Structural optimization

, Volume 16, Issue 2–3, pp 147–154 | Cite as

Minimum weight shape and size optimization of truss structures made of uncertain materials

  • E. Barbieri
  • M. Lomhardi
Research Papers


Truss structures are optimized with respect to minimum weight with constraints on the value of some displacement and on the member stresses. The truss is considered made of an uncertain material, i.e. the value of the material constants are not known in a deterministic way, and each member may then exhibit a different value of stiffness, within a limited range of variation. The optimization must be done so that optimal solutions remain feasible for each value that the material constants may take for the considered uncertainty. In the present work a nonprobabilistic approach to uncertainty is used, and a variation of the material moduli with a, probabilistically speaking, uniform distribution over a convex and linearly bounded domain is considered. The two-step method is used to include the uncertainty within the optimization, where a diagonal quadratic approximation is used for the Objective function and the constraints. Solutions for some of the most classical truss examples are found and compared with those obtained using nominal values of material constants.


Objective Function Civil Engineer Uniform Distribution Limited Range Material Constant 
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Copyright information

© Springer-Verlag 1998

Authors and Affiliations

  • E. Barbieri
    • 1
  • M. Lomhardi
    • 1
  1. 1.Department of Structural MechanicsUniversity of PaviaPaviaItaly

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