计算具有区间参数结构特征值范围的一种新方法  

A new method for computing the eigenvalues bounds of structures with interval parameters

作　　者：王登刚[1] 李杰[2] 

机构地区：[1]上海交通大学建筑工程与力学学院,上海200030 [2]同济大学建筑工程系,上海200092

出　　处：《计算力学学报》2004年第1期56-61,共6页Chinese Journal of Computational Mechanics

基　　金：中国博士后科学基金;国家自然科学基金(10072014;10302023);国家杰出青年基金(59825105)资助项目.

摘　　要：基于区间数学的包含单调性和区间函数所表述的实际物理意义,把广义区间特征值问题转化为两个以非确定参数为优化变量,以关心的特征值为目标函数的全局优化问题,并采用遗传算法对优化问题求解,计算得到结构特征值的区间范围。通过数值算例对本文方法的有效性进行了验证,并和区间摄动法的计算结果进行了比较。By representing uncertain structural parameters as interval numbers, a novel method for computing the upper and lower bounds of the eigenvalues of uncertain structures is proposed in this paper. Based on the inclusion monotone property in interval mathematics and the physical meaning expressed by interval functions, the problem to compute the bounds of the eigenvalues is transformed into two corresponding global optimization problems. In the optimization problems, the uncertain parameters are considered as optimization variables and the concerned eigenvalues are considered as the objective function. Moreover, a real-code genetic algorithm is used to solve these global optimization problems. Numerical results show that the results of interval perturbation method can be improved distinctly and the proposed method is effective.

关 键 词：不确定性 区间分析 区间效学 全局优化 遗传算法 广义特征值 广义区间特征值 区间摄动法 

分 类 号：O241.6[理学—计算数学]