Predominantly solid-void three-dimensional topology optimisation using open source software

[摘要] Inspired by Sigmund's 99-line MATLAB code for minimum compliance (maximum stiffness)topology optimisation, this thesis presents an open source software (OSS) version developedin Python, denoted ToPy. ToPy extends the 99-line code of Sigmund in a number ofways.Firstly, ToPy can solve three different problem types, namely minimum compliance, heatconduction and mechanism synthesis, in two-dimensional (2D) or three-dimensional (3D)space. This is accomplished by simply changing an input file. Secondly, by using establishedopen source software (Pysparse and its iterative solver) for solving the sparse finite element(FE) systems of equations, the ToPy code provides improved speed and scalability.ToPy also provides for grey-scale filtering (GSF) to yield predominantly, or even purely,solid-void or black-and-white designs in 2D and 3D space.In addition, an exponential approximation to the objective function is implemented. Thisapproximation is a generalisation of the reciprocal approximation so popular in structuraloptimisation; the values of the exponents may be based on gradient information in previouslyvisited iterates, or fixed exponents may be prescribed, in the spirit of optimalitycriterion (OC) methods.As a further generalisation, the diagonal quadratic approximation to the exponential approximationin an SAO setting is also implemented. What is more: the diagonal quadraticapproximation to the exponential approximation was successfully used in combination withGSF. This is a novelty of some importance as it was previously suggested that GSF can onlybe used in combination with strictly monotonic objective functions, like the reciprocal approximation.

[发布机构] Stellenbosch University