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標題: 最佳清晰度之結構形勢最佳化設計
Topology Optimization of Structures with Less Uncertain Element
作者: 謝嘉擎
Shieh, Chia-Chyng
關鍵字: topology;形勢;optimization;最佳化
出版社: 機械工程學系
本文針對結構形勢最佳化的問題, 在順從度最小化與基礎特徵值最大
化兩目標需求下,加入材料使用量和清晰度的限制條件, 並應用 MSC/
NASTRAN 和 P3/PATRAN 兩種軟體進行有限元素分析及其前後及處理, 在
UNIX 作業系統環境中, 以連續線性規劃法進行多目標結構形勢最佳化設
計. 本研究以各元素的比密度為設計變數, 每個元素的楊氏係數為其
比密度的函數, 並以折衷法及模糊理論為求解多目標問題的兩種方法, 分
別探討使用這兩種方法所遭遇的困難, 嘗試使用基礎結構,集中質量,適應
權重加權法和各種歸屬函數來解決這些問題, 並求出結構的最佳形勢. 對
於最佳化結果常會發生形勢不清晰的現象, 藉由採用高階元素或外加束制
條件的方式可達到提高清晰度的效果, 讓設計結果在最少後處理後便能使
用. 本文以三個實例驗證所提出的多種構想, 並得到預期的效果.

This thesis studies structural topology optimization. Two
objectives are pursued. One is to minimize the compliance and
the other one is to maximizethe fundamental eigenvalue. The
constraints are imposed on the material usedand high clear-cut
topology in a specified design space. MSC/NASTRAN and P3/PATRAN
are used to analyze the structures and do the pre- and post-
processes, respectively. A Unix shell script is developed to
accomplish the design optimization loop. The sequential linear
programming algorithm is utilized to slove the optimization
problem. The design variable is the normalized density
of each finite element, and the Young's modulus is assumed to be
a function of the normalized density. Thecompromise programming
and the fuzzy theory are used to treat the mult-objective
optimization problems. The difficulties when using the two
methods are discussed and some methods, such as using base
structures, lumped mass, adaptive weighting and many kinds of
membership functions are proposed toovercome the problems. For
many results of optimum topology designs, uncertainelements
often exist. Using higher order elements and clear-cut topology
contraint can reduce the numbers of uncertain elements and thus
make the design ready for use with minimum post-processing
works. Three examples demonstrate the proposed methods and get
the expected results.
Appears in Collections:機械工程學系所

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