Equivalent method for accurate solution to linear interval equations  

作　　者：王冲 邱志平 

机构地区：[1]Institute of Solid Mechanics, Beihang University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2013年第8期1031-1042,共12页应用数学和力学（英文版）

基　　金：supported by the National Natural Science Foundation of China(Nos.90816024,10872017,and 10876100);the Defense Industrial Technology Development Program(Nos.A2120110001 and 2120110011);the 111 Project(No.B07009)

摘　　要：Based on linear interval equations, an accurate interval finite element method for solving structural static problems with uncertain parameters in terms of optimization is discussed. On the premise of ensuring the consistency of solution sets, the original interval equations are equivalently transformed into some deterministic inequations. On this basis, calculating the structural displacement response with interval parameters is predigested to a number of deterministic linear optimization problems. The results are proved to be accurate to the interval governing equations. Finally, a numerical example is given to demonstrate the feasibility and efficiency of the proposed method.Based on linear interval equations, an accurate interval finite element method for solving structural static problems with uncertain parameters in terms of optimization is discussed. On the premise of ensuring the consistency of solution sets, the original interval equations are equivalently transformed into some deterministic inequations. On this basis, calculating the structural displacement response with interval parameters is predigested to a number of deterministic linear optimization problems. The results are proved to be accurate to the interval governing equations. Finally, a numerical example is given to demonstrate the feasibility and efficiency of the proposed method.

关 键 词：linear interval equation interval finite element uncertain parameter linearoptimization 

分 类 号：O241.82[理学—计算数学]