Heaviside projection based topology optimization by a PDE-filtered scalar function |
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Authors: | Atsushi Kawamoto Tadayoshi Matsumori Shintaro Yamasaki Tsuyoshi Nomura Tsuguo Kondoh Shinji Nishiwaki |
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Affiliation: | (1) Toyota Central R&D Labs., Inc., Nagakute Aichi 480-1192, Japan;(2) Shibaura Institute of Technology, 307 Fukasaku, Minuma, Saitama Saitama, 337-8570, Japan;(3) Kyoto University, Yoshida Honmachi, Sakyo-ku, Kyoto Kyoto, 606-8501, Japan |
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Abstract: | This paper deals with topology optimization based on the Heaviside projection method using a scalar function as design variables.
The scalar function is then regularized by a PDE based filter. Several image-processing based filtering techniques have so
far been proposed for regularization or restricting the minimum length scale. They are conventionally applied to the design
sensitivities rather than the design variables themselves. However, it causes discrepancies between the filtered sensitivities
and the actual sensitivities that may confuse the optimization process and disturb the convergence. In this paper, we propose
a Heaviside projection based topology optimization method with a scalar function that is filtered by a Helmholtz type partial
differential equation. Therefore, the optimality can be strictly discussed in terms of the KKT condition. In order to demonstrate
the effectiveness of the proposed method, a minimum compliance problem is solved. |
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