A topology optimization method based on the level set method incorporating a fictitious interface energy |
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| Authors: | Takayuki Yamada Kazuhiro Izui Shinji Nishiwaki Akihiro Takezawa |
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| Affiliation: | 1. Graduate School of Engineering, Kyoto University, Yoshida-honmachi, Sakyo-ku, Kyoto 606-8501, Japan;2. Graduate School of Engineering, Hiroshima University, 1-4-1 Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8527, Japan;1. National Technological University, Regional Faculty of Córdoba (UTN/FRC - CONICET), Maestro M. López esq. Cruz Roja Argentina, X5016ZAA - Córdoba, Argentina;2. CIMNE–Centre Internacional de Metodes Numerics en Enginyeria, Campus Nord UPC, Edifici C-1, c/Jordi Girona 1-3, 08034 Barcelona, Spain;3. Escola Superior d’Enginyeries Industrial, Aeroespacial i Audiovisual de Terrassa, Campus de Terrassa, Edificio TR45. C. Colom, 11 08222 Terrassa, Spain;4. E.T.S. d’Enginyers de Camins, Canals i Ports, Technical University of Catalonia, Campus Nord UPC, Edifici C-1, c/Jordi Girona 1-3, 08034 Barcelona, Spain;1. State Key Lab of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, 1037 Luoyu Road, Wuhan, Hubei 430074, China;2. School of Electrical, Mechanical and Mechatronic Systems, The University of Technology, Sydney, 15 Broadway, Ultimo, NSW 2007, Australia;1. Department of Mechanical Engineering and Science, Graduate School of Engineering, Kyoto University, Kyoto 615-8540, Japan;2. Department of Mechanical Systems Engineering, Faculty of Engineering, Shinshu University, Nagano 380-8553, Japan;3. Department of Mechanical Engineering and Science, Graduate School of Engineering, Nagoya University, Aichi 464-8603, Japan |
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| Abstract: | This paper proposes a new topology optimization method, which can adjust the geometrical complexity of optimal configurations, using the level set method and incorporating a fictitious interface energy derived from the phase field method. First, a topology optimization problem is formulated based on the level set method, and the method of regularizing the optimization problem by introducing fictitious interface energy is explained. Next, the reaction–diffusion equation that updates the level set function is derived and an optimization algorithm is then constructed, which uses the finite element method to solve the equilibrium equations and the reaction–diffusion equation when updating the level set function. Finally, several optimum design examples are shown to confirm the validity and utility of the proposed topology optimization method. |
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