Another interesting area we investigate is topology optimization with geometric control. Our initial research interests in topology optimization with geometric width control were motivated by the challenge of how to get more manufacturable compliant mechanism designs for MEMS devices. Considering MEMS fabrication technologies, say LIGA, it is natural that designs with specified feature width are more preferable with respect to those with free-form geometries. We propose a variational approach to this problem. A novel quadratic energy functional is employed to govern the geometric feature width of the design. This geometry describing functional is added to the performance-describing functionals. In this way both the performance and the geometric width of the design are optimized simultaneously. The preliminary results show that this method is capable of generating strip-like (or beam) designs with specified feature width, which is a highly desirable characteristic and uniquely distinguishes the proposed method. / Compliant mechanisms are involved in many applications both in the macro and in the micro world. But for a long time, the design procedure of compliant mechanisms was rather a handicraft than a technology. The conventional way is made on an ad hoc basis which to a large extent depends on the designers intuition, experience and inspiration. The limitations of such a trial-and-error approach are obvious: it is not always guaranteed to work, especially when the design is very complicated or when topology and multi-material problems are taken into account. The practical design and application of compliant mechanisms are in need of a systematic approach to create conceptual design. Here, we take a level-set-based new approach to solve this problem. / Considering the actual requirements on reliability, we also investigate how to get conceptual designs with distributed compliance, which is the core part of this thesis. We find the intrinsic defects in the widely used spring model and prove that it will inevitably cause designs with both large output displacements and low strain energies. We will show low strain energy does not guarantee high stiffness. To evenly distribute the compliance, we propose a new method considering the "characteristic stiffness" at interested points. In this way, the strength (stiffness) at the output port of the system is involved into the objective function and optimized directly. This new method is applied to some benchmark examples of both structure optimization and compliant mechanism optimization to validate its performance. / In our proposed method, the compliant mechanism design problem is recast as an infinite dimensional optimization problem, where the design variable is the geometric shape of the compliant mechanism and the goal is to find a suitable shape in the admissible design space so that the objective functional can reach a minimum. The geometric shape of the compliant mechanism is represented as the zero level set of a one-higher dimensional level set function, and the dynamic variations of the shape are governed by the Hamilton-Jacobi partial differential equation. The application of level set methods endows the optimization process with the particular quality that topological changes of the boundary, such as merging or splitting, can be handled in a natural fashion. By making a connection between the velocity fields in the Hamilton-Jacobi partial differential equation with the shape gradient of the objective functional, we go further to transform the optimization problem into that of finding a steady state solution of the partial differential equation. / Our research follows the route from ease to difficulty, reflecting our understanding of the compliant mechanism design problem at different stages. The first problem addressed in this thesis is how to maintain the structural connectivity during the topology optimization process. De facto hinges are known to be a fairly typical phenomenon in topology optimization of compliant mechanisms; they represent highly localized compliance regions. A most adverse side effect caused by de facto hinges is that they are prone to cause a structurally disconnected design, especially to that with a low volume ratio. To solve this problem, a digital topological connectivity scheme is integrated within the level set model, which ensures connectivity while allows topology changes. This is our first step in the research process. / Chen, Shikui. / "January 2007." / Adviser: Michael Yu Wang. / Source: Dissertation Abstracts International, Volume: 68-08, Section: B, page: 5513. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 149-162). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_343808 |
| Date | January 2007 |
| Contributors | Chen, Shikui, Chinese University of Hong Kong Graduate School. Division of Automation and Computer-Aided Engineering. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, theses |
| Format | electronic resource, microform, microfiche, 1 online resource (xv, 162 p. : ill.) |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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