Abstract
In conventional level set methods for topology optimization, the evolution of level set function is solved by upwind scheme and needs to be reinitialized frequently throughout the optimization. The upwind scheme is complicated in numerical implementation and the reinitialization is time-consuming and slows down the optimization efficiency. This paper presents a level set method updated with finite difference scheme for structural topology optimization. The velocity field used to update the level set function is interpolated by piecewise basis function in order to incorporate the universal mathematical programming algorithm into the optimization. The diffusion is introduced into the Hamilton-Jacobi equation and the three-step splitting method is adopted to solve the equation. By applying the proposed method, the evolution of the level set can be updated by simple central difference scheme and the procedure of reinitialization is avoided without sacrificing the numerical stability. The classical mean compliance minimization problem with several numerical examples is used to test the validity of the proposed method.
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This research was supported by the Fundamental Research Funds for the Central Universities (Grant No.2017FZA4002).
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The numerical examples of the compliance minimum problem can be implemented by using the MATLAB codes provided as the supplementary material.
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Lin, Y., Zhu, W., Li, J. et al. Structural topology optimization using a level set method with finite difference updating scheme. Struct Multidisc Optim 63, 1839–1852 (2021). https://doi.org/10.1007/s00158-020-02779-x
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DOI: https://doi.org/10.1007/s00158-020-02779-x