考慮應變硬化的桁架結構之主對偶連續式極限分析

Sequential Limit Analysis of Strain-Hardening Trusses Based on a Primal-dual Method

呂學育(S. Y. Leu) ； 李嶸杉(R. S. Li) ； 林彥均(Y. C. Lin)

《中華科技大學學報》 51期 (2012/04) Pp. 137-148

https://doi.org/10.7095/JCUST.201204.0132

摘要

本文旨在利用基於主對偶法的連續式極限分析，探討考慮應變硬化性質的結構承載能力。極限分析基於下限或上限定理以直接估算結構的塑性反應，可作為結構設計及安全評估。另一方面，連續式極限分析藉由降伏強度及結構變形幾何的漸次迭代更新，可視為古典極限分析之延伸，已被廣泛地驗證為一精確及具效率的大變形分析工具。此外，下限與上限問題陳述的對偶性質，可應用於極限分析的數值計算，不僅同時計算上限及下限解，也可迅速收斂得到主對偶之最佳解。文中以桁架結構為數值案例，其為一古典之極限分析問題，惟當考慮具有應變硬化性質，則下限法或上限法無法直接應用於問題之求解，此時連續式極限分析將突破古典極限分析的設限，順利地求解考慮應變硬化性質的極限承載能力。文中除引用主對偶內點法進行連續式極限分析，以探討桁架結構的極限承載能力；同時基於比對驗證之目的，亦將利用有限元素法套裝軟體進行彈塑性之逐步分析。最後，本文比較極限分析之直接法與有限元素彈塑性之逐步分析的分析結果，並對基於主對偶方法的連續式極限分析作進一步探討。

關鍵字

極限分析 ； 應變硬化 ； 主對偶法 ； 數學規劃

並列摘要

The paper is aimed to study the load bearing capacity of strain-hardening structures by using sequential limit analysis based on a primal-dual method. By sequential limit analysis, it is to conduct a sequence of limit analysis problems with updating the yield criterion and the deformed configuration. On the other hand, sequential limit analysis has been demonstrated extensively to be an accurate and efficient tool for the large deformation analysis. The duality relationship between the static and the kinematic formulations can be applied to improve the numerical investigation of limit analysis. It not only calculates the upper bound and the lower bound simultaneously but also converges rapidly to the primal-dual optimal solution. Illustrative examples are focused on truss structures. It is more appropriate to apply sequential limit analysis to investigate the strain-hardening trusses. The primal-dual interior-point algorithm provided by Matlab is incorporated with the concept of sequential limit analysis and compared to the results obtained by the elastic-plastic analysis performed by the computer code Abaqus. Finally, future work on sequential limit analysis based on the primal-dual method is discussed.

並列關鍵字

Limit analysis ； Strain hardening ； Primal-dual method ； Mathematical programming