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Global Topology Optimisation

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Technical Report,01 Aug 2015,31 Jul 2016

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University Of Bath Bath United Kingdom

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A new method for stochastic shape optimization of engineering structures is presented. The method generalizes an existing deterministic scheme, in which the structure is represented by a level-set method, and evolves by steepest descent of the objective function. In non-convex optimization problems, the deterministic algorithm can get trapped in local optima the stochastic generalization enables sampling of multiple local optima, which aids the search for the globally-optimal structure. The method is demonstrated for several simple geometrical problems, and a proof-of principle calculation is shown for a simple engineering structure. There are two conclusions from this analysis. First, even if the level-set function is an accurate description of a shape, one expects uncertainties in sensitivities, due to discretization errors. This can effect the convergence of the deterministic method to a minimum of F, and the extent to which the stochastic method samples. Accurate estimation of sensitivities is therefore an important part of any future application of this method. Second, re-initialization of the level set can lead to small but significant movements of boundary points, which are large enough that local sensitivities change considerably. In deterministic optimization, the frequency of re-initialization reduces as the system converges to the optimum, and this effect is not too pronounced. On the other hand, in stochastic optimization, re-initialization is more frequent, and can affect the shapes generated by the method. A more detailed analysis of these effects is a direction for potential future work.

Subject Categories:

  • Statistics and Probability
  • Operations Research
  • Structural Engineering and Building Technology
  • Mechanics

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