Introducing Loading Uncertainty in Level Set-Based Structural Topology Optimisation

  • Peter Dunning

Student thesis: Doctoral ThesisPhD


Structural topology optimisation aims to provide solutions that are independent of the initial layout, allowing the greatest opportunity to find the best design. Recent developments have seen increased interest in level set based optimisation, as the solutions obtained possess smooth boundaries and are free of numerical instabilities that affect traditional element based methods. The direct level set based structural topology optimisation method has been successful in solving a range of problems. However, it does suffer from some drawbacks and limitations. Two of the main issues with the direct level set method are accurate and efficient sensitivity computation on the boundary and initial design dependent solutions for two dimensional problems. These issues are addressed in this thesis by investigating and improving the efficient area-weighted fixed grid method and creating a novel hole creation method for two dimensional problems based on a pseudo third dimension. Uncertainty is important to include during design and optimisation to produce structures that are reliable and robust. Loading magnitude and direction uncertainty is introduced into the minimisation of compliance problem by considering the robust expected compliance objective. An efficient formulation is derived using an analytical approach where uncertainties are normally distributed. The robust problem is then extended to include compliance variance and sensitivities are derived using the adjoint method.
Date of Award1 May 2011
Original languageEnglish
Awarding Institution
  • University of Bath
SupervisorHyunsun Kim (Supervisor) & Glen Mullineux (Supervisor)

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