結構最佳化之指數移動漸進線近似法

Abstract

本文將結構最佳化中之保守近似法一般化，並提出基於移動漸進線近似法與高階凸線性近似法之保守近似法，稱為指數移動漸進線近似法。在此法之中，以兩連續設計點之函數值與靈敏度值建構近似函數，並利用設計變數之上下界增加近似函數之保守度。經由此近似法，可將結構之行為函數，諸如應力、位移、自然頻率及動態響應等，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。本文並結合最佳化理論與有限元素分析軟體，發展一套整合程式以求解結構最佳設計問題。結果顯示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 generalizes the conservative approximation method for structural optimization and presents a new approach which is based on the method of moving asymptotes and higher order convex approximation, named exponential MMA. In this method, approximated functions are constructed by the function values and sensitivities of two successive design points; in addition, the functional convexities are improved by means of the bounds of design variables. With the use of the proposed approximation method, the structural behavior functions, such as stress, displacement, natural frequency or dynamic response, can be converted to the explicit form of design variables. Therefore, utilizing the conventional optimization techniques can efficiently solve the approximated problems. A computer program is also developed by integrating the optimization theorem and the finite element software ANSYS to solve structural optimum design problems. The result demonstrates that the proposed method can quickly find the convergent and accurate solutions for general structural optimization problems, and it also proves that this method is efficient and practical in structural optimization.