Applications of Level Set Topology Optimisation

  • Christopher Brampton

Student thesis: Doctoral ThesisPhD


Level set method is a boundary tracking method that uses an implicit function to define the boundary location. By using the implicit function to define the structural boundary the level set method can be used for topology optimisation. The level set method has previously been used to solve a range of structural optimisation problems.The aim of this thesis is to extend the application of the level set method to additional applications of structural optimisation. A robust method of 3D level set topology optimisation is developed and tested. The use of a hole insertion method was found to be advantageous, but not vital, for 3D level set topology optimisation. The level set method is used to optimise the internal structure of a proximal femur. Similarities between the optimal structure and real internal trabecular bone architecture suggest that the internal bone structure may be mechanically optimal. Stress constrained level set topology optimisation is performed in 2D. Stress shape sensitivities are derived and interpolated to obtain smooth boundary sensitivity, resulting in feasible stress constrained solution in numerical examples. A new generic objective hole insertion method is used to reduce dependence on the initial solution. A level set method for optimising the design of fibre angles in composite structures is also introduced. Fibre paths are implicitly defined using the level set function. Sensitivity analysis is used to update the level set function values and optimise the fibre path. The method implicitly ensures continuous fibre paths in the optimum solution, that could be manufactured using advanced fibre placement.
Date of Award8 Sept 2015
Original languageEnglish
Awarding Institution
  • University of Bath
SupervisorJames Cunningham (Supervisor) & Hyunsun Kim (Supervisor)


  • Level set method
  • Topology optimisation
  • Bone Remodeling
  • Carbon Fibre Composite
  • Stress

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