Static response analysis of structures with interval parameters using the second-order Taylor series expansion and the DCA for QB  

作　　者：Qi Li Zhiping Qiu Xudong Zhang 

机构地区：[1]Institute of Solid Mechanics, Beihang University (Beijing University of Aeronautics and Astronautics)

出　　处：《Acta Mechanica Sinica》2015年第6期845-854,共10页力学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grants 11002013, 11372025);the Defense Industrial Technology Development Program (Grants A0820132001, JCKY2013601B);the Aeronautical Science Foundation of China (Grant 2012ZA51010);111 Project (Grant B07009) for support

摘　　要：In this paper, based on the second-order Taylor series expansion and the difference of convex functions algo- rithm for quadratic problems with box constraints （the DCA for QB）, a new method is proposed to solve the static response problem of structures with fairly large uncertainties in interval parameters. Although current methods are effective for solving the static response problem of structures with interval parameters with small uncertainties, these methods may fail to estimate the region of the static response of uncertain structures if the uncertainties in the parameters are fairly large. To resolve this problem, first, the general expression of the static response of structures in terms of structural parameters is derived based on the second-order Taylor series expansion. Then the problem of determining the bounds of the static response of uncertain structures is transformed into a series of quadratic problems with box constraints. These quadratic problems with box constraints can be solved using the DCA approach effectively. The numerical examples are given to illustrate the accuracy and the efficiency of the proposed method when comparing with other existing methods.In this paper, based on the second-order Taylor series expansion and the difference of convex functions algo- rithm for quadratic problems with box constraints （the DCA for QB）, a new method is proposed to solve the static response problem of structures with fairly large uncertainties in interval parameters. Although current methods are effective for solving the static response problem of structures with interval parameters with small uncertainties, these methods may fail to estimate the region of the static response of uncertain structures if the uncertainties in the parameters are fairly large. To resolve this problem, first, the general expression of the static response of structures in terms of structural parameters is derived based on the second-order Taylor series expansion. Then the problem of determining the bounds of the static response of uncertain structures is transformed into a series of quadratic problems with box constraints. These quadratic problems with box constraints can be solved using the DCA approach effectively. The numerical examples are given to illustrate the accuracy and the efficiency of the proposed method when comparing with other existing methods.

关 键 词：Interval parameters · Second-order Taylorseries expansion · Static response of uncertain structures Quadratic programming problems · DCA 

分 类 号：O316[理学—一般力学与力学基础] O302[理学—力学]