Shape and topology optimization of compliant mechanisms using a parameterization level set method |
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| Institution: | 1. School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, NSW 2006, Australia;2. Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin N.T., Hong Kong SAR, PR China;3. Center for Singapore-MIT Alliance, National University of Singapore, E4-04-10, 4 Engineering Drive 3, Singapore 117576, Singapore;1. State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China;2. School of Software Engineering, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China;1. Guangdong Province Key laboratory of Precision Equipment and Manufacturing Technology, South China University of Technology, Guangzhou, Guangdong, 510640, China;2. Division Microrobotics Department of Computing Science, University of Oldenburg, Uhlhornsweg 84, A1, 26111 Oldenburg, Germany;1. The State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan, China;2. Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, NT, Hong Kong;1. State Key Laboratory of Subtropical Building Science, School of Civil Engineering and Transportation, South China University of Technology, Guangzhou, Guangdong, China;2. Architecture and Civil Engineering Institute, Guangdong University of Petrochemical Technology, Maoming, Guangdong, China |
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| Abstract: | In this paper, a parameterization level set method is presented to simultaneously perform shape and topology optimization of compliant mechanisms. The structural shape boundary is implicitly embedded into a higher-dimensional scalar function as its zero level set, resultantly, establishing the level set model. By applying the compactly supported radial basis function with favorable smoothness and accuracy to interpolate the level set function, the temporal and spatial Hamilton–Jacobi equation from the conventional level set method is then discretized into a series of algebraic equations. Accordingly, the original shape and topology optimization is now fully transformed into a parameterization problem, namely, size optimization with the expansion coefficients of interpolants as a limited number of design variables.Design of compliant mechanisms is mathematically formulated as a general optimization problem with a nonconvex objective function and two additionally specified constraints. The structural shape boundary is then advanced as a process of renewing the level set function by iteratively finding the expansion coefficients of the size optimization with a sequential convex programming method. It is highlighted that the present method can not only inherit the merits of the implicit boundary representation, but also avoid some unfavorable features of the conventional discrete level set method, such as the CFL condition restriction, the re-initialization procedure and the velocity extension algorithm. Finally, an extensively investigated example is presented to demonstrate the benefits and advantages of the present method, especially, its capability of creating new holes inside the design domain. |
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