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Topology optimization by using a level set function and design elements
Kegl, Marko ; Harl, Boštjan ; Dinevski, Dejan
This paper discusses topology optimization of continuous structures by using a level set function and design elements. The level set function is used to define implicitly the boundary between ...material and void regions. However, in contrast to the level set methods, the approach discussed here does not rely on the Hamilton-Jacobi differential equation in order to compute the evolution of material boundaries. Instead of this, the level set function is parametrized by employing design elements based on Bernstein interpolating polynomials. One parameter, acting as a design variable, is assigned to each control point of the design element. The parametrized level set function is used to define a material map function, related to material stiffness and density, inside individual finite elements by using its interpolation functions in the isoparametric sense. Kinematically linear finite elements are employed and the adjoint technique is used to do the sensitivity analysis. Numerical experience has shown that the proposed approach may behave well but its stability is related to some tuning parameters of the method. The method is illustrated with a numerical example.
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