本文根據兩點指數近似法,提出一個新的結構最佳化近似方法,稱為加強兩點指數近似法。在兩點指數近似法中,當中介變數的指數值無法由前一個設計點的靈敏度值決定時,兩點指數近似法的準確度會降低,在這種情況下,加強兩點指數近似法使用替代方程式來建立近似函數。經由此近似法,可將結構之行為函數,例如應力、位移等,轉換成設計變數的顯函數,如此一來,結構最佳化問題即可運用傳統數值最佳化方法來求解。此外,本文整合了電腦繪圖軟體、有限元素分析軟體、和程式開發軟體,發展出一套結構最佳化程式,並利用此程式求解數個典型的結構最佳化問題,其結果指出,利用加強兩點指數近似法能快速找到最佳解,驗證了此近似法在結構最佳化中的效率和實用性。
This thesis proposes a new approximation method called enhanced two-point exponential approximation (ETPEA), which is derived based on a previous approximation method, two-point exponential approximation (TPEA). In TPEA, when the exponents of intervening variables cannot be calculated by fitting the sensitivities of the previous design point, the accuracy of TPEA is decreased. In such cases, ETPEA uses a substitution function to construct the approximate function. With this new approximation method, structural behavior functions, such as stress and displacement functions, can be converted into explicit functions of design variables. In this way, structural optimization problems can be solved by conventional numerical optimization methods. Moreover, a structural optimization program is developed by integrating the CAD software AutoCAD, the finite element software ANSYS, and Microsoft Visual Studio C++. The program is used to solve some typical structural optimization problems, and the results indicate that the optimum design can be found quickly with the new approximation method. It is verified that the new approximation method is efficient and practical in structural optimizations.