本研究之目的為改良結構最佳化設計之保守近似法,並根據移動漸近線近似法發展一種新的兩點近似法,稱為兩點適應移動漸近線近似法。在此方法中,藉由修改移動漸近線近似法之中介變數來產生斜漸近線,並利用兩連續設計點之函數值及靈敏度值自動調整斜漸近線之斜率。換言之,本方法會考量結構行為的單調性來建立近似函數以確保近似品質。另外,本研究提出一種採用分段近似函數的新修改策略,以避免過往保守近似法中奇異點與不當近似的產生。經由此近似法,可將結構之行為函數轉換成以設計變數表示的顯函數,如此一來,最佳解便能透過數學優化法對連續近似最佳化問題加以求解而得到。此研究亦整合最佳化程式、電腦輔助繪圖軟體及有限元素分析軟體進行自動化結構最佳設計,並以多個結構最佳化問題驗證本近似法及修改策略。結果顯示,利用兩點適應移動漸近線近似法可準確而快速地找出最佳解,並且利用修改策略可有效地處理奇異點及不當近似。這驗證了本研究之理論在結構最佳化中的實用性。
The purpose of this thesis is to improve conservative approximation methods for structural optimization. A new two-point approximation method based on method of moving asymptotes approximation (MMA) is developed, which is called two-point adaptive method of moving asymptotes approximation (TAMMA). It modifies intervening variables of MMA to generate oblique asymptotes and utilizes function values and sensitivities at two successive design points to adjust the slopes of the oblique asymptotes automatically. In other words, it can consider the monotonicity of structural behavior to construct approximate functions to ensure the approximation quality. Also, a new modification strategy which adopts piecewise approximate functions is proposed to avoid the singularity and inappropriate approximation that existing conservative approximation schemes would encounter. With the use of TAMMA, several kinds of structural behavior can be represented as explicit functions of design variables. Therefore, the optimum design can be found with sequential approximate optimizations solved by mathematical optimization techniques. Moreover, a program integrating ANSYS, AutoCAD and Microsoft Visual C++ is developed for automated structural optimization. TAMMA and the modification strategy are tested in several structural optimization problems. The results indicate that TAMMA can converge to accurate optimum designs quickly, and the modification strategy can deal with singularities and inappropriate approximations effectively. Those prove that the proposed methods are practical in structural optimization.