基於MATLAB主對偶法的混合式硬化桁架連續式極限分析

Sequential Limit Analysis of Trusses with Combined Hardening by the Primal-dual Method of MATLAB

呂學育(S. Y. Leu) ； 李璟鑫(C. S. Lee) ； 黃俊偉(C. W. Huang)

《中華科技大學學報》 54期 (2013/01) Pp. 121-133

摘要

本文基於線性規劃問題的對偶性質，利用MATLAB主對偶法的計算功能，以同時求解主問題及對偶問題，進行線性規劃問題的最佳解計算。在文中我們首先考慮典型線性規劃的極值問題，分別針對其主問題及對偶問題進行圖解法計算及主對偶法計算，以闡述主對偶性質及驗證MATLAB線性規劃的效用。此外，我們也考慮具混合式硬化性質的桁架結構之連續式極限分析問題，藉由主對偶法計算以同時掌握桁架結構的極限載重與各接點之速度資料，漸次迭代更新降伏強度及結構變形幾何，探討材料硬化性質對桁架結構的極限載重之影響。最後，發現本文基於主對偶法的連續式極限分析結果，與文獻上解析結果具有良好吻合度。

關鍵字

線性規劃 ； 主對偶法 ； 極限分析 ； 連續式極限分析 ； 混合式硬化

並列摘要

The paper utilizes the duality of linear programming to solve simultaneously the primal and dual problems by the prim-dual algorithm provided by MATLAB. We first consider a typical linear programming problem. For comparisons and validations, the graphical method and the primal-dual algorithm are then applied to solve the primal and dual problems. On the other hand, we also investigated sequential limit analysis of truss structures with combined hardening by updating the yield function and deformed configuration. Accordingly, the effects of combined hardening on the plastic limit load are studied. It is found that there exists good agreement between the results obtained by the primal-dual method and the analytical solutions.

並列關鍵字

Linear programming ； Primal-dual method ； Limit analysis ； Sequential limit analysis ； Combined hardening