Design parameterization for topology optimization by intersection of an implicit function

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This paper introduces a new approach to topology optimization where the
structural boundary is defined by the intersection of an implicit signed-distance
function and a cutting surface. The cutting surface is discretized using finite
element shape-function polynomials and the nodal values become the design
variables during optimization. Thus, the design parameterization is separated
from the analysis discretization, which enables a reduction in the number
of design variables, compared with methods that use element-wise variables.
The proposed method can obtain solutions with smooth boundaries and the
parameterization allows solution by standard optimization methods. Several
2D and 3D examples are used to demonstrate the effectiveness of the method,
including minimization of compliance and complaint mechanism problems. The
results show that the method can obtain good solutions to well-known problems with smooth, clearly defined boundaries and that this can be achieved using significantly fewer design variables compared with element-based methods.
Original languageEnglish
Pages (from-to)993-1011
Number of pages19
JournalComputer Methods in Applied Mechanics and Engineering
Early online date17 Jan 2017
Publication statusPublished - 15 Apr 2017


  • topology optimisation
  • implicit function
  • mathematical programming


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