Rechnergestützter Entwurf von Mikrosystem-Bauelementen: Automatische Topologieoptimierung elektrostatisch angeregter Aktoren und Sensoren
Zusammenfassung der Projektergebnisse
In this project, we pursued the following steps to satisfy several particular necessities for efficient MEMS design using the structural topology optimization method. 1 Using the R-function method, an analytical expression of the level set surface is constructed. The smoothness of this method is better than the sign distance surface which is constructed using the mathematical Boolean function. At the same time, the surface can satisfy the specified Dirichlet and Neumann boundary conditions so that it can be used as the initial value for the optimization equation. 2 Using the modified PDE method, a stable finite element discretization of the level set equation is implemented. This method can balance the numerical oscillation and the sharpness of the material boundaries. 3 Using the Lagrangian multipliers, we re-write the whole optimization model using the Lagrange functional and then derive the corresponding strong-form optimization equation. The optimization equation can be accurately solved simultaneously with the forward physical problem in the Fernlab. 4 Programming of the level set type structural topology optimization using the commercial software Femlab. The original program can be freely downloaded from our homepage. 5 Two types of mesh adaptation methods, the r-adaptive and the h-adaptive methods are integrated with structural optimization. The smoothness of the material boundary can be improved by using these two types of mesh adaptation. 6 For structural optimization with multiple phases of materials we extend the single level set method to the two level sets method using Femlab. 7 For the design dependent load, such as the electrostatic force, we use the moving mesh method to derive a unified PDE expression for this kind of optimization problem. 8 A novel compliant rotational mirror is designed using our optimization method and a prototype is fabricated at IMTEK. The simulation result and measurement of the input displacement and rotational angle show correlate well. Following the fabrication of a prototype rotational mirror, we are re-designing the compliant mechanism to micrometer dimensions. In this part, we are collaborating with the Laboratory for microactuator, IMTEK, University of Freiburg. The fabrication will be performed in the cleanroom at IMTEK. Implementation of a graphical user interface (GUI) for the structural optimization can provide a simple way to allow MEMS engineers to try out their own ideas. We are using the Femlab script language to program a client side GUI. Since it takes time to make this GUI fully available for the user, we have put our benchmark Femlab program on our homepage which can be freely downloaded (http://www.imtek.de/simulation).
Projektbezogene Publikationen (Auswahl)
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Multiphysics for topology optimization in MEMS, EuroSIME 2005: 214-218.
J.G. Korvink, Z. Liu
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Structural topology optimization: fully coupled level set method via FEMLAB, Structural Multidisplinary Optimization, Vol 29 2005: 407-417.
Z. Liu, J.G. Korvink, R. Huang
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Design of compliant rotational mirror with structural topology optimization method, Actuator 2006: 716- 719.
Z. Liu, J.G. Korvink, U. Wallrabe, C. Müller
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Implementation of structural topology optimization in COMSOL, Comsol Conference 2006:157-161.
B. Lemke, Z. Liu, J.G. Korvink
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Multiphysics for structural topology optimization, Sensors Letter, Vol 4 2006:191-199.
Z. Liu, J.G. Korvink, M.L. Reed
