Boundary variation method and material distribution method are distinct approaches for structural optimization. In the early days, due to the fact that boundary variation methods were generally not able to handle topological changes, it was applied only in shape optimization problems where the topology of initial design is fixed during optimization process. To enable topological changes that are essential to deliver major performance improvements, material distribution method was introduced in the work of Bendsoe and Kikuchi, and thereafter widely adopted in nearly all aspects of topology optimization. Recently a novel boundary variation method for topology optimization was developed based on level set method, in which topological changes is allowed for. In the thesis, we study the level set based boundary variation method and material distribution method for structure optimization problem. / Finally, we studied the semi-Lagrange scheme to solve the Hamilton-Jacobi equation in level set based boundary variation method. In level set method, the free boundary of a structure is optimized via solution of a Hamilton-Jacobi equation. The numerical stability condition in explicit schemes for discrete Hamilton-Jacobi equation severely restricts the time step. To improve the numerical efficiency, we employ a semi-Lagrange scheme to solve Hamilton-Jacobi equation. Therefore, much larger time steps can be obtained and the number of iterations before convergence is greatly reduced. / Firstly, we studied the minimum compliance optimization problem of thermoelastic structures. In this optimization problem, we find that the optimal structures given by the state-of-art material distribution method, SIMP i method, generally have large area of intermediate density values that are not feasible in practical engineering applications because of their poor manufacturability and high costs. Therefore, we apply level set based boundary variation method in the optimization problem. As numerical results show, the optimal structures obtained are well suited to engineering applications. / To sum up, we explore in this thesis the boundary variation method and material distribution method for structure optimization problem. Several meaningful results and conclusions are obtained. / We secondly studied the stress minimization problem. In practical applications the most important requirement on a structure is often the strength of structure which characterizes the resistance to failure. In stress minimization problem, the objective is to minimize the distribution of von Mises stress in a structure. Here, level set method gives a significant convenience for stress optimization, in particular, we need not to incorporate any stress amplification factor of material microstructure which would be an important issue in material distribution method. Moreover, in order to derive more control of maximum stress, we utilize the Kreisselmeier-Steinhauser function to aggregate stresses at each point in a structure into a single global function. / Xia, Qi. / "October 2007." / Adviser: Michael Yu Wang. / Source: Dissertation Abstracts International, Volume: 69-08, Section: B, page: 4993. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 102-111). / 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_344120 |
| Date | January 2007 |
| Contributors | Xia, Qi., 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 (xiii, 111 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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