Design of distributed compliant micromechanisms with an implicit free boundary representation |
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Authors: | Zhen Luo Liyong Tong Michael Yu Wang |
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Affiliation: | (1) School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, Sydney, NSW, 2006, Australia;(2) Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin N.T., Hong Kong, China |
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Abstract: | In this paper, a parameterization approach is presented for structural shape and topology optimization of compliant mechanisms
using a moving boundary representation. A level set model is developed to implicitly describe the structural boundary by embedding
into a scalar function of higher dimension as zero level set. The compactly supported radial basis function of favorable smoothness
and accuracy is used to interpolate the level set function. Thus, the temporal and spatial initial value problem is now converted
into a time-separable parameterization problem. Accordingly, the more difficult shape and topology optimization of the Hamilton–Jacobi
equation is then transferred into a relatively easy size optimization with the expansion coefficients as design variables.
The design boundary is therefore advanced by applying the optimality criteria method to iteratively evaluate the size optimization
so as to update the level set function in accordance with expansion coefficients of the interpolation. The optimization problem
of the compliant mechanism is established by including both the mechanical efficiency as the objective function and the prescribed
material usage as the constraint. The design sensitivity analysis is performed by utilizing the shape derivative. It is noted
that the present method is not only capable of simultaneously addressing shape fidelity and topology changes with a smooth
structural boundary but also able to avoid some of the unfavorable numerical issues such as the Courant–Friedrich–Levy condition,
the velocity extension algorithm, and the reinitialization procedure in the conventional level set method. In particular,
the present method can generate new holes inside the material domain, which makes the final design less insensitive to the
initial guess. The compliant inverter is applied to demonstrate the availability of the present method in the framework of
the implicit free boundary representation. |
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Keywords: | Shape and topology optimization Compliant mechanisms Level set methods Radial basis functions Optimality criteria method |
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