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題 名 | On the Convergence of a General Algorithm for Limit Analysis Involving Rate-Sensitive Materials=應用於含應變率效應極限分析之計算法的收斂性探討 |
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作 者 | 呂學育; | 書刊名 | 中國工程學刊 |
卷 期 | 22:3 1999.05[民88.05] |
頁 次 | 頁351-356 |
分類號 | 440.13 |
關鍵詞 | 極限分析; 應變率相依; 計算法; 收劍性; Limit analysis; Rate sensitive; Algorithm; Convergence; |
語 文 | 英文(English) |
中文摘要 | 本文證明了一應用於含應變率效應極限分析之計算法的收斂性。文中推廣一綜合 圓滑化與持續近似的計算法之適用性,以應用於含應變率效應之極限分析。首先將下限的問 題陳述轉換成上限的問題陳述,再以有限元素法進行離散作業,然後採用這計算法以求解所 衍生的最佳化問題,最後以Holder不等式證明此計算法的收斂性。然而,當不含應變率效 應時,則將Holder不等式簡化成Caucy-Schwarz不等式,並得證相關之收斂性。 |
英文摘要 | The convergence of a genera] algorithm for limit analysis involving rate-sensitive materials is proved. The application of this combined smoothing and successive approximation (CSSA) algorithm was extended to deal with plasticity problems involving rate-sensitive materials. A plasticity problem was stated by the upper bound formulation derived rigorously from the lower bound formulation. Applying a finite-element discretization, we then employed the CSSA algorithm to solve the resulting optimization problem iteratively. Finally, the Holder inequality was adopted to prove the convergence of the CSSA algorithm. Moreover, it is the familiar Cauchy-Schwarz inequality, a reduced form of the Holder inequality, which is utilized to prove the convergence of the CSSA algorithm applied to plasticity problems involving rate-insensitive materials. |
本系統中英文摘要資訊取自各篇刊載內容。