Structural and Multidisciplinary Optimization

, Volume 35, Issue 1, pp 55–68 | Cite as

Simultaneous material selection and geometry design of statically determinate trusses using continuous optimization

Research Paper


In this work, we explore simultaneous geometry design and material selection for statically determinate trusses by posing it as a continuous optimization problem. The underlying principles of our approach are structural optimization and Ashby’s procedure for material selection from a database. For simplicity and ease of initial implementation, only static loads are considered in this work with the intent of maximum stiffness, minimum weight/cost, and safety against failure. Safety of tensile and compression members in the truss is treated differently to prevent yield and buckling failures, respectively. Geometry variables such as lengths and orientations of members are taken to be the design variables in an assumed layout. Areas of cross-section of the members are determined to satisfy the failure constraints in each member. Along the lines of Ashby’s material indices, a new design index is derived for trusses. The design index helps in choosing the most suitable material for any geometry of the truss. Using the design index, both the design space and the material database are searched simultaneously using gradient-based optimization algorithms. The important feature of our approach is that the formulated optimization problem is continuous, although the material selection from a database is an inherently discrete problem. A few illustrative examples are included. It is observed that the method is capable of determining the optimal topology in addition to optimal geometry when the assumed layout contains more links than are necessary for optimality.


Material selection Geometry optimization Failure criteria Buckling Truss design 


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  1. Achtziger W (1996) Truss topology optimization including properties different for tension and compression. Struct Optim 12:63–74CrossRefGoogle Scholar
  2. Ananthasuresh GK (ed) (2003) Optimal synthesis methods for MEMS. Kluwer, Norwell, MAGoogle Scholar
  3. Ananthasuresh GK, Ashby MF (2003) Concurrent design and material selection for trusses. Proceedings of the workshop on optimal design Laboratoire de Mechanique des Solides Ecole Polytechnique Palaiseau, France, November 26–28, 2003Google Scholar
  4. Ashby MF (1999) Materials selection in mechanical design, 2nd edn. Butterworth Heinemann, New YorkGoogle Scholar
  5. Bendsoe, Sigmund (2003) Topology optimization theory, methods and applications, 2nd edn. Springer, Berlin Heidelberg New YorkGoogle Scholar
  6. Bendsoe MP, Guedes JM, Haber RB, Pedersen P, Taylor JE (1994) An analytical model to predict optimal material properties in the context of optimal structural design. J Appl Mech 61(4):930–937MathSciNetGoogle Scholar
  7. Calladine CR (1978) Buckminster Fuller’s “tensegrity” structures and Clerk Maxwell’s rules for and construction of stiff frames. Int J Solids Struct 14(2):161–172MATHCrossRefGoogle Scholar
  8. Dutta D, Prinz FB, Rosen D, Weiss L (2001) Layered manufacturing: current status and future trends. J Comput Inf Sci Eng 1:60–71CrossRefGoogle Scholar
  9. Erdman AG, Sandor GN, Kota Sridhar (1984) Mechanism design: analysis and synthesis, vol. I, 4th edn. Prentice Hall, New YorkGoogle Scholar
  10. Gibiansky LV, Sigmund O (2000) Multiphase composites with extremal bulk modulus. J Mech Phys Solids 48:461–498MATHCrossRefMathSciNetGoogle Scholar
  11. Guedes JM, Bendsoe MP, Rodrigues H (2005) Hierarchical optimization of material and structure for thermal transient problems. In: Bendsoe MP, Olhoff N, Sigmund O (eds) IUTAM Symposium, Rungstedgaard, Copenhagen, Denmark, (October 26–29, 2005), pp 309–318Google Scholar
  12. Haftka Gurdal (1994) Principles of structural optimization, 3rd edn. Kluwer, Norwell, MAGoogle Scholar
  13. Rodrigues H, Guedes JM, Bendsoe MP (2002) Hierarchical optimization of material and structure. Struct Multidiscipl Optim 24:1–10CrossRefGoogle Scholar
  14. Rozvany GIN, Birker (1994) On singular topologies in exact layout optimization. Struct Optim 8:228–235CrossRefGoogle Scholar
  15. Rozvany GIN, Bendsoe MP, Kirsch U (1995) Layout optimization of structures. Appl Mech Rev 48:41–119CrossRefGoogle Scholar
  16. Sigmund O (1994) Materials with prescribed constitutive parameters: an inverse homogenization problem. Int J Solids Struct 31(17):2313–2329MATHCrossRefMathSciNetGoogle Scholar
  17. Stegmann Jan, Lund Erik (2005) On discrete material optimization of laminated composites using global and local criteria. In: Bendsoe O, Sigmund O (eds) IUTAM symposium, Rungstedgaard, Copenhagen, Denmark, October 26–29, 2005, pp 385–396Google Scholar
  18. Stolpe M, Svanberg K (2004) A stress-constrained truss-topology and material-selection problem that can be solved by linear programming. Struct Multidiscipl Optim 27:126–129CrossRefMathSciNetGoogle Scholar
  19. Turteltaub S (2002) Optimal control and optimization of functionally graded materials for thermomechanical processes. Int J Solids Struct 39(12):3175–3197MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  1. 1.Mechanical Engineering DepartmentIndian Institute of ScienceBangaloreIndia

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