本文建構回應表面近似函數替代應力及位移的可靠度限制條件來進行最佳化，應用於發展求解隱性破壞函數的工程設計問題。本文首先敘述求解顯函數的一次二階矩與求解隱函數的回應表面可靠度分析方法，並結合最佳化設計軟體Visual FDM進行最佳化設計，最後形成互動式設計的解題模型與流程。首先選取適當的起始值，建立回應表面近似函數，在最佳化設計的解題過程中，用回應近似函數建立可靠度的限制條件進行搜尋設計解的迭代，將迭代後所得的起始點進行有限元分析及修正設計點，建構新的回應近似函數，進行可靠度分析。如此重複建構回應函數，可靠度分析，修正設計點，進行可靠度分析，直至可靠度值收斂之後，進行最佳化設計解搜尋。若設計解尚未收歛，將此設計解設為起始點，繼續建構回應函數，一直到設計解收斂。本文的方法可應用於實際含有可靠度限制條件的工程結構與機械最佳化設計問題。 This thesis first studies the numerical method of first-order second moment (FOSM) for structural reliability analysis ,named H-L and H-R approach. A second-order approximation method establishes the response surface for the limit state function is explored and then combine H-R approach in reliability based structural optimization problems. The approximation function use intermediate checking point technique to regulate the design point in the iteration process for a better approximate reliability index. The example shows the approximate reliability is accurate and usable for replacing the real limit state function. Visual feasible direction method (Visual FDM) in optimization is conveniently united with H-R approach and response surface technique for obtaining the reliability index. The problem solved in this work only contains the reliability required in design constraints.The finite element analysis act as the experimental design basis that generates design points for establishing implicit limit state function constructed by response surface approximation. A visual iterative reliability based optimization can be done by utilizing the feature in Visual DOC of single run execution. It is very convenient for a an optimization engineer to solve the problem of using the commercial finite element analysis software.
