineering, Northwestern Polytechnical University, Xi’an, 710072, China

    WeiHong Zhang, ZhiDong Zhang, JiHong Zhu & Tong Gao

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  1. WeiHong Zhang
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  2. ZhiDong Zhang
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  3. JiHong Zhu
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  4. Tong Gao
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Correspondence to WeiHong Zhang.

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Zhang, W., Zhang, Z., Zhu, J. et al. Structural topology optimization: Extensibility and attainability. Sci. China Technol. Sci. 57, 1310–1321 (2014). https://doi.org/10.1007/s11431-014-5580-7

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  • DOI: https://doi.org/10.1007/s11431-014-5580-7

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