最佳化結構設計都存在單調性及非單調性的行為函數。若使用近似法最佳化，為了能掌握正確性及求解效率，需要能處理單調性及非單調性的近似函數。本文建構及探討TANA-TDQA系列近似函數，稱之為 TANA3-TDQA2以及TANA1-TDQA2的兩種混合近似函數。經由數值測試確認TANA-TDQA混合近似函數比個別的TANA及TDQA近似函數的誤差小。本文詳細敘述及探討混合近似法最佳化之解題程序、參考點的選取及收斂策略。此等最佳化流程被應用在簡結構設計問題上，包含應用有限元素分析(ANSYS)及應用最佳化求解器 (Visual Doc)，能以較少的有限元分析次數，提升近似法於最佳化設計的效率。以簡結構的設計經驗，應用在大型鋼結構設計最佳化，光學檢測結構設計最佳化，以及微致動器結構設計最佳化，皆可得到全域設計效果。TANA3-TDQA2的近似法最佳化為本研究最為推薦，該近似法的求解穩健性及精確性略優於TANA1-TDQA2。 Approximation technique can be applied for solving large scale structural optimization problems. Most structural optimization contains monotonic and non-monotonic behavior functions that seriously influences the computational efficiency. Mixed approximation method has been recognized as an effective way of dealing with this monotonicity behavior. Most published paper mentioned MMA series mixed approximation method. In this thesis, a mixed approximation function with TANA-TDQA series has be presented. The TANA approximation can well handle non-monotonic function. The TDQA can well handle monotonic function. This thesis presents two mixed approximation function TANA3-TDQA2 and TANA1-TDQA2. A numerical examples used to investigate TANA-TDQA series and also compare with individual TANA and TDQA. The error of TANA-TDQA function is generally less then individual TANA or TDQA function. Several relative simple structures are presented to illustrate how the TANA-TDQA optimization works. The finite element and analysis (ANSYS) and design optimization (Visual Doc) are integrated for solving the problem. It can be seen that the number of finite element analysis can be reduced. Three large-scale design problems are applied for further examing the performance of presenting TANA-TDQA function. The steel building structural design shows the presented approximation methods are efficient and accurate. The optical instrumental structure contain two design objectives. The micro thermal-actuator structure requires to find the maximum displacement for grasping human cell. This problem only spend about 2 hours in stead of 6 hours ,as compare with original work. TANA3-TDQA2 is the most recommended from this study, since it is more efficient than TANA1-TDQA2.
