結構最佳化設計之準二次兩點保守近似法

Abstract

本文改良結構最佳化設計之傳統保守近似法，並提出準二次兩點保守近似法。在本近似法中，除了採用目前設計點之函數值與靈敏度值，也參考前一設計點的函數值與靈敏度值來建構近似函數，以提昇近似函數的準確性。藉由本近似法，可將結構的各種行為函數如應力、位移、共振頻率、動態響應等轉換成為設計變數的顯函數，如此一來，結構最佳化設計問題便可以輕易地透過一般的最佳化數值方法加以求解。最後，發展一套結合準二次兩點保守近似法與有限元素分析軟體ANSYS之結構最佳化設計程式，並利用此程式來驗證數個結構最佳化問題。從這些實例的數值結果可得知，本文提出的方法能以較少的迭代次數獲得收斂且準確的結果，證明此準二次兩點保守近似法在結構最佳設計的實用性。

This thesis improves the conventional conservative approximation method for structural optimization. A new quasi-quadratic two-point conservative approximation method is presented in this thesis. Two-point fitting scheme is applied to construct the approximation function. Both the derivatives and the functional values of the previous design point are adopted to improve the approximation accuracy. By using the new approximation method, the structural behavior functions, such as stress, displacement, natural frequency and dynamic response, can be converted to explicit functions. Therefore, utilizing the conventional optimum techniques can efficiently solve the explicit approximation problem. A computer program is also developed by integrating the approximation method with the finite element software ANSYS. Optimization of several structure design problems can be obtained with fewer design iterations. The results demonstrate that the proposed method can quickly find the convergent and accurate solutions for general structural optimization problems. It proves that the proposed method is efficient and practical in structural optimization.