應用移動漸近線法於結構之最佳化設計

Optimum Design of Structures by Method of Moving Asymptotes

郭純孜(Chun-Tzu Kuo)

指導教授 ： 張永康

淡江大學/工學院/航空太空工程學系碩士班/碩士(2008年)

https://doi.org/10.6846/TKU.2008.00960

摘要

移動漸近線法的原理是將一個函數利用倒數近似法加上中介變數轉換為近似原問題的函數。因移動漸近線法可以處理各種設計參數並因應各式目標函數與限制條件，本研究應用移動漸近線法之特性得到函數之近似式並利用對偶法對最佳化問題求解。對偶法為將原本的最小化問題以與之有關的最大化對偶函數取代。也就是將原設計問題轉換為凸性且為可分離的子問題，這有助於結構最佳化問題能夠快速地求解。因此本研究應用移動漸近線法得到結構行為之近似函數，再採用對偶法執行結構之最佳化設計。
　　數值分析中將對各種結構作分析，分別以結構輕量化設計或提高結構之第一自然振動頻率為目的。本研究以ANSYS有限元素分析軟體中的APDL語法與FORTRAN程式結合成一系統程式，並使用有限差分法計算靈敏度以獲得執行移動漸近線法所需之數據。範例中證明移動漸近線法於結構之最佳化設計上可以得到比其他文獻更好的結果。

關鍵字

移動漸近線法 ； 對偶法 ； 靈敏度分析

並列摘要

Method of Moving Asymptotes (MMA) is used by reciprocal approximate and moving asymptotes to approximate a original function. Because MMA can deal with various kinds of design parameters and handle all kinds of objective and constraint functions, this study applies the characteristics of MMA to obtain the approximation function and then uses dual method to solve the problem. Dual method is that the original minimization problem is replaced by maximization of dual function relating to it. That is, the dual method was used to solve design problem by a subproblem, which is convex and separable. Therefore, this study applies MMA to get the approximate function of structural behavior, and then adopts dual method to obtain the optimum design of structures.
　　Optimum design of different structures will be analyzed in Numerical examples. A systematic program which combined APDL with FORTRAN to calculate sensitivity and necessary data for MMA was developed in this study. Optimum design of structures by MMA can obtain better results than other references was proved in this study.

並列關鍵字

Method of Moving Asymptotes ； Dual Method ； Sensitivity analysis

參考文獻

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