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 本文綜合上界限理論以及變分法，分析圓桿胚料通過流線模成正多邊 形截面之擠製加工。首先假設呈隱函數型態的流線函數，建立符合該擠製 問題的動可容速度場，再根據上界限理論求出總功率消耗的泛函數，最後 以變分法最小化總功率消耗的泛函數，以求所預先假設之流線函數的限制 條件，並用以求上界限解。和傳統上界限解比較，最主要之不同處乃在於 可得到傳統上界限解析所忽略之靜可容邊界條件，以作為求解的限制條件 。 根據上述方法所獲得的結果，本文除探討加工條件對模具外形 及擠製力的影響外，文中亦論及靜可容邊界條件對上界限解析的影響，並 和Gunasekera以及Hoshino之解析結果作比較。
 We use upper bound theorem and variational method to analize the extrusion of polygonal section through streamlined dies in this paper. First we assumestreamlined function which is implicit to build kinematic admissible velocity field that satisfies this extrusion problem. Then according to upper bound theorem we can derive the functional of total power consumption. At least,in use of the variational method,we can minimize the funtional of total power consumption to get the constraints of the streamlined function that assumed previously. Comparing with the traditional upper bound solution the major difference is that we can get the static admissible boundary conditions whichis neglected by traditional upper bound analysis and use them as constraintsof solution. According to the results derived by this method,we do not only discuss the influence of the operation conditions on the die profile and extruded forcebut also mention the influence of static admissible boundary condition on the upper bound solution,and compare our results with Gunasekera and Hoshino's.
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 1 以變分上界限法分析任意面對稱截面之擠製加工問題 2 雙金屬圓桿擠製之變分上界限解析

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 1 以變分上界限法分析任意面對稱截面之擠製加工問題

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