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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/15739
標題: | 結構最佳化之新式混合兩點近似法 A New Mixed Two-Point Approximation Method for Structural Optimization |
作者: | Chun-Chieh Chen 陳俊傑 |
指導教授: | 鍾添東 |
關鍵字: | 結構最佳化,混合近似法,兩點近似方法,有限元素方法, Structural optimization,Mixed approximation method,Two-point approximation method,Finite element method, |
出版年 : | 2012 |
學位: | 碩士 |
摘要: | 本文根據兩點指數近似法及基於梯度的移動漸進線近似法,提出一個新的結構最佳化近似方法,稱為兩點指數近似法及基於梯度的移動漸進線近似法之混合近似方法。在此方法中,近似函數是藉由兩個連續設計點的函數值以及靈敏度值所建立。除此之外,當兩個連續設計點之靈敏度值有正且有負,函數的精確度將會藉由基於梯度的移動漸進線近似法而改善。並且,在兩點指數近似法及基於梯度的移動漸進線近似法之混合近似方法中,指數的限制將會根據前一個設計點的函數值自動調整。經由此近似法,可將結構之行為函數,諸如應力、位移等,轉換成設計變數的顯函數。如此一來,運用傳統數值最佳化方法即能有效求解近似問題。此外,本文也整合最佳化理論與有限元素分析軟體以及程式設計程式,發展一套整合程式以求解結構最佳設計問題。結果指出在一般結構最佳設計問題之中,利用此法能快速找到收斂並且正確的解;同時也顯示出本法在結構最佳化中之效率及實用性。 This thesis presents a new approximation method for structural optimization, which is based on the TPEA and the GBMMA approximations, named TPEA-GBMMA. In this method, approximate functions are constructed by the function values and sensitivities of two successive design points. In addition, the functional precision is improved by using GBMMA when the sensitivities of two successive design points have different signs. Moreover, the exponential limitation in TPEA-GBMMA is adjusted automatically according to the function value of previous design point. The structural behavior functions, such as stress and displacement, can be converted to the explicit form of design variables with the use of the proposed method. Hence, the conventional optimization techniques can work efficiently to solve the approximate problems. A computer program is developed by integrating the finite element software ANSYS, Microsoft Visual Studio 2008, and numerical search methods to solve structural optimum design problems. The results indicate that the new approximation can quickly find the convergent and accurate solutions for general optimization problems. Also, the practicability and efficiency of the new approximation in structural optimization is proved. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/15739 |
全文授權: | 未授權 |
顯示於系所單位: | 機械工程學系 |
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